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REPORT NO.
UCB/EERC-91/11
NOVEMBER 1991
PB9 3-11 4809
EARTHQUAKE ENGINEERING RESEARCH CENTER
SEISMIC PERFORMANCE OFAN INSTRUMENTED SIX-STORYSTEEL BUILDING
by
JAMES C. ANDERSON
VITELMO V. BERTERO
Report to the National Science Foundation
COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA AT BERKELEYREPRODUCED BY
U.S. DEPARTMENT OF COMMERCENATIONAL TECHNICAL INFORMATION SERVICESPRINGFIELD, VA. 22161
For sale by the National Technical Information
Service, U.S. Department of Commerce, Springfield, Virginia 22161
See back of report for up to date listing of EERC
reports.
DISClAIMERAny opinions, findings, and conclusions orrecommendations expressed in this publicationare those of the authors and do not necessarilyreflect the views of the National ScienceFoundation or the Earthquake EngineeringResearch Center, University of California atBerkeley.
~0271·101
REPORT DOCUMENTATION \1. REPORT NO.
PAGE NSF/ENG - 910124. Title and Subtitle
"Seismic Performance of an Instrumented Six-Story SteelBuilding"
7. AlIthor(s)
James C. Anderson and Vitelmo V. Bertrero9. Performing Organization Name and Address
Earthquake Engineering Research CenterUniversity of California, Berkeley1301 So. 46th StreetRichmond, Calif. 94804
12.. Sponsoring Organiutlon Name end Address
National Science Foundation1800 G. Street, N.W.Washington, D.C. 20550
15. Supplementary Notes
PB93-114809
5. Report Date
November 1991
l!. Perlorm/nll 0l1tanizlltion Rept. No.UCB/EERC - 91/11
10. ProlectfTuklWorl< Unit No.
(C)
(G) CES - 8804305
u.
-
-
16. Ab:straet (Limit: 200 words) I!
This study investigates the seismic performance of a six-story steel building instrumented with thirteen accelerome- IIters at the time of the Whittier Narrows earthquake (October, 1987). The lateral force system is a moment-resistant perimeter frame. The building was not severely tested by the motions recorded at its base during this earthquake. Thedynamic seismic response was entirely linear elastic. System identification techniques are used to identify the periods ofvibration from the recorded response. Recorded data are also used to evaluate the contribution of gravity, framing andnonstructural components to the dynamic properties. A detailed stress check of all members is performed for the designloading. Using a three-dimensional elastic model of the structure, the directional effects are shown to increase the stressin the critical members by 9%. I
Static nonlinear analyses are used to identify the potential failure mechanism and regions of increased ductility.. demand. and show that the structure has an overstrength which resulted in an ultimate lateral resistance more than 20%
over the code required strength. Nonlinear dynamic analyses are used to evaluate the behavior of the building understronger motions which have recently been recorded on similar sites. The value of Rw for this moment-resistant frame isshown to vary between 5.6 and 7.4, well below the value of 12 specified in the 1985 UBC.
17. Document Analy:sis a. Oescripton
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147z:z. Price
OPTIONAL fORM 27Z (<4-77(Formerly NTIS-:3S)Department eX Commerce
SEISMIC PERFORMANCE OF AN INSTRUMENTED
SIX-STORY STEEL BUILDING
by
James C. Anderson
and
Vi'telmo V. Ber'tero
Repor't 'to 'the Na'tional Science Founda'tion
Repor't No. UCB/EERC-9l/llEar'thquake Engineering Research Cen'ter
College of EngineeringUniversi'ty of California a't Berkeley
November 1991
ic...
ABS'l'RACT
This study investigates the seismic performance of a six
story steel building which was instrumented with thirteen
accelerometers at the time of the Whittier Narrows earthquake
(October, 1987). The lateral force system is a moment-resistant
perimeter frame. The building was not severely tested by the
motions recorded at its base during the Whittier narrows
earthquake. The dynamic seismic response was entirely linear
elastic. System identification techniques are used to identify
the periods of vibration from the recorded response. Recorded
data are also used to evaluate the finite element model of the
structure and to evaluate the contribution of gravity, framing
and nonstructural components to the dynamic properties. A
detailed stress check of all members is performed for the design
loading. Using a three-dimensional elastic model of the
structure, the effect of the direction of the earthquake input
is evaluated by considering the developed stress ratios. The
directional effects are shown to in_crease the stress in the
critical members by 9%.
Static nonlinear analyses are used to identify the
potential failure mechanism and regions of increased ductility
demand. Relationships between global and local ductility are
investigated along with the distribution of inelastic behavior
throughout the frame. The static nonlinear analysis shows that
the structure has an overstrength which resulted in an ultimate
lateral resistance of more than 20% over the .code required
ii
strength. Nonlinear dynamic analyses are used to evaluate the
behavior of the building under stronger motions which have been
recorded on similar sites during recent earthquakes. using
these results, the structural system coefficient, Rw, is
evaluated.
The value of Rw for this moment-resistant frame is shown to
vary between 5.6 and 7.4, well below the value of 12 specified
in the 1985 UBC.
iii
ACKNOWLEDGEMENTS
The research reported herein is part of a research project
on "Response of Engineered Buildings to the Whittier Narrows
Earthquake, " supported by National Science Foundation (NSF)
Grant No. CES-880430S. The support provided by NSF is
gratefully acknowledged. The authors also acknowledge the
continuing support of NSF Program Manager Dr. S.C. Liu. The
opinions, discussions, findings and conclusions expressed in
this report are solely those of the authors, and do not
necessarily reflect those of the sponsor.
iv
v
TABLE OF CONTENTS
ABSTRACT . . . . .
ACKNOWLEDGEMENTS .
TABLE OF CONTENTS
LIST OF TABLES .
LIST OF FIGURES
1. INTRODUCTION
2. BUILDING DETAILS
3. INSTRUHENTATION AND RECORDED DATA .
i
iii
v
vi
vii
1
2
4
4. SYSTEM IDENTIFICATION STUDIES. . . . . . . . . . . 64.1 Linear Elastic Response Spectra (LERS) . . .. 74.2 Fourier Analyses. . • . . . . . . . . . 84.3 Inelastic Response Spectra. • . 12
5. NATHEMATlCAL MODELS FOR ELASTIC RESPONSE .5.1 Two and Three-dimensional Models5.2 Weight (Mass) Determination
6. CODE ANALYSIS AND STRESS CHECK . • .. . .6.1 1973 Code Seismic Design Requirement ..•..6.2 1973 Code Wind Design Requirement .6.3 Initial Stress Check .6.4 1988 Code Seismic Design Requirement .6.5 1988 Code Wind Design Requirement
7. ELASTIC RESPONSE ANALYSES .7.1 Modal Analyses ~ .7.2 Dynamic Response Analyses7.3 Directional Input Analyses ..
8. NONLINEAR STATIC ANALYSES . . ...
9. ANALYSIS OF STRUCTURAL OVERSTRENGTH
131315
151617171920
21212425
26
35
10. NONLINEAR RESPONSE ANALYSIS . . . . .• 3910.1 Inelastic Response Spectra . . . . . . . .. 4110.2 Multiple Degree of Freedom Response Analyses 4210.3 Linear Dynamic Analyses. . . . . . . . . .. 4310.4 Nonlinear Dynamic Analyses . . . . . . • .. 4310.5 Effect of Increased Ground Accelerations 48
11. SUMMARY AND CONCLUSIONS
FIGURES
REFERENCES .
Preceding page blank
50
55
127
vi
LIST OF TABLES
TABLE 1. BUILDING RECORDS, WHITTIER NARROWS EARTHQUAKE 3
TABLE 2. PEAK RECORDED RESPONSES . . . . . . . . . · 5
TABLE 3. IDENTIFICATION OF TRANSLATIONAL MODAL PERIODS 9
TABLE 4. PERIODS OF VIBRATION, 3D MODELS . . . · . . 21
TABLE 5. PERIODS OF VIBRATION, 2D MODEL · . . 22
vii
LIST OF FIGURES
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
CSMIP Strong Motion Stations near Whittier
Plan View of the Building
Elevation View of the Building
Location of Building Instrumentation
Recorded Acceleration at Ground Level
(a) Channell, Up, NW Corner(b) Channel 13, N-S, NW Corner
Figure 6 Recorded Acceleration at Ground Level(a) Channel 8, E-W, NW Corner(b) Channel 9, E-W, SW Corner
Figure 7 Recorded Acceleration at Second Floor Level(a) Channel 6, E-W, NW Corner(b) Channel 7, E-W, SW Corner(c) Channel 12, N-S, NW Corner
Figure 8 Recorded Acceleration at Third Floor Level(a) Channel 4, E-W, NW Corner(b) Channel 5, E-W, SW Corner(c) Channel 11, N-S, NW Corner
Figure 9 Recorded Acceleration at Roof Level(a) Channel 2, E-W, NW Corner(b) Channel 3, E-W, SW Corner(c) Channel 10, N-S, NW Corner
Figure 10 Spectra Comparison, Torsional Effects(a) Base(b) Roof
Figure 11 Spectra Comparison, Amplification Effects(a) E-W Motions(b) N-S Motions
Figure 12 Fourier Amplitude Spectra for Base Motions(a) North-South, Channel 13(b) East-West, Channel 9
Figure 13 Fourier Amplitude Spectra, E-W, NW Corner(a) Roof Level(b) Third Floor(c) Second Floor
viii
Figure 14 Fourier Amplitude Spectra, E-W, SW Corner
(a) Roof Level(b) Third Floor(c) Second Floor
Figure 15 Fourier Amplitude Spectra, N-S, NW Corner(a) Roof Level(b) Third Floor(c) Second Floor
Figure 16 Transfer Functions, E-W, SW Corner(a) Roof Level(b) Third Floor(c) Second Floor
Figure 17 Transfer Functions, E-W, NW Corner(a) Roof Level(b) Third Floor(c) Second Floor
Figure 18 Transfer Functions, N-S, NW Corner(a) Roof Level(b) Third Floor(c) Second Floor
Figure 19 Moving Window Fourier Analyses, Base, Vertical
Figure 20 Moving Window Fourier Analyses, Base, E-W
Figure 21 Moving Window Fourier Analyses, Base, N-S
Figure 22 Moving Window Fourier Analyses, E-W, Roof Level
Figure 23 Moving Window Fourier Analyses, E-W, Third Floor
Figure 24 Moving Window Fourier Analyses, E-W, Second Floor
Figure 25 Moving Window Fourier Analyses, N-S, Roof Level
Figure 26 Moving Window Fourier Analyses, N-S, Third Floor
Figure 27 Moving Window Fourier Analyses, N-S, Second Floor
Figure 28 Fourier Amplitude Spectra, Torsional Effects(a) Base Level(b) Second Floor(c) Third Floor(d) Roof Level
Figure 29 Inelastic Response Spectra(a) Recorded Base Motion, N-S(b) Recorded Base Motion, E-W
ix
Figure 30 Elastic Finite Element Building Models(a) Two Dimensional(b) Three Dimensional
Figure 31 Code Loading and Resulting Deformations(a) Gravity Loading(b) Deformed Shape, Gravity Load(c) Lateral Seismic Loading(d) Deformed Shape, Lateral Seismic Load
Figure 32 Interstory Drift Index, Code Lateral Loads
Figure 33 Stress Ratios for Code Loads(a) Gravity Load(b) Gravity Load plus Lateral Seismic Load
Figure 34 Three Dimensional ETABS Building Model
Figure 35 Mode Shapes, 3D Building- Model(a) First Mode(b) Second Mode(c) Third Mode
Figure 36 Mode Shapes, 2D Building Model(a) First Mode(b) Second Mode(c) Third Mode
Figure 37 Building Model Including Interior Gravity Frame
Figure 38 Roof Response Spectra(a) Damping Ratios = 5%, 5%, 5%, 5%(b) Damping Ratios = 7%, 10%, 13%, 15%
Figure 39 Acceleration Time Histories, Roof Level(a) Channel 2, E-W(b) Channel 3, E-W(c) Channel 10, N-S
Figure 40 Third Floor Response Comparisons(a) Floor Response Spectra(b) Channel 4, E-W(c) Channel 5, E-W(d) Channel 11,N-S
Figure 41 Stress Ratios, Input Angle = 00
Figure 42 Stress Ratios, Input Angle = 150
Figure 43 Stress Ratios, Input Angle = 300
Figure 44 Stress Ratios, Input Angle = 450
Figure 45 Stress Ratios, Input Angle = 600
x
Figure 46 Stress Ratios, Input Angle = 750
Figure 47 Stress Ratios, Input Angle = 90 0
Figure 48 Roof Displacement vs. Base Shear, Uniform Lateral
Figure 49 Uniform vs. Triangular Lateral Loading
Figure 50 Lateral Load Distribution and Lateral Resistance
Figure 51 Resistance, Nominal vs. Actual Steel Strength
Figure 52 Steel Strength and Lateral Resistance
Figure 53 Strain Hardening and Lateral Resistance
Figure 54 Interstory Shear vs. Displacement, Triangular Load
Figure 55 Ductility Requirements vs. Story Level
Figure 56 Rotation Requirements vs. Story Level
Figure 57 Sequence of Plastic Hinge Formation
Figure 58 Idealized Elastic-Plastic Shear vs. Displacement
Figure 59 Stresses in an Idealized Member
Figure 60 LERS for Recent Earthquakes
Figure 61 Motion Recorded at Obregon Park, Whittier Narrows(a) Acceleration Time History(b) Response Spectra Comparison
Figure 62 Acceleration Time Histories of Recent Earthquakes(a) Bucharest, 1977(b) Hollister, 1989(c) James Road, 1979(d) SCT, Mexico City, 1985
Figure 63 Inelastic Response Spectra(a) Bucharest, 1977(b) Hollister, 19~9
(c) James Road, 1979(d) SCT, Mexico City, 1985
Figure 64 Acceleration Comparisons, Nonlinear Model(a) Roof Level(b) Third Floor
Figure 65 Base Shear Time Histories, Whittier Narrows(a) Building Base(b) Obregon Park
xi
Figure 66 Base Shear Time Histories, Recent Earthquakes(a) Bucharest, 1977(b) Hollister, 1989(c) James Road, 1979(d) SCT, Mexico City, 1985
Figure 67 Maximum Displacement Response(a) Lateral Displacement(b) Interstory Drift Index
Figure 68 Curvature Ductility Demand(a) Girders(b) Columns
Figure 69 Maximum Rotation Demand(a) Girders(b) Columns
Figure 70 Maximum Story Shear Envelopes
Figure 71 Story Shear vs. Interstory Displacement, Bucharest(a) Sixth Story(b) Fifth Story(c) Fourth Story(d) Third Story(e) Second Story(f) First Story
Figure 72 Story Shear vs. Interstory Displacement, Hollister(a) Sixth Story(b) Fifth Story(c) Fourth Story(d) Third Story(e) Second Story(f) First Story
Figure 73 Input Energy From Recent Earthquakes
Figure 74 Maximum Displacement Response, Increased PGA(a) Lateral Displacement(b) Interstory Drift Index
Figure 75 Curvature Ductility Demand, Increased PGA(a) Girders(b) Columns
Figure 76 Maximum Rotation Demand, Increased PGA(a) Girders(b) Columns
Figure 77 Base Shear vs. Interstory Disp., Increased PGA(a) Bucharest(b) Hollister
1
1. INTRODUCTION
The Whittier Narrows Earthquake occurred at 7: 42 am on the
morning of October 1, 1987 and was assigned a local Richter
Magnitude of 5.9 (ML ). The epicenter was north of Whittier,
California, approximately nine miles (15 km) east of downtown
Los Angeles. Following the earthquake, the California Strong
Motion Instrumentation Program (CSMIP) obtained records from 27
extensively instrumented building structures [1]. In addition,
the U. S . Geological Survey (USGS) collected data in
approximately ten instrumented buildings [2] and the University
of Southern California collected data in four. Other data may
have been obtained but is not readily available in the public
domain. It is estimated that over 200 buildings in Los Angeles
have been instrumented by the building owners in compliance with
the local building code. However, a recent code change in the
city of Los Angeles has reduced the seismic instrumentation
requirement to only a single instrument at the roof level. As a
result of this change, many structures which had recorders at
three levels at the time of the San Fernando Earthquake (1979)
now have only a single recorder at the roof, rendering them
unusable for analytical studies. Unfortunately, this is a step
backward in the continuing efforts to improve understanding and
prediction of the seismic behavior of buildings.
In order to perform detailed studies of structural response
during an earthquake, it is necessary to use a copy of both the
structural plans and the architectural plans. A partial list of
2
the major structures from the above database of instrumented
buildings for which the structural plans are available is given
in Table 1. Here it can be seen that most of the available data
is for low to mid-rise structures and that only limited data is
available for high-rise buildings over 25 stories. The one
exception is the 33-story structure at 1100 wilshire Boulevard,
instrumented by USGS. From this list, the six-story steel
building in Burbank, instrumented by CSMIP [1] was selected for
detailed study. The structure uses a steel perimeter moment
frame for resistance to lateral loads. A map of the CSMIP strong
motion stations is shown in Fig. 1. The building is station
number 370, which is located approximately 16 miles (26 km) from
the epicenter.
2. BUILDING DETAILS
The building in Burbank was designed in 1976 to the
requirements of the 1973 Uniform Building Code [3] as amended by
the city of Burbank. The primary structural system for carrying
lateral load is a steel moment-resisting frame around the
perimeter of the building, which is shown in the plan view
of the structure in Fig. 2a. Note that the moment continuity of
the peripheral frame is broken at the corners where a
connection is required to the weak axis of a wide flange column.
At these four locations a simple, shear connection is used
instead of a moment connection. This pin connection is
represented by a circle in Figs. 2 and 3. Gravity loads are
carried by an interior framing system consisting of much
3
TABLE 1. BUILDING RECORDS, WHITTIER NARROWS EARTHQUAKE
Building Height(Stories)
FramingSystem
RecordedAccelerations
1. OfficeBuilding
2. ApartmentBuilding
3. FinancialBuilding
4. CommercialStorage
5. ApartmentBuilding
6. OfficeBuilding
7. Hotel
8. Dormitory
9. ClassroomBuilding
10. FinancialBuilding
8
10
6
14
10
12
20
11
10
13
Shear Wall/Frame
Shear Wall
SteelPerimeter
MomentFrame
Shear Wall
PrecastShear Wall
SteelPerimeter
Moment Frame
RCMomentFrame
Shear Wall
SteelPerimeter
Moment Frame
RCMoment
Frame
Base2ndRoof
BaseFifthRoof
Base2nd3rdRoof
Base8th12thRoof
Base4th8thRoof
Base6thRoof
Base3rd9th16thRoof
Base6thRoof
Base6thRoof
Base2nd8thRoof
0.390.410.48
0.630.630.61
0.220.210.240.30
0.120.190.140.21
0.220.310.280.54
0.300.470.28
0.110.190.120.130.17
0.100.180.29
0.140.080.07
0.260.180.130.14
4
connected by simple, shear connections. Soil conditions at the
site consist of silty sands extending to a depth of 25 feet
having a blow count of 1-2. Below 25 feet the sands become well
graded and the blow count increases to 14-15. Because of these
soil conditions, the exterior columns of the lateral force
system are supported on two 3D-inch diameter reinforced concrete
piles which are 32 feet long. Interior columns are supported on
spread footings. An elevation of a typical moment frame is
shown in Fig. 3. In the initial stage of this study, the
structure is assumed to be fixed at the base. The validity of
this assumption will be checked by comparing the calculated
response with the recorded response. At the second floor level
and at the roof, the floor deck extends a distance of 6 1/2 feet
beyond the perimeter moment frame, giving it a plan dimension of
132 feet by 132 feet. No damage was reported in the structure.
3. INSTRUMENTATION AND RECORDED DATA
The building was instrumented with 13 strong motion
recorders at the time of the Whittier Narrows Earthquake. The
location and orientation of these instruments is shown in Fig.
4, which is taken from reference [1]. Peak recorded responses
are summarized in Table 2. The vertical acceleration recorded
at the base of the structure is given by channel 1, which is
shown in Fig. 5a. Here it can be seen that the peak vertical
acceleration was about 0.09g and that there is not an apparent
long period motion which would indicate rocking motions of the
building. The horizontal acceleration in the north-south
5
direction at the base is given by channel 13 which is shown in
Fig. 5b. Here the relatively short duration and high frequency
of the base motion become readily apparent. The peak
acceleration is approximately 0.22g, but this is due to a high
frequency acceleration spike, and the duration of strong motion
is only about five seconds.
TABLE 2. PEAK RECORDED RESPONSES
Ident. Location Component Accel.(cm/s2)
velocity(cm/s)
Disp.(em)
Chan. 1
Chan. 2
Chan. 3
Chan. 4
Chan. 5
Chan. 6
Chan. 7
Ground
Roof N.W.
Roof S.W.
3RD N.W.
3RD S.W.
2ND N.W.
2ND S.W.
Up
090
090
090
090
090
090
84.98
183.58
156.73
176.65
146.75
146.27
143.86
3.61
21.29
18.48
12.32
10.90
10.37
9.99
0.38
4.03
3.66
2.12
1.96
1. 70
1.50
Chan. 8 Ground N.W.
Chan. 9 Ground S.W.
Chan. 10 Roof N.W.
Chan. 11 3RD N.W.
Chan. 12 2ND N.W.
Chan. 13 Ground N.W.
090
090
180
180
180
180
165.77
162.23
283.72
233.16
194.64
221. 74
9.74
9.56
31.98
18.44
15.94
12.51
1.20
1.19
6.30
2.49
1.68
1.27
Horizontal motions at the base in the east-west direction
are given by channels 8 and 9, which are shown in Fig. 6a and 6b
respectively. Here it can be seen that the peak acceleration in
6
this direction is also due to a high frequency acceleration
spike having an amplitude of 0.17g, and that the duration of
strong motion shaking is even shorter than in the north-south
direction. Horizontal accelerations at the second floor level
are given by channels 6, 7 and 12 which are shown in Fig. 7.
Similar data for the third floor level are given by channels 4,
5 and 11 which are shown in Fig. 8. Roof accelerations in the
horizontal direction are given by channels 2, 3 and 10 which are
shown in Fig. 9. From a comparison of the three acceleration
plots, it would appear that the period of vibration in both
directions is approximately the same, having a value of about
1.2 to 1.3 seconds. The peak roof acceleration was recorded in
the north-south direction by channel 10 and has a value of
0.29g.
A cursory examination of the time history plots at the roof
level indicates that there is no appreciable increase in the
period of vibration over the entire time history. This indicates
that the response is linear elastic.
4. SYSTEM IDENTIFICATION STUDIES
In order to understand the recorded dYnamic response of the
building better and to evaluate the dYnamic characteristics of
the building prior to performing the detailed response analyses,
the recorded response data was processed using Fourier amplitude
spectra, transfer functions, moving window Fourier analyses,
linear elastic response spectra and inelastic response spectra.
7
The results of these studies are discussed in the following
sections.
4.1 Linear Elastic Response Spectra (LRRS)
In order to obtain a better evaluation of the recorded
response, LERS for 5% damping were generated and plotted for
selected recorded building motions. Rotation of the structure
was evaluated using the spectra shown in Fig. 10. LERS for the
base are compared in Fig lOa using motions recorded on channels
8 and 9. These channels recorded base accelerations on the north
and south sides of the structure in the E-W direction.
Comparison of the response spectra shows that the two spectra
are identical and therefore there is little or no rotation at
the base. Similar data for channels 2 and 3 on the roof are
shown in Fig. lOb. There is some variation between the spectra
in the period range below 0.7 second which could include the
torsional mode of the building but the variation is small.
An LERS for motions in the east-west direction at the roof
level are shown in Fig. 11a. Here it can be seen that the
fundamental period of the response occurs at approximately 1.3
seconds which agrees with that observed from the zero crossing
of the time history data. Amplified response between the base
and the roof in this direction can be evaluated by comparing the
spectral values for channels 2 and 8. As would be expected, the
largest amplification occurs for the fundamental mode and has a
value of approximately 6.3 with smaller amplification for the
second and higher modes. Similar spectra for the north-south
8
direction are shown in Fig. 11b. Here a fundamental mode can be
identified at a period of 1.3 seconds and the second mode can be
seen at a period of 0.44 second. The maximum amplification
between base and roof occurs in this direction and has a value
of approximately 9.2.
4.2 Fourier Analyses
Fourier amplitude spectra (FAS) of the recorded
accelerations at the base of the structure are shown in Fig. 12,
for the motion in the north-south direction in Fig. 12a, and for
the east-west direction in Fig. 12b. In the north-south
direction, the strongest input has a frequency content between
0.5 and 2.0 Hz with a strong peak between 0.75 and 1.0 Hz. In
the east-west direction the strongest input is between 0.5 and
1.75 Hz.
Fourier amplitude spectra for motions recorded at other
locations in the building are compared with the corresponding
base FAS in Figs. 13 and 14 for east-west motions and Fig. 15
for north-south motions. All plots have a similar characteristic
shape showing a strong peak at 0.75 Hz (1.33 second) and another
at 2.2 Hz (0.45 second).
Transfer functions for the motions recorded in the
east-west direction are shown in Figs. 16 and 17. From Fig. 16,
it is possible to identify the first three modes in this
direction as occurring at the following frequencies: the first
mode has a frequency of 1.0 Hz (T=1.0 second), the second mode
occurs at a frequency of 2.4 Hz (T=0.42 second), and the third
9
mode occurs at a frequency of 3.2 Hz (T=0.31 second). Similar
results can be seen in Fig. 17 for the other side of the
structure. In the north-south direction, the transfer functions
shown in Fig. 18, show that the first mode is dominant at all
three levels and occurs at a frequency of 0.75 Hz (T=1.33
seconds). In this direction the second mode shows up clearly at
the second and third floor levels and has a value of 2.25 Hz
(T=0.44 second). A third mode can also be seen in this direction
at approximately 3.2 Hz (T=0.31 second). The modal frequencies
and periods identified from the Fourier analyses are summarized
in Table 3.
TABLE 3. IDENTIFICATION OF TRANSLATIONAL MODAL PERIODS
Direction
East-West
North-South
Mode 1
1.00
1.33
Mode 2
0.42
0.44
Mode 3
0.32
0.32
In order to identify changes in the frequency content of
the input motions during the earthquake, moving window Fourier
analyses are performed using the recorded base motions. In these
analyses, the FAS has been calculated for ten second window
lengths starting from the beginning of the record and then
offsetting the window by five seconds at each step. For each
window, the length of the record was extended by adding zeros to
obtain good resolution in the spectra.
The result for the vertical component of the base motion is
shown in Fig. 19. This figure shows that although the amplitude
is small, the frequency content during the first ten seconds is
10
relatively uniform over a wide band. Two dominant frequencies
appear during the second ten second interval. After ten seconds
the amplitudes drop to almost zero. Moving window analysis of
the base motion in the east-west direction is shown in Fig. 20.
Here it can be seen that during the first ten seconds there is
a relatively strong input in a frequency band between 0.5 Hz and
1.75 Hz. This diminishes significantly during the next window
and reduces to very small amplitudes in succeeding windows. In
the north-south direction, Fig. 21, the moving window analysis
shows that during the first ten second window the input
frequency band extends from 0.7 Hz to 2.5 Hz with a strong peak
at 2.0 Hz.
Moving window analyses of motions in the east-west
direction are shown in Figs. 22, 23 and 24. The moving window
analysis of the motion at the roof level is shown in Fig. 22
where it can be seen that the response is predominantly first
mode at a frequency of 0.75 Hz. Corresponding results for the
third floor level are shown in Fig. 23. Here it can be seen that
there is an increased contribution from the second mode at a
frequency of 2.4 Hz. particularly during the first twenty
seconds. The moving window FAS at the second floor has
characteristics which are similar to the base motion,
particularly during the first ten second window. In succeeding
windows, the FAS at the second mode diminishes and the first
mode becomes dominant.
11
Moving window analyses of motions in the north-south
direction are shown in Figs. 25, 26 and 27. At the roof level,
shown in Fig. 25, the response is predominantly first mode
although there is some second mode response during the first ten
second window. The moving window analyses for the third level
which are shown in Fig. 26, indicate that there is a significant
second mode response at this level during the first ten second
period. This diminishes significantly during the second window
and after ten seconds the first mode becomes dominant. A similar
result is obtained for the second floor, which is shown in Fig.
27. During the first window, the response is influenced by the
base motion and the second mode is dominant. As at the third
level, the second mode diminishes during the second window and
the first mode becomes dominant after ten seconds.
Torsional effects can be evaluated by comparing the FAS of
motions recorded on opposite sides of the building. Results of
this analysis are presented in Fig. 28. The spectra shown in
Fig. 28a represent the motions at the base of the structure and
here it can be seen that there is no difference in the input
motions. This result is similar to that obtained from a
comparison of LERS. At the second floor level, Fig. 28b, it can
be seen that there is a small torsional effect at frequencies of
0.75, 2.3 and 3.2 Hz, which represent the first three modes of
vibration. A similar effect can be seen at the third and roof
levels shown in Fig. 28c and 28d. In all cases the torsional
12
effect is very small and can probably be neglected in the
structural analyses.
4.3 Inelastic Response Spectra
Inelastic response spectra were generated for the recorded
base motions using a modified version of the NONSPEC [4]
program. Results from this program are presented in terms of the
yielding seismic resistance coefficient of the structure,
defined as
(1)
where Ry = yield resistance of the structure, and
We = total seismic dead load which in most casesis taken as the total dead load, W.
The nonlinear spectra for the motions recorded on base channel
9 in the E-W direction are shown in Fig. 29b. The solid line
represents a ductility requirement of one (elastic behavior) and
the dashed or broken lines represent ductilities of 2, 3, 4, 5,
and 6. Considering the fundamental period of the structure to be
1.2 seconds, this figure indicates that a yielding seismic
resistance coefficient of about 0.09 will be required to ensure
elastic response of this structure if the response in the
fundamental mode is dominant. Considering a similar spectrum for
motions recorded on base channel 13 (Fig. 29a) in the N-S
direction, it can be seen that at the fundamental period of the
structure, a yielding seismic resistance coefficient of 0.1 is
required for an equivalent single-degree-of-freedom system to
obtain elastic response.
13
5. MATHEMATICAL MODELS FOR ELASTIC RESPONSE
5.1 Two and Three-dimensional Models
Both two dimensional and three-dimensional models were
developed for the structure. Because of the symmetry of the
structure and the framing system, two dimensional models can be
used with the resulting savings in coding effort and
computational time. Elastic analyses were done using the SAP90
[5] and ETABS [6] computer programs, although it is recognized
that several alternative programs could have been used for this
phase of the response analysis. The reasons for selecting the
SAP90 program included the following:
1. The program has large capacity which permits
modeling the structure in detail in either two or
three dimensions on a personal computer.
2. The program allows the user to plot the time history
response of any node. This feature was crucial for
comparison of calculated results with the recorded
response.
3. The program permits consideration of a rigid floor
diaphragm through the use of a master node. This
greatly reduces the time required to perform a
dynamic analysis, particularly for a three
dimensional system.
4. The program has a postprocessor [7] which performs a
stress check of every member for the provisions of
the AISC Specification [8]. This greatly facilitates
14
an evaluation of the stress level in the structure
under both the code design loading and the recorded
earthquake loading.
The current version of the ETABS program can not produce
time history response plots and therefore does not permit a
comparison of recorded response with calculated response.
Otherwise, this program could have been used for all response
analyses for this structure. Its one significant capability that
SAP90 does not have is the ability to calculate the stress
ratios in each member for a time history ground motion applied
in any direction with respect to the principal axes of the
structure. Therefore, this program was used to study the
directionality effects of the input motion.
The two-dimensional finite element model of a typical
perimeter moment frame is shown in Fig. 30a. Here the joint
numbering is shown along with the pinned moment releases at one
end of the frame. The three-dimensional model is shown in Fig.
30b. Although not shown in this figure, pinned element releases
are incorporated at one end of each frame in a similar manner to
the two dimensional model. Nodes 169 through 174 in the middle
of the figure are master nodes which connect to all nodes at a
particular story level and define the displacement response of
the story level.
5.2 weight (Mass) Determination
A set of the architectural drawings for the structure was
not available, rendering it necessary to estimate the weights of
15
some of the finish materials. The weight of the structure was
estimated based on the following unit loads:
ROOF:Roof Deck 46.0 psf
20 gage metal deck 3" deep with3 1/4" lightweight concrete on top
Roo f ing 6. 0 psfHung Ceiling 8.0 psfMechanical Equipment Penthouse ......•..•• 43.0 psf
TYPICAL FLOOR:Floor Deck 46.0 psf
20 gage metal deck 3" deep with3 1/4" lightweight concrete on top
Hung Ceiling "............. 8.0Floor Finish 1. 0
Columns .7.1 psf3.7 psf
PartitionsSteel
Beams
.............................. . 15 . 0
and joists .
psfpsfpsf
PERIMETER WALL:Glass with mullions .........••.••..•..•... 10.0 psf
The weight of the second floor is higher than that of a
typical floor because of the effect of the 6 1/2 foot overhang
of the floor deck at that level. The weight of the roof is also
higher than that of a typical floor because of the overhang of
the roof deck and the addition of a mechanical equipment
penthouse. The total weight of the structure is estimated as
7785 kips.
6. CODE ANALYSIS AND STRESS CHECK
The structure was designed to the requirements of the 1973
uniform Building Code. Therefore, the existing strength will be
based on this lateral force requirement. The structure will also
be checked for the current requirements of the 1988 Uniform
16
Building Code. Lateral forces specified in building codes are
defined in terms of the base shear and have the general form:
V=C~ ~
where Cs is the design seismic resistance coefficient and We is
the total seismic dead load.
6.1 1973 Code Seismic Design Requirement
The seismic lateral force requirements of the 1973 Uniform
Building Code are expressed in terms of a base shear which is
given by the formula
where
v = (ZKCIS)W
T = O.lN = 0.6 sec.
C = 1/(15 ~) = 0.086
K = 0.67
(3)
(4)
(5)
(6)
(7)
If z, S and I are taken as unity, the design seismic
resistance coefficient becomes
Cs = 1.0*0.67*0.086*1.0*1.0 = 0.0577
and the base shear V, can be calculated as
Vcode = 0.0577*7785 = 449 kips. (8)
It should be noted that the expression used in the 1973
code to estimate the period tends to underestimate the actual
building period by more than 50%. As discussed earlier, the
recorded data from the building indicates that the fundamental
period is approximately 1.3 seconds in each direction. This may
be due in part to the fact that the estimate of period given by
Eq. 4 is based on experience with moment-resistant space frames
and not moment-resistant perimeter frames. In the Commentary to
17
the 1975 SEAOC Recommendations, it was suggested that the
following expression be used to estimate the period,
T = 0.45 N 2/3 (9)
which results in a value of T=1.48 seconds for this building.
The underestimation of period tends to increase the seismic
design requirement by 41% over what it would be if the period
were estimated more accurately.
6.2 1973 Code wind Design Requirement
The lateral forces due to design winds in the 1973 code are
based on a wind pressure map given in the code. The basic wind
pressure for southern California is 20 psf. The distribution of
wind pressure over the height of the building is the following:
Story height
< 30'30' to 49'50' to 99'
Wind pressure
15 psf20 psf25 psf
Based on these values, the base shear is determined to be 180
kips which is well below the seismic requirement for the
structure.
6.3 Initial Stress Check
The initial stress check considered the loads for which the
structure was originally designed, and was performed on the two-
dimensional SAP90 model. Therefore, it was assumed that the
total lateral force was equally divided between the two
perimeter frames parallel to the direction of the lateral, force
and the effects of the exterior end frames and the interior
gravity frames were neglected. Because of the square plan of the
18
structure, the effect of accidental torsion was approximated by
increasing the lateral seismic force by 5%. In this manner, the
base shear for a single plane frame was calculated as
v = 448 * 1.05/2 = 235 kips (10)
The code loading and resulting deformation of the frame are
shown in Fig. 31. Gravity loading is input as a uniformly
distributed load as shown in Fig. 31a, and this results in the
deformed shape of the frame shown in Fig. 31b. The controlling
lateral force is due to earthquake and the equivalent lateral
forces are shown in Fig. 31c. These result in deformation of the
frame as shown in Fig. 31d where it can be seen that the maximum
deformation at the roof level is 2.07 inches. The relative
displacements (story drifts) under design wind load and design
seismic load are shown in Fig. 32. Here, the seismic deformation
is based on the lateral loads multiplied by l/k as specified in
the building code. Normal design procedure usually limits the
drift under design wind load to 0.002 to 0.003 to prevent motion
of the structure which is discernable to the occupants. It can
be seen from the figure that the calculated wind drift is in the
middle of this range. The drift under seismic load is 0.0035
which is well within the code limit of 0.005.
The stress ratio (SR) is defined as the ratio of the
actual stress in the member to the allowable stress. Therefore,
to meet the allowable stress design criteria commonly used for
steel structures, the stress ratio of all members must be less
than or at most equal to unity. Stress ratios for the members of
19
the frame are shown in Fig. 33. The stress ratios due to gravity
load acting alone are shown in Fig. 33a. In the case of combined
gravity load and seismic load, shown in Fig. 33b, the allowable
stresses have been increased by 33% as permitted in the code. It
can be seen that the larger stress ratios are the result of the
combined gravity load and seismic load and that the critical
values occur in the columns of the first floor. The maximum
value of the stress ratio can be seen to be 0.69 which implies
that the structure has a design conservatism for this combined
load condition of 1./0.69 or 45%.
6.4 1988 Code Seismic Design Requirement
The 1988 uniform Building Code defines the base shear as
v = (ZIC/Rw)We = CsWe (11)
where
C = 1.25S/T2/3
and the period, T, may be estimated as either
T = O. 035h3/ 4
(12)
(13)
which results in the following estimate:
T = 0.035*(82.5)3/4 = 0.96 sec. (14)
Alternatively, the period can be estimated using a Rayleigh
procedure as
T (Rayleigh) = 1.48 seconds (15)
Use of these estimates of the period along with Rw = 12,
Z = 0.4, S=1.0 and I = 1.0 results in design seismic resistance
coefficients of either
Cs (T=0.96) = 0.0428 or Cs (T=1.48) = 0.0321
20
and corresponding base shears of either
V(T=0.96) = 333.1 kips or V(T=1.48) = 249.4 kips
Since the value of 249.4 kips is 75% of the 333.1 value, the
minimum base shear is limited to 0.8*333.1 = 266.4 kips which
results in a design seismic resistance coefficient of 0.0342. It
can be seen that t:hese values are 74% and 59% of the 1973 code
value. It can also be noted that the actual recorded building
period of 1.3 seconds is between the two estimates of the
period, T=0.96 and T=1.48.
6.5 1988 Code Wind Design Requirement
The lateral forces due to design winds in the 1988 Code are
based on a basic wind speed map given in the code. The design
wind speed for southern California is given as 70 mph and the
design wind pressure as
p = CeCqqs1
where 1=1, Cq=O.8+0.5=1.3 and Ce is determined from
(4)
Height0-20
20-4040-6060-100
Ce0.70.81.01.1
Use of these values results in a base shear due to wind of 139.3
kips which is 77% of the 1973 code value. Therefore it can be
concluded that the lateral forces used in the original design
will still govern the design and that the structure as built
will satisfy the current code requirements.
21
7. ELASTIC RESPONSE ANALYSES
7.1 Modal Analyses
Using the three-dimensional SAP90 model of the structure
and the corresponding ETABS model shown in Fig. 34, the mode
shapes and frequencies for the first nine modes were evaluated.
The deflected shapes of the first three modes obtained from the
SAP90 model are shown in Fig. 35. Here it can be seen that the
first two modes are translational modes and that the third mode
is a torsional mode. The dynamic properties of the two models
are summarized in Table 4.
TABLE 4. PERIODS OF VIBRATION, 3D MODELS
Mode 1 2 3 4 5 6 7 8 9
SAP90
ETABS
1.42 1.42 0.83 0.51 0.51 0.30 0.29 0.29 0.19
1.42 1.42 0.82 0.51 0.51 0.30 0.29 0.29 0.20
It can be seen that, because of symmetry, the translational
modes are the same in each orthogonal direction. It should also
be noted that the value for the fundamental mode compares well
with the estimate of period obtained from the code using the
Rayleigh procedure {1. 48} and the recorded response {1. 33} .
However, it should be recalled that this represents the period
of the bare frame and not the existing frame which will be
stiffened by the addition of the gravity load framing and the
nonstructural components as indicated by the recorded value. Use
of nine modes of vibration represents 98.7% of the participating
mass which is well above the 90% requirement in the code. In
22
this model, the first mode contributed 83% of the participating
mass.
The deflected shapes for the first three modes obtained
using the two dimensional model are shown in Fig. 36. These
modes compare with modes 1, 4 and 7 of the three-dimensional
model. The modal periods for the two dimensional model are
summarized in Table 5 below.
TABLE 5. PERIODS OF VIBRATION, 2D MODEL
Mode
SAP90
ETABS
1
1.447
1.425
2
0.525
0.506
3
0.304
0.291
4
0.209
0.198
5
0.157
0.147
In this case using three modes of vibration represents
99.9% of the participating mass, with the first mode
contributing 84.1%, the second mode contributing 11.9%, and the
third mode contributing 2.9%.
From the system identification studies described
previously, the fundamental period of the building based on the
recorded response is approximately 1.3 seconds which is about 9%
lower than the calculated bare frame period. This implies that
the structure at this level of base excitation is about 21%
stiffer than indicated by the bare frame analysis. This
additional stiffness is due to several sources including the
following: (a) the composite action between the concrete and
steel deck and the main girders, (b) the influence of the
23
internal gravity framing, which is assumed to have pinned
connections but which has a certain flexural stiffness, and (c)
the influence of the nonstructural components such as the
exterior cladding and the interior partitions. Modifying the
models developed above, an attempt was made to evaluate the
contribution of these sources of additional stiffness.
The three-dimensional model, including the interior gravity
frame, is shown in Fig. 37. In this investigation, the simple
framing is assumed to be completely rigid to give an upper bound
to the increase in stiffness. A modal analysis of this system
shows that the fundamental period of vibration is reduced by
only 5%. The deck system consists of three components. The metal
decking is welded to the steel girders and then filled with 3
inches of normal weight concrete. On top of this is added
another 3 1/2 inches of lightweight concrete. If the steel
decking with 3 inches of concrete acts in a composite manner
with the girder, the fundamental period of the structure is
reduced by an additional 4%, resulting in a total reduction of
9.2%. The directional properties of the steel decking may
account for the difference in period in the two orthogonal
directions noted in the system identification studies. In the
elastic response analyses that follow, these effects are lumped
together by the use of an effective modulus of elasticity of
42,000 ksi rather than 29,000 ksi. Since the period of the fixed
base model agrees reasonably well with the recorded period,
additional flexibility at the base was not considered in this
24
study. Although the base is not completely fixed in the actual
structure, at the low acceleration levels experienced by the
building during this earthquake it may have acted as though it
were fixed.
7.2 Dynamic Response Analyses
In these analyses, the three-dimensional SAP90 model was
subjected simultaneously to base accelerations recorded in the
north-south and east-west directions. The response spectrum for
the accelerations calculated at the roof level is compared with
that for the recorded accelerations in Fig. 38. In the spectra
presented in Fig. 38a, the calculations assume there is 5% of
critical damping in all modes, and the spectra are developed for
5% damping. The periods for the first four translational modes
for the structure using the higher modulus are 1.2, 0.44, 0.25,
o•17 seconds. These can be seen as the four peaks on the
response spectra. The match for the first mode is quite good,
while in the higher modes the calculated values exceed the
recorded values. This result can be adjusted by increasing the
damping in the higher modes. The results shown in Fig. 38b are
for damping values of 7, 10, 13, and 15% of critical damping in
the first four modes. This produces a good match of the recorded
spectra over most of the period range with the possible
exception of the fourth mode.
Time history responses at the roof level are compared in
Fig. 39 for the three recording channels. In all cases, the
comparison is good for the peak values although there are
25
differences in the lower responses after 20 seconds. In these
comparisons, the calculated accelerations are for the master
node at the center of the structure. Some differences with the
recorded results may be due to torsional effects.
The calculated and recorded responses at the third story
level are compared in Fig. 40.A representative floor spectrum
at the third level is shown in Fig 40a. Here the match of the
spectral values over the period range of the first two modes is
good with a small deviation in the higher modes. The time
histories of the acceleration at the three recording stations on
the third level are compared in Figs. 40b, 40c and 40d and again
show a reasonable correlation.
7.3 Directional Input Analyses
The three-dimensional ETABS model was used to study the
effect of the direction of the input motion on the stresses in
the members of the' structure. Only one component of recorded
base acceleration could be used, and that recorded on Channel 13
in the north-south direction was selected. This input motion was
then rotated through a total angle of 90 degrees in increments
of 15 degrees and the corresponding stress ratios were
calculated. The stress ratios (SR) resulting from the motion
acting in the north-south direction are shown in Fig. 41. Here
it can be seen that the maximum stresses occur in the frames
parallel to the input motion and that the time history values
for this input compare well with the code values obtained
earlier. This implies that this earthquake was close to the
26
minimum requirement specified in the building codes. Note that
the maximum value of 0.67 in the critical column of the first
story compares with 0.69 obtained in the static code analysis.
The effect of applying the input motion at an angle of 15
degrees is shown in Fig. 42. Here it can be seen that the SR in
the critical column increases to 0.71. Further rotation of the
input motion through 30 degrees increases the critical SR to
0.73 as shown in Fig. 43. Note that as the angle of incidence
increases the stresses in the east-west frames begin to increase
as would be expected. As the angle of incidence reaches 45
degrees (Fig. 44), the stress ratio in the critical column
reduces to 0.70. However, the critical column is now in the
east-west frame with a SR of 0.71. Further rotations to 60, 75
and 90 degrees are shown in Figs. 45, 46 and 47, respectively.
In these figures the stresses in the critical members of the
north-south frame are reduced while those in the east-west
frames are increased. In both directions, the maximum SR in the
columns of the first story reached a value of 0.73, which is 9%
larger than the value of 0.67 in the recorded position of zero
degrees.
8. NONLINEAR STATI.C ANALYSES
Nonlinear static analyses were performed on the two
dimensional model of the frame in order to obtain estimates of
the following: (a) yield strength (resistance) of the frame, (b)
ultimate strength (resistance) of the frame, (c) overall
displacement ductility, Cd) corresponding curvature ductility of
27
individual elements, (e) total rotation requirements of
individual elements, (f) ultimate interstory drift and (g) story
displacement ductility. Two computer programs were used to
investigate the nonlinear static behavior. Both assume the
loading is applied in a proportional manner and that the
plasticity is concentrated in plastic hinges.
The ULARC [9] program is event driven, where an event
corresponds to either the formation of a new plastic hinge or
the unloading of an existing plastic hinge. If the structure is
assumed to be piecewise linear between events, the load
increment required to produce a new event can be determined by
linear scaling. Loads may be applied at the joints and the
element resistance is assumed to be elasto-plastic: however,
bilinear behavior can be handled by adding an additional element
in parallel with the elasto-plastic elements.
The NODYN2 program, developed by one of the investigators,
uses a step-by-step procedure to determine the nonlinear
behavior. This procedure is used because the program was
originally developed and primarily used for the step-by-step
determination of nonlinear dynamic response. Therefore,
application to nonlinear static response in this manner was a
straightforward modification. Using this procedure, the total
load is divided into a given number of equal load increments
which are then applied sequentially to the structure. Linear
behavior is assumed to occur between each load increment. Moment
resistance of the individual elements is bilinear and gravity
28
loads may be applied as equivalent fixed end forces.
Elasto-plastic behavior can be approximated using a small
percentage of strain hardening in the bilinear element. Analyses
using the ULARC program are terminated whenever one of the
following conditions occurs: a collapse mechanism is formed, the
full specified load is applied or a specified maximum
displacement is reached. The NODYN2 program is terminated when
the full specified load is applied.
In the analyses that follow, the lateral resistance of the
building is evaluated by plotting the lateral roof displacement
versus the base shear. A plot of this type comparing the results
obtained using SAP90, ULARC and NODYN2 is shown in Fig. 48. Here
the. resistance in the SAP90 program is linear elastic, the
resistance in the ULARC program is elasto-plastic and the
resistance in the NODYN2 program is bilinear with the rate of
strain hardening equal to 0.5%. In this example, the lateral
loading is taken as uniform over the height of the building. In
the linear elastic range, all three programs give the same
result. In the inelastic range, the results of the ULARC and
NODYN2 programs are very similar. Both depart from the linear
SAP90 curve at a base shear of approximately 640 kips, reach an
ultimate load of 760 kips and attain a maximum displacement of
10.3 inches. Because of the inclusion of strain hardening in the
NODYN2 model, it is able to carry load beyond that indicated by
the ULARC model. However, at some point, the deformation
demands on the individual elements will become excessive and
29
these in turn will place a bound on the overall displacement. In
this case the total load was adjusted to produce the same
displacement as that obtained using the ULARC model.
It is also of interest to consider the effect of the
vertical distribution of the lateral load on the lateral
resistance of this building. Reasonable lateral load
distribution functions include
(a) <P(x) = constant (uniform)
(b) <P(x) = x/h (linear)
(c) <P(x) = sin(1tx/2h)
(d) <P(x) = 1 - cos(1tx/2h)
where h is the height of the structure and x is the height
of the story level above the base.
Differences between the triangular and uniform
distributions are shown in Fig. 49. Here it can be seen that
since the triangular distribution raises the height of the
lateral force resultant, the lateral displacement at the roof
level increases substantially. However, the lateral load
capacity of the frame does not change. The shear versus
displacement curves for the other lateral load distributions are
shown in Fig. 50. Here it can be seen that the largest lateral
resistance of the structure is obtained when the resultant
lateral force is at its lowest position. This condition also
results in the least displacement at the roof level. Conversely,
the least lateral resistance occurs when the resultant lateral
load is at its highest position with the resulting maximum roof
30
displacement. For this building the ultimate resistance is
relatively insensitive to the lateral load distribution. This is
a function of the failure mechanism and the distribution of
plastic hinges in the building. For other buildings the
difference in ultimate resistance as a function of load
distribution may be more significant.
Up to this point, the resistance curves have been developed
using the nominal yield stress of 36 ksi for the A36 steel used
in the building. Coupon tests on the steel used in the building
indicate that the true yield stress of the material is
approximately 44 ksi. If this value is used in the model with a
triangular load distribution, the resistance changes
considerably as shown in Fig. 51. For the same total load and
the higher yield stress, the building resistance is almost
linear and first yielding does not occur until a base shear of
780 kips is reached. In order to determine the maximum lateral
resistance of the building with the increased yield strength, it
is necessary to increase the total applied load. Results of
increasing the lateral load are shown in Fig. 52. The curve for
the 36 ksi steel is included for comparison. Also included is a
curve for the nominal resistance of the building had Grade 50
steel been used for the columns. It can be seen that the
ultimate resistance of the building with 44 ksi steel increases
to 910 kips. The use of the 50 ksi columns gives a resistance
similar to the 44 ksi steel throughout.
31
The influence of strain hardening on the lateral resistance
of the frame is shown in Fig. 53, where the difference in
lateral force capacity for strain hardening rates of 0.5% and
3.0% is also shown.
It is also of interest to consider the lateral story
displacement (relative displacement) as a function of the story
shear, using the triangular loading results in the resistance
curves shown in Fig. 54. Here it can be seen that the 6th story
is linear elastic and that the maximum inelastic displacement
occurs in the first story. The second story level has the
largest lateral stiffness, because the column size is the same
as the first story but the story height is less. Using these
curves, the displacement ductility requirements of the
individual stories can be estimated. For these calculations, the
story ductility will be defined as the ratio of maximum relative
displacement to relative displacement at first yield. This data
will then be compared with the curvature ductility requirements
of individual members.
The maximum curvature ductility requirement for the beams
and columns of a particular story level is compared with the
story displacement ductility requirement in Fig. 55. Here it can
be seen that the maximum requirement for the beams is 3.25 at
the first level. Although this is not excessive for a compact
section, it may cause problems at the connection to the column.
On the other hand, the maximum ductility requirement for the
columns of the first story is 3.47, which for a column under
32
combined axial load and flexure is approaching that which can
reasonably be obtained. The story ductility, which is based on
displacement, compares well with the curvature ductility of the
individual members for this system, reaching a maximum value of
3.75 at the first level.
The maximum total rotation for the beams and columns of a
particular story level is shown in Fig. 56 along with the
interstory drift index (drift angle). The interstory drift index
is obtained by dividing the maximum relative (interstory)
displacement by the story height. For the beams the maximum
total rotation is just over 2% which is close to the capacity of
a typical beam-to-column moment connection [10, 11]. For the
columns of the bottom floor, the maximum total rotation is close
to 3.5% which is excessive and provides the justification for
limiting the total lateral load applied to the frame at this
point. A similar result can be seen for the interstory drift
ratios. In the first story level, the interstory drift is close
to 2.6% which is large and along with the column rotation is
reason for limiting the applied lateral load.
The nonlinear static behavior of this structure can be
further illustrated by considering the sequence of plastic hinge
formation shown in Fig. 57. This data was taken from a ULARC
analysis using the nominal yield strength and a triangular load
distribution. It clearly shows that with the formation of the
30th plastic hinge, a sway mechanism is formed in the first
story level which in turn results in the severe ductility and
33
drift requirements on the columns of this level. This is a
limitation of the design which results in a soft story at
ultimate load. It can also be seen that at ultimate lateral
load, only one plastic hinge has formed in the columns of the
second story level. This is due to the design practice of
holding the column size constant for at least two story levels.
Because of the increased story height of the bottom story, the
columns of the second story are considerably larger than
required for strength. This tends to concentrate the inelastic
deformation in the first story level and leads to the formation
of a soft story at ultimate load.
By referring to the base shear versus roof displacement
shown in Fig. 58, the overall displacement ductility of the
structure can be approximated. Since the shear versus
displacement curve has a smooth transition from linear behavior
to inelastic behavior, it does not exactly fit the context of
displacement ductility which is defined for a perfectly
elasto-plastic relationship. The displacement ductility is
defined as the ratio of the maximum displacement to the
displacement at yield. with a smooth transition, there can be
several definitions of displacement at yield. Two of these are
the following: (a) the displacement at yield is the displacement
when yielding occurs at the first critical section and (b) the
displacement at yield is determined by comparison with an
idealized elasto-plastic response curve. In the NODYN2 response
curve, first yield occurs at a load of 640 kips and a
34
corresponding displacement of 6.5 inches. Using this value, the
displacement ductility of the frame becomes 13.5/6.5 or 2.08. If
an idealized elasto-plastic curve is constructed (Fig. 58), the
yield displacement is 7.5 and the displacement ductility becomes
13.5/7.5 or 1.8. Note that both of these values are considerably
less than the values of 4 or 5 often quoted in building code
commentaries.
The results of this type of analysis also provide a means
for evaluating the seismic resistance coefficient for this
structure. The yielding seismic resistance coefficient has been
defined previously as
Cy = Ry/We
In this equation, the yield resistance, Ry, is taken as the
lateral resistance of an equivalent elasto-plastic system.
Considering both frames, the yield seismic resistance
coefficient for this structure becomes
Cy = 2*750/7785 = 0.19
Referring to the elastic response spectra shown in Fig. llb
for the recorded base motion (Channel 13), it can be seen that
for this earthquake the demand seismic resistance coefficient,
Cd' is approximately 0.07. It is of interest to recall that this
value is above the design seismic resistance coefficient used in
the design (0.058). Since lateral forces specified in the
building codes are based on working stress, this coefficient
must be multiplied by 1.4 to obtain the ultimate seismic
resistance design coefficient (0.081). Comparing the ultimate
35
seismic design coefficient with the yield seismic design
coefficient indicates that this structure has an overstrength
represented by the overstrength ratio (OSR) of
OSR = CY/Cd = 0.190/0.081 = 2.35
The inherent overstrength of this structure will be investigated
in more detail in the following section.
9. ANALYSIS OF STRUCTORAL OVERSTRENGTH
using the results of the previous sections, it is possible
to obtain an estimate of the overstrength ratio for this
structure. The OSR can be assumed to consist of the following
five major components: (a) a factor representing the ratio of
the ultimate strength of a member to the allowable strength, (b)
a factor representing the ratio between the actual stress in the
member and the limiting allowable stress permitted by code, (c)
a factor representing the effect of load redistribution, (d) a
factor representing the effect of strain hardening and (e) a
factor representing the ratio between the nominal yield stress
of the material and the actual yield stress. The allowable
stress for a generic member including the 33% increase for
inclusion of seismic loads can be expressed as
Fa = 0.6*Fy *1.33 = O.SFy
which implies that
Fy = 1.25*Fa
The ratio of ultimate moment to yield moment can be expressed as
MP = (Z/S)My = 1.14*Fy *S = 1.14*1.2S*Ma
MP = 1. 425*Ma
36
and therefore
ultimate strength/allowable strength = 1.425
where
Z = plastic section modulus
S = elastic section modulus
Ma = allowable moment
MY = yield moment
MP = plastic moment capacity.
The stress in a member is usually expressed in terms of the
ratio of the actual stress to the allowable stress (Fig. 33) and
the limiting value of this ratio is unity. From Fig. 33b it can
be seen that for combined gravity and lateral load, the stress
ratio in the critical member is 0.69. In Fig. 33a, the stress
ratio for this member due to gravity load acting alone is 0.25.
For this value to be used with the gravity plus lateral load
above, the allowable stress must be increased by 33% or
conversely the stress ratio must be reduced by 0.75 resulting in
a value of 0.1875. These values along with those developed in
the preceding paragraphs for estimating the ultimate resistance
are represented on an idealized force versus displacement curve
in Fig. 59.
The capacity of the member to carry additional lateral
force up to the allowable value can be obtained by subtracting
the maximum stress ratio (SR) for gravity loads acting alone
(Fig. 33a) from unity to obtain:
Allowable seismic SR supply = 1.0 - 0.1875 = 0.8125
37
Considering the SR due to combined gravity and seismic forces
(Fig. 33b), the SR for the seismic lateral load condition can be
obtained as:
Code seismic SR demand = 0.69 - 0.1875 = 0.5025
using these two values the overstrength due to design
conservatism can be estimated as
Design conservatism = 0.8125/0.5025 = 1.6169
In a similar manner, the overstrength due to the factor of
safety incorporated in the allowable stress design procedure on
first plastic hinge formation can be obtained as
1.425 - 0.1875Factor of safety = -------------- = 1.5231
1. 0 - 0.1875
Combining these two factors, the overstrength on first yield
(plastic hinge formation) can be estimated as
OSR(yield) = 1.617*1.523 = 2.463
and for this structure the base shear at first yield would be
estimated to be
Vy ' = 2.46*Vcode = 2.46*235 = 578.8 kips
From the base shear versus displacement curve shown in Fig.
48, it was noted that the initial yield actually occurred at a
value of 640 kips representing a difference of 9.5%. The seismic
resistance coefficient at first yield, Cy ', can be expressed in
terms of the design seismic resistance coefficient, Cs ' as
Cy ' = 2.46 Cs
Beyond first yield, the increase in strength is due to a
combination of strain hardening and redistribution of internal
38
forces as plastic deformation occurs. Considering the ultimate
shear to be 750 kips without the effect of strain hardening, the
increase due to moment redistribution can be determined as
redistribution = 750/579 = 1.30
The amount of increase due to redistribution of moment is
limited by the formation of a sway mechanism in the first story
level with only a limited amount of inelastic behavior being
distributed to the upper stories. Referring to Fig. 53, the
ultimate shear can be estimated at 800 kips when including
strain hardening, and the increase due to this effect is
strain hardening = 800/750 = 1.06
Summarizing the above results, the OSR for this structure can be
expressed in terms of the four parameters as
OSR = 1.52 (factor of safety)
* 1.62 (design conservatism)
* 1.30 (redistribution)
* 1.06 (strain hardening) = 3.39
The yield seismic resistance coefficient, Cy ' can then be
expressed in terms of the design seismic resistance coefficient
for this building as
Cy = 3.39 Cs
The resistance Ry can now be estimated as
Ry = 3.39*Vcode = 3.39*235 = 797 kips.
This overstrength which is inherent in the current design
process is undoubtedly a significant factor in reducing or
39
preventing earthquake damage, particularly for low to moderate
earthquake motions.
The above discussion of overstrength has been based on the
nominal yield strength of the steel. For most rolled steel
shapes, the actual yield stress can be considerably higher than
the minimum specification. In the case of this building, coupon
tests indicated a yield stress of 44 ksi as compared with the
nominal 36 ksi. From Fig. 52, it can be seen that this increase
in yield stress results in an increase of 910/750=1.21 or 21% in
the structure resistance. If this factor is combined with those
discussed above, the OSR for this structure becomes 4.11.
10. NONLINEAR RESPONSE ANALYSIS
In order to evaluate the inelastic dynamic response of the
structure, it is necessary to select an ensemble of possible
strong motion earthquakes. The design earthquake should then be
the selected ground motion that will drive the structure to its
critical response. Linear elastic response spectra (LERS) for
acceleration records obtained during major earthquakes over the
past 13 years are shown in Fig. 60. Also included in the figure
is a plot of the LERS specified by the 1988 Uniform Building
Code. Of particular interest to this study is the spectrum from
Obregon Park which was obtained from the 1987 Whittier Narrows
Earthquake. This motion, which is shown in Fig 61a, is
representative of the strongest motion to be recorded during
this earthquake. The response spectrum of this motion is
compared with that of the motion recorded at the base of the
40
building in Fig. 61b. Here it can be seen that the Obregon Park
motion is considerably stronger over the entire period range. It
should also be noted that the nBC spectrum, shown in Fig. 60, is
exceeded by a considerable margin in the period range from 0.0
to 3.0 seconds by several of these ground motions.
Acceleration time histories for these strong motion
earthquakes are shown in Fig. 62. The acceleration recorded at
Bucharest, Romania in 1977 is shown in Fig. 62a. The peak ground
acceleration is a modest 0.2g but the motion is characterized by
two long duration acceleration pulses which can have a
significant effect on the dynamic response. The motion recorded
at Hollister during the Loma Prieta Earthquake of 1989 is shown
in Fig. 62b. This motion has a peak acceleration of 0.35g and a
duration of strong shaking of about 7 seconds. The ground motion
recorded at James Road during the 1979 Imperial Valley
Earthquake is shown in Fig. 62c. This motion is also
characterized by two large acceleration pulses. Previous studies
[12] have indicated that this ground motion can create a strong
response in a flexible frame. The final ground motion considered
in this study is the motion recorded in Mexico City at SCT
during the Michoacan Earthquake of 1985 which is shown in Fig.
62d. This motion has a modest peak acceleration of 0.17g but the
duration of strong motion is in excess of 30 seconds. Note that
the peak acceleration does not occur until almost 60 seconds
into the recording.
41
10.1 Inelastic Response Spectra
Nonlinear response analyses of single-degree-of -freedom
systems were performed using the NONSPEC program. Results of
these analyses were used to obtain values of the required yield
seismic resistance coefficient as a function of building period
and displacement ductility for each of the ground motions just
discussed. This data is presented in Fig. 63. These curves are
very useful and can be used in either an analysis or a design
context. From an analysis standpoint, Cy is known and the figures
can be used to estimate the average displacement ductility
requirement. Using the yield seismic resistance coefficient
determined for this structure neglecting the effect of strain
hardening (Cy = 0.19), the average displacement ductility
requirement under the above ground motions can be estimated as
follows: Bucharest = 1.8, Hollister = 3.5, James Road = 3.0 and
Mexico City SCT = 2.0. plots of Cy versus building period have
been developed by Uang and Bertero [13] for other earthquake
ground motions. From a design standpoint, one can enter these
graphs with the estimated periOd and the design ductility and
obtain an estimate of the required seismic yield resistance
coefficient.
10.2 MUltiple Degree of Freedom Response Analyses
The nonlinear dynamic analyses are based on the two
dimensional model of a typical perimeter frame. The analyses are
done using the NODYN2 computer program which was also used for
the static nonlinear analyses. Before considering the inelastic
42
response, the computer model to be used for the nonlinear
response calculations was used to calculate the elastic response
and to compare it with that recorded in the building. In order
to include the effect of viscous damping in the nonlinear
response calculation, it is convenient to represent the damping
matrix as a linear combination of the mass and stiffness
matrices. This results in two constants which can be selected to
specify a given percentage of damping in two modes of vibration.
Once these are selected, the damping in the other modes is
defined. Based on the results of the elastic analyses, the
constants were chosen to give 5% of critical damping in the
first mode and 8% of critical in the 4th mode. This resulted in
4.4% of critical in the second mode and 6% in the third mode.
10.3 Linear Dynamic Ana1yses
Using these values and a two dimensional model similar to
that used for the elastic analyses, the elastic response of the
frame was calculated. The acceleration calculated at the roof
level is compared with the recorded acceleration in Fig. 64a. A
similar comparison of accelerations at the third story level is
shown in Fig. 64b. In both cases, the comparisons are quite
good.
The time history of the calculated base shear due to the
recorded base acceleration is shown in Fig. 65a. Here it can be
seen that the peak value of the base shear is about 270 kips
which is well below the initial yield value of 640 kips obtained
from the nonlinear static analysis. The time history for the
43
base shear under the Obregon Park motion is shown in Fig. 65b.
The peak value in this case is 490 kips which is still
considerably less than the 640 kips required to cause initial
yield.
10.4 Nonlinear Dynamic Analyses
The base shear under the Bucharest motion, shown in Fig.
66a has a peak value of 925 kips which is 44% above initial
yield and 22% above the ultimate shear as determined by the
static analysis. This increased base shear in the dYnamic case
above that obtained from a static analysis has been discussed by
Bertero [14]. It is considered reasonable because of the
following factors: (a) the opening and closing of plastic hinges
with time and their migration through the structure, (b) the
time variation of inertia forces and (c) the effect of higher
modes of vibration. The base shear for the Hollister ground
motion, shown in Fig. 66b, has a peak value of 850 kips which is
also above the initial yield and the ultimate values. A similar
result is shown for the base shear due to the James Road motion
which is shown in Fig. 66c and has a peak value of 850 kips. The
base shear for the seT record is shown in Fig. 66d and has a
peak value of 900 kips which is 18% above the ultimate static
value. These studies indicate that the motion recorded at
Bucharest generates the largest base shear and the only records
which are insignificant for considering inelastic response are
those obtained from the Whittier Narrows earthquake.
44
The base shear for a single frame based on the 1988 UBC is
either 124.7 kips or 166.5 kips, depending on how the
fundamental period of the building is estimated (see Section
6.4). Dividing the ultimate base shear of 925 kips by these
values results in structural system factors of 7.4 and 5.6,
respectively. Note that both of these values for Rw are well
below those specified in the building code.
The inelastic displacement response is shown in Fig. 67.
The envelope of maximum lateral displacement for the five ground
motions is shown in Fig. 67a. Also included on this figure is
the displacement required by the building code. It can be seen
that as in the case of the base shear, the Bucharest motion
results in the greatest displacement demand. The displacement
requirement for Obregon Park is considerably less than the
others and much closer to the code requirement. For the
Bucharest, James Road and Mexico City records, most of the
lateral displacement occurs in the first story level, whereas
for the Hollister record there is· also a major displacement
increment between the 4th and 5th levels. The former records are
characterized by some significant acceleration pulses which tend
to concentrate the deformation in the first story, particularly
if the first story tends to be a soft story as indicated from
the static analysis. The later record is more sinusoidal in
character, and this allows the inertia forces to build up in the
upper stories. A similar condition can be seen in the plot of
interstory drift shown in Fig. 67b. The Bucharest record has an
45
interstory drift of 2.9% in the first story. This value is
relatively large but it is still less than the almost 4%
indicated in the static analysis. Note the large interstory
drift requirement of the Hollister record at the 5th story level
The curvature ductility requirements are shown in Fig. 68.
The ductility requirements for the girders are shown in Fig.
68a. Here it can be seen that all values are less than 2.3 which
can readily be developed in a standard moment connection of two
compact members. As noted previously for the displacement
response, the ductility requirements for the Obregon Park record
are the least and, in fact, are considerably less than unity
indicating elastic behavior. It can also be seen that the
ductility required by the static analysis is about 2.5. The
ductility requirements for the column elements are shown in Fig.
68b. The largest ductility requirement occurs in the first story
columns for the Bucharest motion and has a value of 5.2 which is
quite large for a column. Other column ductilities are 3.1 or
less and should be sustainable.
The element rotation requirements are shown in Fig. 69. The
girder rotations shown in Fig. 69a are all less than 1.4% and
should be readily developed with a standard moment connection of
two compact sections. The column rotation requirements are shown
in Fig. 69b. Here it can be seen that the rotation requirements
for the columns of the first floor under all ground motions
except Obregon Park are quite large. It will be difficult to
develop the large rotations required for the Bucharest and
46
Mexico motions. The rotation requirement obtained from the
static analysis gives a good estimate of that which will be
required in the most severe case.
The envelopes of maximum story shear are shown in Fig. 70.
The values given in this figure are based on the sum of the
maximum column shears at a given story level. As such, they
represent an upper bound on the story shear since all of the
maximum column values may not occur at the same time. This
effect can be seen by comparing the base shear to the time
history values given previously in Fig. 66. In addition, the
code loads have been increased by 40% to represent the ultimate
condition. It can be seen that the adjusted code values clearly
represent the minimum shear. The story shears resulting from the
four recent earthquakes are considerably larger than the
adjusted code values and those obtained from the Obregon Park
record. This is further evidence that the Whittier Narrows
earthquake wa~ not a very severe event.
Hysteresis curves of the story shear versus the interstory
displacement are shown in Fig. 71 for the Bucharest ground
motion. At the sixth story, shown in Fig. 71a the behavior is
entirely linear. There is some limited ductility in the fifth
story as shown in Fig. 71b. The fourth story also has only a
limited amount of inelastic deformation, Fig. 71c. At the third
story there is an increase in inelastic deformation followed by
a decrease in the second story, Figs. 71d and 71e. As indicated
previously, the primary inelastic deformation for this ground
47
motion occurs in the first (base) story as can be seen in Fig.
71f.
Similar hysteresis data for the Hollister ground motion is
shown in Fig. 72. Here it can be seen that the sixth and second
floors are elastic, Figs. 72a and 72e. From Figs. 72c and 72d it
can be seen that the fourth and third floors have a limited
amount of inelastic deformation. The main regions of inelastic
deformation for this ground motion are on the fifth and first
(base) floors as shown in Figs. 71b and 71f.
A plot of input energy for four of the ground motions used
in this study are presented in Fig. 73. As in the previous
cases, the Bucharest ground motion results in the largest amount
of input energy indicating that it has the largest damage
potential for this particular structure. It can also be seen
that the energy from the Whittier Narrows earthquake is very low
indicating that this is not a very severe earthquake. The
Hollister record also has a significant amount of input energy
for this structure and as shown previously controls some of the
response parameters, particularly in the upper stories. The
James Road energy input, while being substantial, is not the
controlling one for this structure.
10.5 Effect of Increased Ground Accelerations
The effect of a larger earthquake on the building is
evaluated by increasing the accelerations recorded at Bucharest
and Hollister by 30%. The effect of this increase on the maximum
displacement envelope is shown in Fig. 74a. From this figure, it
48
can be seen that the effect of the increased acceleration on the
displacement is greatest for the Bucharest motion where the roof
displacement increases from 10.5 inches to 15 inches. The effect
on the interstory drift index is shown in Fig. 74b. For both
records the effect of the increase is greatest in the first
story level. For the Hollister motion, the IDI in the first
story increases to 2.1% and for Bucharest it increases to a very
high 3.9%.
The girder ductility, shown in Fig. 75a, is affected in a
similar manner. The largest increase is due to the Bucharest
motion and the largest increase in girder ductility demand
occurs in the bottom three floors. In the case of the column
ductility demand, shown in Fig. 75b, the largest increase is
again due to the Bucharest motion and occurs in the bottom two
floors.
The maximum rotation demand is shown in Fig. 76. For the
girders, shown in Fig. 76a, the maximum increase in the rotation
requirement occurs in the lower three floors and is due to the
Bucharest motion. At the first and third story levels, the
rotation is above 1.5% which is close to that which can be
developed in a moment connection. Considering the columns, shown
in Fig. 76b, the maximum increase in rotation occurs in the
first floor level. For all cases, the amount of rotation
required in the first floor level is above 2%. For the Bucharest
motion the rotation was 3.7% and it in turn increased to almost
49
5%. It is very doubtful that rotations of this magnitude could
be developed in standard beam-to-column moment connections.
The effect of increased acceleration amplitude on the
hysteresis curves of base shear versus interstory displacement
of the first story is shown in Fig. 77. The hysteresis for the
Bucharest motion is shown in Fig. 77a. Comparing this curve with
that of Fig. 71f indicates that the interstory displacement has
increased from 5.0 inches to 7.0 inches, an increase of 40%.
However, the base shear increases only from 900 kips to 950
kips, an increase of 5.5%. This clearly indicates that in the
inelastic range, the base shear becomes relatively insensitive
to changes in seismic demand and that large changes can occur in
the displacement response which are not reflected in the changes
in the base shear. In the case of the Hollister motion, shown in
Fig. 77b, the base shear increases from 860 kips to 890 kips, an
increase of 3.5%. However, the maximum interstory displacement
increases from 3.0 to 3.9 inches, an increase of 30%. Obviously,
the maximum base shear is not going to be a very accurate
parameter for evaluating damage potential.
11. SUMMARY AND CONCLUSIONS
This study has investigated the seismic behavior of a six
story steel building which was instrumented with thirteen strong
motion accelerometers at the time of the Whittier Narrows
earthquake. The building has a square plan with lateral
resistance provided by a perimeter moment-resistant frame.
Recorded peak accelerations were in the north-south direction
50
and ranged from O.226g at the base to O.289g at the roof. No
damage was reported as a result of this motion.
System identification techniques were applied to the
recorded data to identify the predominant periods of vibration.
Moving window Fourier analyses were performed to investigate
changes in the period of vibration during the earthquake. The
effect of torsion was also evaluated using Fourier amplitude
spectra and linear elastic response spectra. Linear elastic
two dimensional and three-dimensional models of the building
were developed to study the behavior of the building under code
lateral forces and the recorded base motion. Two dimensional
nonlinear models of the building were developed and used to
evaluate the ultimate strength of the building under
monotonically applied static lateral forces. Using these
results, the overstrength of the structure was estimated. The
two dimensional nonlinear models were also used to evaluate the
behavior of the building when subjected to the ground motions of
selected strong motion earthquakes which have been recorded
previously.
On the basis of these extensive studies, the following
general conclusions are presented:
1. This building was not severely tested by the ground motion
recorded at the base during the Whittier Narrows Earthquake. The
base accelerations were short duration acceleration spikes which
did not result in a significant energy input to the structure.
Furthermore, the duration of strong motion shaking was a
51
relatively short three seconds. Results show that the dYnamic
response was completely linear elastic.
2. Using commercially available computer programs, two
dimensional and three-dimensional mathematical models can be
developed which accurately predict the linear elastic dYnamic
response as represented by recorded accelerations at various
locations in the building.
3. The design seismic resistance coefficient' specified by
current building codes has been reduced substantially for a
building of this type when compared with the value used in the
original design in 1973. It is not clear to the investigators
how this significant reduction can be justified.
4. The directional effects of the input ground motion are shown
to increase the stress in the critical members of this structure
by 9%. With current computer programs, this effect can easily be
incorporated into the design analysis.
5. Nonlinear static analyses can be very useful in estimating
the following mechanical characteristics of the structure which
can be used as an indication of inelastic dYnamic response
behavior:
(a) The ultimate resistance of the structure as
represented by the base shear versus roof
displacement relationship.
(b) The maximum rotation requirements and ductility
52
requirements of critical members.
(c) The distribution of inelastic behavior (plastic
hinges) at ultimate load.
(d) Determination of the yield seismic resistance
coefficient for the building.
6. The concept of the yield seismic resistance coefficient can
be very useful in estimating the seismic behavior of a structure
for purposes of design. Using a nonlinear static analysis of the
building, the yield seismic resistance coefficient, Cy ' can be
determined. Using Cy ' the fundamental period of the building and
inelastic response spectra for single-degree-of-freedom systems,
the average ductility requirements for various strong motions
earthquakes can be estimated.
7. The structure considered in this study has an inherent
overstrength which resulted in an ultimate lateral resistance
which was more than 200% above the code requirement. This has
undoubtedly had a significant effect on the favorable seismic
response of this structure, particularly under the relatively
low seismic input of this earthquake.
8. Using the nominal values for the material yield stress, the
perimeter frame formed a sway mechanism in the first story level
at ultimate load. This behavior is undeSirable since it limits
the redistribution of plastic hinges (inelastic deformation)
into the upper floors and results in a reduced resistance at
53
ultimate lateral load. It also causes the resistance curve to
have a relatively flat post yield characteristic which results
in large lateral displacements for small increases in the
lateral force.
9. The displacement ductility requirement of the individual
story levels shows a relatively good correlation with the
curvature ductility of individual members in the story. However,
the overall displacement ductility is considerably less than
either the story displacement ductility or the member curvature
ductility.
10. The design practice of keeping a column size constant for
at least two story levels causes the inelastic deformation at
ultimate load to be concentrated in a limited number of story
levels rather than being distributed over the height of the
frame in a more uniform manner. This becomes readily apparent
from the results of a nonlinear static analysis.
11. Input motions characterized by strong acceleration pulses
(Bucharest and James Road) tend to affect the lower floors of
buildings. If these floors become soft stories at ultimate load,
the combination of pulse load and soft story can lead to poor
seismic performance. Motions characterized by numerous zero
crossings and longer duration (Hollister, SeT) tend to have more
effect on the upper floors of the structure.
54
12. The structural system factor, Rw, evaluated for this moment
resistant steel frame is shown to vary between 5.6 and 7.4. Both
values are well below the value of 12 specified in the 1988 UBC.
55
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,....0.30 ..l-,.-.-.-.,-,-,.-r'T-rl--r-r-rrr..-r~f_rT,..,._TT"1__rT+rTT1--rTT-rrj-- 0.300.00 10.00 20.00 30.00 40.00
.TIME (SECONDS)
(a) Channell, Up, NW Corner
0.00 10.00 20.00 30.00 40.00O. 30 -f-L...J....L..L.L.JU-L...L.+.l...L...lL.l-l...J....L..L...Y-L.L...L..L.L..L...1-L.Lt--'-LLl...L.L.L.L.J'-t- 0 .30
BU BANK (WHITI ER)BASE C NNEL 13
Z 0.1 0 -t--tt-H--+-----J----+----+0.10
o~a::::w-'wU -0.10 -t--Hf-'H--+------t----f---_+_O. 10
U«
-0.30 -+-r...,..T"""r1-r-r-rl-T"""r1,.....,...,.....r-r-1-rr....rT"T.,..,...+-r-~.,..,....,....,rl__ 0.300.00 10.00 20.00 30.00 40.00
. TIME (SECONDS)
(b) Channel 13, N-S, NW Corner
Fig. 5 Recorded Acceleration at Ground Level
59
0.00 10.00 20.00 30.00 40.000.30 ·..:j..:1...LJ-L...L.L..u....:yJBJ.
U..L
RB.L
AW
NWK
-1....L(+-HwlTTc..LI..LER..l..;).l...l-l~.L.LJ-..L.I-J....L.'--'--TO .30
BAS CHANNEL
0.10 -+--U--+---+-----t----r0.10zo~a:::w-IW +--~--+----+----+-----j--0.10U -0.10
U«
-0.30 -h-,--,-,,..,,.........+-r....-r-r-r-l-rr,...j--,rr-r......rrr-.+,....,--.--r.,-r-n-t - 0.300.00 10.00 20.00 30.00 40.00
TIME (SECONDS)
(a) Channel 8, E-W, NW Corner
0.00 10.00 20.00 30.00 40.000.30 +J-.LJ..JL.L..1.J....L.L.t-J...L..1-.L.1...Jc..L..L-4-'L.L.1...L.LLL.L-'-t-.L...L.J...J.-J-..l...1-L...I-.f-O.30
BURBANK ( HITTlER)BAS CHANNEL
0.10 +--+l-----I-----+-----!-----I-0.10Zo~a:::w-IWU -0.1 0 --l--~lI-----+----_+---__+----+-0.1 aU«
-0.30 -h-,--,-,,--,--,.......rh-rr,-,,-rr-rl-rrr..-rn-r-,+,.,.,--.--r.,-r-rr+- - 0.300.00 10.00 20.00 30.00 40.00
TIME (SECONDS)(b) Channel 9, E-W, SW Corner
Fig. 6 Recorded Acceleration at Ground Level
60
0.00 10.00 20.00 .30.00 40.000.30 +'-L..J-.>...L..J....w...L-\-UU-J...u...Ju...Lt-'-'...u....';'-'-'"'-'-l-"::':"W-'.""'-'-'-'-j-0.30
BU BANK (WHITI ER)2ND FLOO CHANNEL 6
,r-o,
o'--'Z 0.10 -!--+--+----+-----I----+0.10
o~
'ex:w....JWU -0.10 -t--.L.f-.j----1----f----+-0.10U«
(a) Channel 6, E-W, NW Corner
-0.30 -f-,-.,.,..,.,..,....,...,.-h-.-rT"T"T"n-r'!-rT"""'''''''''''-rr'''''''"T"T''""TT" -0..300.00 10.00 20.00 30.00 40.00
TIME (SECONDS)
0.00 10.00 20.00 30.00 40.000.30 -j-'-L..J-.>...L..J................-t-'-U-J...u...J':!-'-t-'-'-..J...W'::'-'-.o...i.:f...u....o...w.........40.30
BU ANK (WHITT ER)2ND FLOO CHANNEL 7
,r-o,
'-''--'
Z 0.10 -r---j--t----t----+---40.10
o~ex:w....JWU -0.10 -t--r-'-t----t----l----4--0.10()«
(b) Channel 7, E-W, SW Corner0.00 10.00 20.00 .30.00 40.00
0.30 +'-L.Uo...u....W..J..¥-'......................u....\--U-""'-'-'...L..J....1-4.u...J..........U-L-'-\-O.30BU BANK (WHITT ER)
2RD flOOR HANNtL 12
-0.30 +r..,...,..,..,....,...,.fT"~,.-,..,.,...,..1-r-rTT"'r_r_r~_.._r~TT_.-rl--0.300.00 10.00 20.00 30.00 40.00
. TIME (SECONDS)
Z 0.10 -j---fIHJI--1----t-----+----+0.10
o~ex:w....JWU -0.10 -t---fltHl'--f----I----f----+-0.10U«
(c) Channel 12, N-S, NW Cor~er
-0.30 +r.,-,...,.,..,..T"'T"T+n~,._,..,.,...,..h_r......,n-T'rr+..,..,_,.,..,..T""rT_.+-0. 300.00 iO.OO 20.00 .30.00 40.00
TIME (SECONDS)
Fig. 7 Recorded Acceleration at Second Floor Level
61
0.00 10.00 20.00 30.00 40.000.30 -t-'-...........L.J...Ju..L+-'-'-..u...u....L~i-'-'-.LJ-.<..u...'-'+.LJ-.<-'-'-u......"'+ 0.30
BU BANK (WHITT ER)3RO FLOO CHANNEL 4
".-..C)'-"Z 0.10 +--t-:--+----l-------+----+0.l0
o~a:::w-IWU -0.10 +---'-t-+----l-------+----+-0.l0
U-<
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0.10
30.0020.0010.00
B,!~BANK (WHITT ER)3RQ FLOO~ CHANNEL 5
~1~N ~~J~ ...L M k.~~ IA~
'1'( II''''' r • ~ ~ . w
0.000.30
-0.30 -h-.,..,..,.-rnn-r.j-,-,-....,..,-,..,.,.-,...j-,-.,..,....,,..,.,...,.-f-r-,-,.,.,..,..,..,.,...,- - 0.30. 0.00 10.00 20.00 30.00 40.00
.TIME (SECONDS) (a) Channel 4, E-W, NW Corner
40.000.30
".-..C)'-"Z 0.10
o~0:::W-IWu-0.10
U-<
-0.300.00 10.00 20.00 30.00
TIME (SECONDS)
-0.3040.00
(b) ChannelS, E-W, SW Corner
0.00 10.00 20.00 30.00 40.00O. 30 +'-L-U...L.J...Ju..Lj.-u...u...u....L~i-'-'-L-U...L.J...J'-'+L..U...L.J...Ju...J-.L.j-0.3a
BU BANK (WHITT ER)3RQ FLOOR HANNtL I 1
Z 0.10 -l--1llHll+l-----f----j-----t-0 .10
o~0:::W-I
t3 -0.10 -l--J!IIH,..J'-1.f--l----Ir----+----t--0. 10
U-<
-0.30 -j-,-.,.,...,....,..,-,..,.+.-...,.......,..,..,.....,..j--n-..,.,...,....,..,...".,.............,..,-,..,.-r+ -0.300.00 10.00 20.00 30.00 40.00
TIME (SECONDS) (c) Channel 11, N-S, NW Corner
Fig. 8 Recorded Acceleration at Third Floor Level'
62
0.00 10.00 20.00 30.00 40.000.30 +L.L.J...J...u.J'-'-'-j-w-.L.J...J....J-.,':JaL..:':u±'"AL..:':NK~(WL..:':H::ITI~E;:;R-::') ~"""""""'T 0.30
ROOF CANNEL 2
,-...'-'.........
0.10 -l--.t+.1f-:--f_--_+----l----t0. 10zo~a:::w-l
~ -0.10 -l--y~+-+f_--_+-----j----t-O.10
()«
-0.30 +r,...,..,..,..,...."T"rt-n-TT"T.....-n"*"':'"""""T.....-n~:tr::,...,..,.TT"T-:40;;t.OO.0.300.00 10.00 20.00 30.00
TIME (SECONDS) (a) Channel 2, E-W, NW Corner
-0.10
0.10
40.000.30
30.0020001000
aUf BANK (WHITI ER)ROOF C ANNEL 3
-
r'P~~f\~ r-J~ AA .AhfthU N'JINVv'I~ ~ '\I V IHVVvVV
0.10
0000.30
zo~a:::w-lW() -0.10
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-0.300.00 10.00 20.00 30.00
TIME (SECONDS)
-0.3040.00
(b) Channel 3, E-W, SW Corner
ROOFB~F~ANK (WHITI ER)ANNEL 10
~ IW HrtAIIAAAIVw vvvn '. v
0000.30
0.10Zo~a:::w-lW() -0.10
()«
1000 2000 3000 40.000.30
0.10
-0.10
0.3040.0010.00 20.00 30.00
. TIME (SECONDS)
-0.300.00
(c) Channel 10, N-S, NW Corner
Fig. 9 Recorded Acceleration at Roof Level
63
'" 10-2 lO-1 10° 10\ 102",0 S
A --BASE <81"\
~'0 -----Bf\SE 191 ",'.::;.~~U
WN(/)N
S"- S.z
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0IT 0
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0 S10-2 10-1 10° 101 102
PERIOD
(a) Base
Fig. 10 Spectra Comparison, Torsional Effects
64
..., /0-2 10-1 100 /01 102",!:! !:!
--BASE 181-----ROllf 121
WWIf) N N
" !:! ~
z
>- 10.I-.-.~ 0
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10-2 10-] 100 101 102PERIOD
(a) E-W Motions
..., /0-2 10-1 10° 101 IO~~
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--BASE (13)r-. "\-----ROOF IIOJ ~.. ~w ~<)wIf) N
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PERIOD
(b) N-S Motions
Fig. 11 Spectra Comparison, Amplification Effects
65
Record 13; location I; y-direclion; Ground3
2.5
---<.)
'"'"::2u
i!:lCl:Jt:
r~i 1.5:2:< (\ ,c<:: 1\ jL!Jrv 1\1:J
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0.5 v
00 0.5 1.5 2 2.5 3 3.5
fREQUENCY (Hz)
(a) North-South, Channel 13
Record 9; IOC:llion 2; x-<lircction; Ground2.5.----.----,-----,.---r------r-------,------,.-----,
2
O.S /J
i!': 1I i I,i: I\I\ '\ f\!
43.532.52O.SOL.L---'----'-----'---_L.--__-'---__-'-__--'-__--'o
r-REQUENCY (Hz)
(b) East-West, Channel 9
Fig. 12 Fourier Amplitude Spectra for Base Motions
20
IK
Ill·
I I'
;;r§ 12...:;~<'"'"2::>f2
66
l"'OUrict amplitu6c of recotd '2 &.~ motion
n:-C'on:J2:-._gwund: ._••
30S
FREQUE.>;CY (Hz)
(a) Roof Level
Fowier amplirude: o( record .: &.:.~~ motion
rec=ord,4:-
gJ"Outld: •••••
4
3.5
FREQUE."CY 1Hz)
(b) Third Floor
rc.,:orJ6; ••. -
.FR~Q(jE"CY .HLI
(c) Second Floor
Fig. 13 Fourier Amplitude Spectra, E-W, NW Corner
67
Fourier ampliludc 01 record 3 /.I. gnlUnd m()(ion(rccord q)16r--~~="':"':'--_--~------~----'
record 3: ._
g,rnollu: .....
3.5
FREQUENCY (H,)
(a) Roof Level
Fowler amplicude of t1:COrd $ & ground motion(record 9)
record S: ---
ground: ...••
fREQUENCY (Hz)
(b) Third Floor
f'ouncr ampliluJc of (('.;oro.1 1 &:. srounJ motion(rccorti 'il)
FREQliESCY (11.<)
(c) Second Floor
Fig. 14 Fourier Amplitude Spectra, E-W, SW Corner
68
r'OUnc:r &InrlicucJe o( record 10 &,,~ motion(rcc:onII3)~
4S
40
I 3S
;;rg 30
t:..J...::;-<'""'~::2
25
FREQUENCY (1-'..<)
(a) Roof Level
record to: .._
ground: ..•..
35
20
18
16~
% 14~
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":>0u.
~ IFourier arnplirude o( n:cord 1-2 &:. ~.:.-.J mocion(record 13)
n:corc1
ground: ....•
3.j
(b) Third Flo'or
121__~FO_U_ri_<,_,~n.:-,p_lil_Ud_C_O~(_r"'_O_'d_12_&_'.:..'"""_-~_'_"""_ion~(=_O_'d_I..:3:..)~_---,
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(c) Second Floor
Fig. 15 Fourier Amplitude Spectra, N-S, NW Corner
69
I{,----,,.·
(~ .
tu·
K· )~II!I
u.s
FREQUENCY (Htl
(a) Roof Level
ReccrQ 5; loc:nion 2; x-duection: Third F1
2..5 3.5
4.5 •
J.
FR(QUENCY (UtI
(b) Third Floor
1':'l,"CII(t! 7: l(tC1liuu 1:. x.dir.:ction: SC~Q(1d rl
FREQUE."CY (ll,)
(c) Second Floor
3.5
Fig. 16 Transfer Functions, E-W, SW Corner
70
FREQUENCY (II,)
(b) Third Floor
I2r----·---_~_,--_~------
10-
~ Co- I,-~
(c) Second Floor
Fig. 17 Transfer Functions, E-W, NW Corner
4~
4U
)5 '
3n·
25..':t
2U
71
1~":l'tllIl I(); Incaiioll I: y~iteCtiun:Roof
FREQUENCY (lb.)
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Record II; locJ.tion l~ y-ditc:aion: Third F1
3.S
IAI
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IS
16
I"
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10
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0.5 1.5 2.5 3.5
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Fig. 18 Transfer Functions, N-S, NW Corner
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93
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o "0u0-..JW>-..J .Ol\~II 0 0
CC 0 S!t-U ~w .U •
0-(J)
.001 .0001, ,0 0. ,
10-2 10. 1 100 101 102
PERIOD
(a) Floor Response Spectra (b) Channel 4, E-W
2000
ii
f-- CALCULAT::D (SAP90).•...• R~CORD::C!(CHAN 5)
38 CO
0.10Zo
(c) Channel 5, E-W (d) Channel 11, N-S
Fig. 40 Third Floor Response Comparisons
0.63
0 0 = aTouv ~nduI 'sor~eH ssaJ~S Tv -ora
Ir- CD --l :::::0 en I -<I'l 00 :J> --In Q --I -0 --l ;:a
~---j I'l 1--1 I'l
:z: ~ 0'" a enJ:> CJ c..n en f"-JCP 0 CSl CSl CSl CSl ~ 0(J) -i . - . . . <:.
::r: CSl ()< '-J '0 CSl r<r< ;:D
X::0
~6
95
x 0::0:: LL.J
~LL.J lSi 0'- l:"'--- IJ) lSi ::r: c.n::> . . - - - I--o ~ lSi lSi IS) lSi 0 COI"'-J en en 0
I <I:en C) '.-0 ':7f--LLJ r---1 LLJ
D::::: r- 0- r- c..::J LLJr- <I C) C) LLJ>- en D::::: r- ef] --.J
Fig. 42 Stress Ratios, Input Angle = ISo.
89'0
0.70
oOE = aTDuv 4ndUI Iso14~H ssa~4S Ev ·DI~
Ir- eo ---1 :::::0 c..n I -<
f'II'l C) C) I> ---1(7) ---1 U ---1 :::::0
~----j I'l I---l I'l
---". ~ cr-, c=J c..n::I> '""'-'
CJ c..n c..n r......JCO 0 (Sl (Sl (Sl (Sl ~O
CD --i . . C:I: (Sl c.n '-J '0 (Sl r>r> :::0:::0 X
96
97
>< 0:::0::: w..J
7w..J IS) Ch c--.... Lf1 IS) ::r: U)::> - - - - - I--CJ ~ IS) IS) IS) IS) CJ o:Ji ......J en en Cl
I <r:en 0 0 -:;7"
f--l..L.J r----i l..L.JD:::::: I-- 0- I-- c:::J WI-- <I 0 C) l..L.J
>- en D:::::: r-- cD --l
Fig. 44 Stress Ratios, Input Angle = 450
69'0
98
>< 0::0:: W
7w !Sl 0., t--... Lf) !Sl :::c Cf)::> . . . . f-0 !Sl !Sl !Sl !Sl 0 coI,,-J c.n c.n 0
I <Ic.n c:::) ...-0 :z: f--LL.J t--i LL.J0:::: I-- 0- I-- ~ WI-- <I C) C) LL.J
>- c.n 0:::: I-- eD ...--J
Fig. 45 Stress Ratios, Input Angle = 60°
v9'0
99
>< a:::0::: w
c\ w is 0', t'-.. uJ tSl ::c UJ=:> - . - ~
~0 !Sl !Sl tSl tSl 0 COJ---J u; uJ CJ
I <I:/ uJ CJ ..J::J :z: f--1t. LLJ .---; LLJ
Ct::: I-- 0- I-- c:J LL.JI-- <I CJ CJ LLJ
>- cf) D::.::: I-- cD ~
Fig. 46 Stress Ratios, Input Angle = 75°
95'0
0.46
0 06 = alouv ~nduI 'soT~e~ ssa~~s Lv ·OTd
Ir- eo --I :::::0 c..n I -<
n ITJ C) C) ::I> --I(7) --I -0 --I :::::0
b---1 ITJ f----l ITJ--;><'
~ 0"'. C) c..nI>
~
CJ c..n c..nI"-JCO 0 lSI lSI lSI lSI ~Oen --i - . . . <: ~:r: lSI en '-J '0 iSJ fT1
1'1 ::0::0 ><
001
V
SAP90 (ELASTI )y~/
V/
1/ f---- NC DYN2 (L NIFORM)- - - - UlARC (L NIFORM)
/
V2 4 6 8 10
DISPLACEMENT (IN.)
1200.00
,,--....1000.00(f)
0.-~'-../ 800.00
er:::«W 600.00I(f)
W 400.00(f)
«m200.00
0.00
o
o
2 4
101
6 8 10 12
12
Fig. 48 Roof Displacement vs. Base Shear, Uniform Lateral
(ELA'I
SAP90 TIC)/j
';p-I ~-I ~
.~
II
I 1/ -- NODYN2 tTR11 NGULAR)II NODYN2 UNI ORM)I
/'/
:IIV
5 10 15
DISPLACEMENT (IN.)
1200.00
,,--....1000.00(f)
0.-
2S 800.00
er:::«W 600.00I(f)
W 400.00(f)
«m
200.00
0.00
o
a
5 10 15 20
20
Fig. 49 Uniform vs., Triangular Lateral Loading
//; -::,- -'"-- ---- .. -- --- -~-----
.. - ... -~ , I''I ~
t I •
'I '", I 't I :
II'I/ ,I,I ,,
1/ ,I / ,1:[ ,II
1 I
I'/ f'/ f'/ f ---- Ut IFORM'/ f'/ f ---- SI NE"'/ -Tf' IANGULA"'/ - - -- 1 - COSlt E
1/5 10 15 20 25
DISPLACEMENT (IN.)
800.00
,...-.....(J)0.- 600.00
Y::"-../
0::::«W 400.00::r::(J)
W(J)
d5 200.00
0.00
a
o
5 10
102
15 20 25 30800.00
600.00
400.00
200.00
0.0030
Fig. 50 Lateral Load Distribution and Lateral Resistance
400.00
A/S~pgrV
/
/ --3E ksi. STEEL-4 ksi. STEEL
1/5 10 15
DISPLACEMENT (IN.)
1000.00
(J;' 800.00
0.-
~"-../
0:::: 600.00
«WI(J)
w(J)
«CD 200.00
0.00
o
o
5 10 15 201000.00
800.00
600.00
400.00
200.00
0.0020
Fig. 51 Resistance, Nominal vs. Actual Steel Strength
103
15105o 20--f-l-...L.L-'-'-L..L..J--L..j-....L...L..J.....L.-'-'-L..L..J--f-l-...L.L-'-'-L..L..J--L..j-....L...L...L.L-'-'-L.L.J4-1 1000 .0 01000.00
,,---..800.00 800.00(J)
0....-Y::'--./
0:::600.00 600.00
«W:r(J) 400.00 400.00
W --G ADE 36 STE L(J) ----- G ADE 50 COL MNS« --- 4 ksi BMS. A o eOLS.m 200.00 200.00
5 10 15
DISPLACEMENT (IN.)o
0.00 -f-r-rr.,....-r-rt--r+......,....,....,....-r-rt-l-r-rr.,....-r-rt--r+......-rr.,....-"....,-+-O.0020
Fig. 52 Steel Strength and Lateral Resistance
5 10
800.00
600.00
400.00
200.00
5 10
DISPLACEMENT (IN.)
Fig. 53 Strain Hardening and Lateral Resistance
104
54321o 6-t-'--.L-L..L...L-L..L..J....JTl....L..l-l....'-W'--I...1.-iW-L.JW-L.J....LJ....J+-'--l..I-J..J....J....L..J...Lf-l-...LLL...L.I....L..L.L..t...L.I....L.L..L..L..L..L..L.-l- 800 .0 0800.00
_.... - ..... -- -*,,--.....,(f)
CL 600.00 600.00~
'----../
cr::«w
400.00I 400.006 H
(f) 5 H4 H
>- ......... 3 0cr:: 2 00 1 Tr- 200.00 200.00(f)
5
(I N.)1 2 3 4
INTERSTORY DISP.o
o.00 -f-r-,...,....,,...,....,rr-t--r-rr-r-r-r->r-r-r1-'-'-'-'-'-'r-r-r-I-h-T-r-rr...,...,...,..-r+-r--r-r-r.,..,,...-rr+T"T""T"T"T""T"T"TT"t- 0 .0 06
Fig. 54 Interstory Shear vs. Displacement, Triangular Load
NONLINEAR STATIC
BEAMSCOLUMNS
... STORY
105
0.00 1.00 2.00 3.00 4.006 -f-.l-..L.L-¥-J.....Y--4-..L.L.J.....LLLl--l....L+L-LLl-LL..L.L.L..f-L.L..i-..L.L.J.....LLL.j- 6
..-J~ 4+----+--~~----+----+-r 4
~ )' ~o / r~ 2-J.-----+---~+-_«O-:-':'-_-::-__-.",-,-L,-,-,--~~2
-...'.:: - _.." I
~r
o+-r-,rrT'"'T"TT..,...,+,..,...,--,--,rrT'"'rh-TTT--rrr-,-,--je...,,-,....,..-r-.,-,--,--.+~ 00.000 1.000 2.000 3.000 L.OOO
DUCTILITY
Fig. 55 Ductility Requirements vs. Story Level
0.00 0.01 0.02 0.03 0.046-+-'-..J...+-J.....l.o(-LL....L..j-.J.....LLLl....L.L..L..Lt-J-l....L.L..L.L.LL.J4-J.-..L.L.J.....LL..LJ....Ll-6
NONLINEAR STATIC
..-JW4 4>W BEAMS..-J COLUMNS
"" .. ... STORY>-~
0~2 2
,'n -.
O+r-,-,-,--,--,rr-r--,-l-.,....,...-r-r-r..,....-,-,-h-,...,....-,-,-,.....,-,-l-.-~~r-r-r--.-J.-O
0.000 0.010 0.020 0.030 0.040
ROTATION (RAD.)
Fig. 56 Rotation Requirements vs. story Level
----
0,i
II
II
II I
II
II
I0
II
II
II
0
I3
I21
23
~26
281_
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.,
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Fig
.5
7S
eq
uen
ce
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Pla
sti
cH
ing
eF
orm
ati
on
107
0 5 10 15800.00 800.00
r--- -f
/I
~
(f)600.000- 600.00
-~
'-....-/
0::::«
400.00W 400.00I(f)
WRIANGULAR LOAD(f)QUIVALENT ELAS a-PLASTICciS 200.00 200.00
5 10
DISPLACEMENT (IN.)o
O. 00 --h.....,.-,r-r-"""--""'--""+""-'-""""--'--,-,r-r-,....,--h---,-,..,.-,--,--,-,-r+-- 0 .0015
Fig. 58 Idealized Elastic-Plastic Shear vs. Displacement
0.69Fa (Gra'li t\:) + Lateral)
wU0:::oLL
--l-«0:::wf--«--l
f _1.125Fa (Ultimate)
1.25Fa (Yield)
1.0Fa (A llowab le)
LATERAL DISPLACEMENT
Fig. 59 Stresses in an Idealized Member
0.0
2.0
4.0
6.0
8.0
8.0
6.0
BU
CH
AR
ES
T(1
97
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(19
9)
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8
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0
z o1.
00
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W --.J
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«..---...
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-/
co o .-i
Fig
.60
LE
RS
for
Recen
tE
art
hq
ua
kes
109
0.00 10.00 20.00 30.00O.50 +,t--L..L-.L-L.~..L-l+L-l.....L..l~.LJ......L.-l+J...J.-..l.--'t--L.J.....)..-'-,-+0.50
OBREGON P RKHintER NARROW 1987
0.30 -j---t+I------+-------+-------t-O.30
-t-t------+-------+-0.10
-+--+r-t--------t-------+-0.10zo 0.10
~crW-.-1 -0.10WUU«
-0.30 -t---1----_t_------t-------+--0.30
- a.50 -h-.-....--,-~_.___r_t_".-.__r_r_r_r<_+__.__r..,.-..._r-.-r-.-r-+-- 0.500.00 10.00 20.00 30.00
TIME (SECONDS)
(a) Acceleration Time History
WHJTTJER NRRROWS 198710-2 lO- 1 lOO 101
"6 -:t--'---'--'-'-U-LU-...--1.-L.L.J.-Llll.'--..L....L..J....l.lJ..UL---...I---'-'-
uW(J)ru
'- ~
z
>l-
auo-.lW>-J
~~IUW(L(J)
--OBREGON PAP.K
BURBANK
JOO.
ruo
o
oo
PERIOD
(b) Response Spectra Comparison
Fig. 61 Motion Recorded at Obregon park, Whittier Narrows
HO
LLIS
TER
OMA
PRIE
TA1
98
0.0
05
.00
10.0
015
.00
20
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.62
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.6
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a
112
C\J
o
CRLCULRTEDRECORDED
zo c5
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(a) Roof LevelTIME (SEC)
CRLCULATEDRECORDED
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i ~ I J \ l \ 1 \. t ,t \ J \
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(SEC)16.0
TIME12.00.0
C\J
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(b) Third Floor
Fig. 64 Acceleration Comparisons, Nonlinear Model
113
300
100
0:::<twIIJ)
W -100IJ)
<tm
3010 20
TIME (SEC)
- 300+-r----r-,-.--r-T-.----r--r-r--,-,~~,......,.....~~~~~~~
o
(a) Building Base
I
/1\AI\ f'\ All'!'Ii .!VI M fI JI ,...., I\. _
-\ \ V\JvV lJ vv v \J l,-
V
-- bSREGON PARK
10.00 20.00
TIME (SECONDS)
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0.00e:t:<twIIJ)
-500.00
-1000_000.00
10.00 2000 30001000.00
500.00
0.00
-500.00
-1000.0030.00
(b) Obregon Park
Fig. 65 Base Shear Time Histories, Whittier Narrows
-50
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00
.00
30
.00
30
.00 1
00
0.0
02
0.0
01
0.0
00
.00
10
00
.00
-10
00
.00 0
.60
(c)
~ '""'....
Fig
.66
Ba
seS
hea
rT
ime
His
torie
s,R
ecen
tE
art
hq
ua
kes
115
0.00 4.00 8.00 12.006 TL....L.LJ.---'r,---L..l-+-'-+-.L.L---L..l--L-L.l-.L-L.-H~l.....l;o.L...L...L..J,~ 6
,···,•••··II.,.....-1 :W 4-r----;-'-+--t---~"-f4---t'------+4>W---l
>0::::o012+-----7--r---+fr-----,I------I~--I-------I-2
~ BUCHAREST.........,..... OBREGON PARK............... HOLLISTERG-<H>-<H> JAM ES ROAD--- MEXICO SCT------ CODE x 1/k
o-1S-.---..,--,-,---.-.-.---+-r-.-r--r-r-r-r-r--r-+---r-r---r-1c-r-,...,---.--.-+ 00.00 4.00 8.00 12.00
DISPLACEMENT (IN.)
(a) Lateral Displacement
0.00 0.01 0.02 0.036 6,.,
\,.,,,,,,,,,,---l
,·W4 ·>
4
W---l ............... BUCHAREST
~ OBREGON PARK
>- ............... HOLLISTER0:::: G-<H>-<H> JAMES ROAD
0 .-.-.-...-. MEXICO SCT
012------ CODE x 1/k
, 2,,,·I,:
o--f-,:-r-r-r-.-r---,,-.---h--.-r--.-.-.---..,-'-+..--r--.-r-r-,...,----r-r+ 00.00 0.01 0.02 0.03
INTERSTORY DRI FT
(b) Interstory Drift Index
Fig. 67 Maximum Displacement Response
116
0.00 1.00 2.00 3.00 4.006 -+-,-.L.J...,~~.Lf-L.L.1...J....L.LLJw..+...L.L..LLJ-L..L.L.l-t--'-'-L..L.l-LL.L.1+ 6
~W 4-+----+--t-~~-__f~>---+_---_+_4
>W-l ..---.... BUCHAREST
............... 08 EGON PARK>-- ............... HO ISTERa::: G-<H>-&-<l JAM S ROADo .............. ME CO seT
\ ------ STA IC NON.t12-+---;---+~~:--__f-'<'----t-------+2
.......---.. BUCHAREST~ OBREGON PARKl>-<>-<>-&-e H0 LLISTER<>-<HJ-<H) JAMES ROAD............... MEXICO SCT------ STATIC NON.
0 00.00 1.00 2.00 3.00 4.00
CURVATURE DUCTILITY
(a) Girders
0.00 2.00 4.00 6.006 6
-lW 4,-H-t-i'<JY-----+------I--4>W-l
>cr:of-(J) 21-t---..II~~:'+----_I-----+2
°r-,--,rr-r-r-.,....,--,--r.........-r-rr-r-r-.,.....,-h-.........-r-r.--ro-,+o0.00 2.00 4.00 6.00
CURVATURE DUCTILITY
(b) Columns
Fig. 68 Curvature Ductility Demand
117
0.00 0.01 0.02 0.03 0.04-6 -P--.tJ<;~l-L.L4LJ....J-..J...L...Ll-LL\-LL...Ll-J-L.l..J...L+-LL.L-l.J..J-..L.U,-+ 6
............... BUCHAREST~ 08 EGaN PARK~ HO ISTER>- <>-<HHHJ JAM S ROAD
0::: ME CO SCTo ------ STA Ie NON.
tl2-l---+--~~---:-\-\-+------+-----+2
,,
-lW 4-l-_+-\-~¢,--_..).--+----+--------t-4
>W--.J
"-
'"
'--
a a0.00 0.01 0.02 0.03 0.04-
GIRDER ROTATION (RAD)
(a) Girders
0.00 0.01 0.02 0.03 0.04-6 6
-1w 41-i-~-t-m---+------+----+-4> "W "-.J '. ............... BUCHAREST
...~ ~ OB EGON PARK>- : ............... HO ISTERex ! ~ JAM S ROADo : ----- ME CO SeT~ : ------ STA IC NON.
(/) 2-r-T--'~1=::~-:"""+----t-----+2
a r...--r-rr-r-rr-rh,....,,-.,...-,rrr-r+-rrr-r-r-rr-r-r+-..---.-r-rTT""1ro+ 00.00 0.01 0.02 0.03 0.04-
COLUMN ROTATION (RAO)
(b) Columns
Fig. 69 Maximum Rotation Demand
118
• , I ,.. BUCHARESTA 6 6 6 A OBREGON PARK13 B B B!l HOLLISTERGee eo JAMES ROAD•• ••• MEXICO SCT------ CODE x 1.4
0.00 400.00 800.00 1200.006-+-'L-..J....,-...l.-l--l..-~--l..-,jt-+-~-.-L....L...L....l.---.l--L-j--...l--1---L-..L-.L~~....L.....f-6
\\\\,
\\\\\\\\\\\\
--l ..W 4 -t-------:.,\---t-~-----'llt_~~-----__+_ 4> \w \---.J ..
\,\>- \
0::: \o \tn 2 -t-----..L.\,-J,\------+-- >------4i~_t_2,,,
IIIII\
O-t-,..--,---,--,-,.-.-....-r-+---r-T-r-r-r-..---r-r-"--+-r-'r-r--.--.-.--,..--,.--+-O0.00 400.00 800.00 1200.00
BASE SHEAR (KIPS)
Fig. 70 Maximum Story Shear Envelopes
119
------ ---------- 500.00
-500.00
-------- ---------- 0.00
_________ -1 _
,----- ---- ..... - -_ ... - ... ---
-- BUCHAREST
-500.00 ----------;-------
-1 000.00 +r-rrr,.,.,..,....,~~,.,.,..._t_.~~,...,..j_,_,.~~rr+-1000.00-10 -5 0 5 10
DISPLACEMENT (IN.)
,....V)Q
S2'-./ 500.00
0:::«wIV)
0.00
>Ct::olV)
IIl()
-10 -5 101000.00 +-'-U...........~i-'-'-~ ..........-'-i-<~ ........~+'-' .........'-'-'-.w+ 1000.00
-500.00
10
-10 -5 0 101000.00 -t'-........~-'-'-!:-'-'-~ ..........-'-i-<:w....-........c.w+ww....-.............,:: 1000.00
-- BUCHARESr ,
,,,
------- - -"- -- - - - - ---, --- - ------ - -- - -- - - -- 500.00
---j-J---- '.00
, ,, ,
4 ; ~ ... ---- • _
, ,, ,, ,, ,, ,, ,, ,, ,, .-1 000.00 +r,~~rrl~~.,..,..,._rl_,~~,.,.,..j,..,~~,_,_j:.-1000.00
-10
,....V)Q:;::'-./ 500.00
Ct::«WIV)
0.00
>-Ct::0l-V)
-500.00:r:I-<.0
(b) Fifth Story
-10 -5 a 101000.00 ~W-'.-'-'-'''''''''':''''''W-'.~-+LLLW-'.~+,-w....-........u..t 1000.00
-500.00
,,
.- -- -- - -- .... - - .-- ----
----------,-------
-10 -5 101000.00 +-~~'-'-'-Lw...c.w.L.Lo-'-!-LLL'-'-'-.c.w+'_'-'-'-........._'_'+ 1000.00
-- 8'JCH~REST
,_______ h 500.00
,
---------.---------- 0.00
,....V)Q
S2'-./ 500.00
Ct::«wIV)
0.00
>-0:::0l-V)
-500.0000:::n
-1000.00 -J-..-,.,.,.~....,..,c,-,.,.,..,..,..,.-rh~~~j_,_,.~...,..,..._.+-1000.00-10 -5 6 5 10
DISPLACEMENT (IN,)
-500.00
0.00
500.00
10-5 0 5
DISPLACEMENT (IN.)
-- BUCHAREST
-------- -J-,-- -- ---- 1- q-------l- ---------, , ,, , ,: : :, , .: : :, ,
- ------- - -:- --. - -- -.- --- - - -.- - ~ - -- - - ... - - --0.00
,....V)Q
:;::'-./ 500.00
er::<L>..JIV)
>-e:::
: -~.,L-i--j;--+-, ,, ,, .
-1000.00 .:j...,..rrr,.,.,."""';~~.,..,..,...,-r,~~,.,.,.-j-,-.,~~rrf·- 1000.00-10
(c) Fourth Story (d) Third Story
-10 -5 0 101000.00 ~'-W..................,'::""'~.c.w-+w....-................~w....-.......u..t 1000.00
-1 000.00 +,...,...,.,.~~h-.-,.,.,.~..,.;_~.,..,..,.~_rr_,...,..,..,..,.,..,-t-- 1000.00-10 -5 0 5 10
DISPLACEMENT (IN.)
---. --- -- -:--- -- _.- ... :... - --- -----: ... ---, , ,
; ~ i
- BUCHAREST
101000.001000.00 -,10 ,-,5
- SIJ:HAR::ST, ,
: : J :500.00 ---------;-._--- ---j/----- --i i-------·_- 500.00
, , I II , J I
" : ; ;~ i ':
i-,~:::J[jJr:::::: '::,"-,~J .. ,i", .10-,000.00
-10 ~5 '0 5
O:SPLACEf.:EN-:- (IN.)
-500.00
0.00
500.00
,,
---------,.-------- --
,
,---- ----- ...- ...... -- .----
,
____ • - _._..l. ...... ...,
!fiI
,....V)
0-S2'-./ 500.00
c:::«wV)
0.00>-e:::0l-V)
-500.000ZN
(e) Second Story (f) First Story
Fig. 71 Story Shear vs. Interstory Displacement, Bucharest
120
---------- 0.00
------- ---------- 500.00
,,,,--------- ...- .. _.. _-- -- ----------,
----------;----- -- -,---------- ---------- -500.00
-to -51000.00 +-........~c.u..+_'_'~
-- HOlJis\er
,,------- .. --'-_ .. -- .. -_ ....
.---..V>Q..~"--' 500.00
a:::<{wIV> 0.00
>-a:::0r-V>
-500.00Ir-l{)
-------.-- 500.00
---------- 0.00
---------- -500.00
,,
-,-------_ .. -
,,,,
----- -----:- .. - - ......,
-500.00Ilto
-10 -5 101000.00 j-'-,-,-,..w..u...L+-,-,",-,-",-,-,..u..f-'-"~c.u..",""-,-!""""u...L""""'41000.00
-- Hollisier,,,,,
500.00 ---------:--- .
a::: ,LS 'I 'V> '0.00 ---------~------ _
>a:::orV>
-1000.00 +r~~rTT~~.,..,.,~j_rT..,..,.,~.,.,._j~rTT.,..,.,..,..+-1000.00-10 -5 0 5 10
DISPLACEMENT (IN.)
(a) Sixth Story
-1000.00-10 -5 a :5
DISPLACEMENT (IN.)
(b) Fifth Story
-1000.0010
-1 000.00 -I-r.,..,.,~,..,.,.~CTT',..,.,._.rrn_~~,..,._;_-~,..,.,._.+-1 000.00-10 -5 0 < 10
DISPLACEMENT (IN.)
-500.00
500.00
0.00
,------ ----;------- -~---_ .. ---- -i-"" --- .. ----
Iii, .
-10 -5 0 101000.00 -j-L...........u..........f-'-'-'-'-'-'-'.L'-,f-'-'-...........u.."-'+.........-'-'-'-'-'-'-j- I 000.00
-- Holtis\er
--__-:1-i-,
.---..V>Q..~
:;00.00500.00
a:::<{wIU1
0.000.00 >-a:::
0l-V>
-500.00-500.00 0
a:::n
-10 -5 0 101000.00 -r_""_~_.L'-HO~11~i3+-ie""r c.u.............u..t-':-'-'-'-'-'........'+""'-'-'..u..........+1000.00
,
----r-----)1--------!-------
---------J--------- ----- -----L------ ---,
----- --- -~----- -i -;---------- ,---- ------, , ,, . .
.---..V>Q..~"--' 500.00
a:::<wIV> 0.00
>-co::0I-U1
-500.00
2='¢
(d) Third Story
-500.00
------------------ 0.00
-------- - -:- -- -----
-10 -5 0 101000.00 +i-_'-_~_~~HO~II~;s.L'c~r~................,~ .................~~..u..'-W.-'-t 1000.00
, .__ .. _ • _ .. 4 _ ~ ~ ~ .. _
, ,, ,, ,. ., ., ,, ,, ,, ,
- - - - - - - - - ~I- - - - ~ - - - - - -
UlQ.. 500.00
::<:
a:::<{w 0.00IU1
WV><{ -500.00m
,,
--------i----------t 500.00
: t, ,: ~
I I t- - ----- -- ~- - - -- -- - - - -- --- - - - - -; - - - - - - - - - -~O.OO
t, , t: ; ,~-- ----- --- f--- -- --- --r -500.00, ,, ,, ,: : c: r
.. -------- -:- .. - - .. --_ ..
-10 -5 101000.00 -j-L.........-'-'-'-'-'+'-'-W.~ew..+_'_'..u..'-W.........,-'-'-~ ........'_'+ 1000.00
-- HOllis\er I,
. ,--- ---- -- _.- - .. - ---_ .. - .., .. ,, ,, ,, ,, ,, ,, ,
---.VJ.~
::<:500.00
<:
,10.00
:.::~
~')
-500.00~
Z:'<
-1 000.00 +r.,..,.,~rTT-j-r-~.,..,.,~t_o_T~~......._j~,..,.,.~._c+- 1000.00-10 -5 a 5 10
DISPLACEMENT (IN.)
-1 000.00 +r.,..,.,~,..,.,.;-,.,~~..,...,_;"'r'r~~-~~rTT_.+-1 000.00-10 -5 0 10
DISPLACEMENT (IIi.)
(e) Second Story (f) First Story
Fig. 72 Story Shear vs. Interstory Displacement, Hollister
0.0
01
0.0
02
0.0
03
0.0
02
50
00
.00
~,
,,
,,
,,
,,I'
,,,,
'BU~~ArK
',,,
,",~
25000.00
It
1I
1BU
CH
ARES
T~ (f
)
CLI
Io
uu
eo
I dA
Mt
;-,
K\
IA!
II
20
00
0.0
0_
20
00
0.0
0~
.Z - '-..
../1
5000
.00
3f
I~_
A~V\M~
-t1
50
00
.00
>- (.I) 0::::
~1
00
00
.001
I1\II
I
~10000.00
~~ t-
)
~-
f- =>I
II
\:l::
ICP
II
50
00
.00
CL5
00
0.0
0•
\;Jf'"",
1
Z
0.0
0t
,,1,p
-i/rr
1jl1
1I
II
II
II
II
II
II
II
II
II
II
II
0.0
00
.00
10
.00
20
.00
30
.00
TIM
E(S
EC
ON
DS
)
Fig
.73
Inp
ut
En
erg
yfr
om
Rec
ent
Ea
rth
qu
ak
es
122
0 5 10 15 206 6,,
I,I
=I
II
II
-l I
W4I 4
> II
W II
-l II
I
>- PI
0:::: II
0I
t/)2 2BUCHAREST
aae.., 1.3 x BUCHARESTHOlLl ER
.......... 1.3 x HOLLISTER
0 00 5 10 15 20
DISPLACEMENT (IN.)
(a) Lateral Displacement
0.00 0.01 0.02 0.03 0.04-6 6
- ... -0
-lW 4--l-----1--~+=---+-----t_---__+_4
>W-l
>- BUCHAREST0:::: e S<l.., 1.3 x BUCHAREST
HOLLI ERo .......... 1.3 x HOLLISTERt/)2 +----~""-::---<h~-+_---_+_---___r_2
o+'-...,....--r-rr-rri:""""'-rr-rr"rh...,..,.TT-rr-rr1.--r-rTTTrrr+- 00.00 0.01 0.02 0.03 0.04-
INTERSTORY DRI FT
(b) Interstory Drift Index
Fig. 74 Maximum Displacement Response, Increased PGA
123
0.00 1.00 2.00 3.00 4.006 -j-'...J.....l...L.L~~..J....L.LLL.LJ--L.I.-j-L.L.L.;w...J..-L.L~L.LJ--l...L..J....L..J....4- 6
~W 4+-----+-*-~~~--_+_---_+4
>W-.J
>0::::otn 2+-----t-~~-_+.&_:,----l------+ 2, , ,
" ,, ,'tl
GIRDERSo-+-r,,--rrTT"TT"h-rr......,rr-T-.+..-r-,--,--r-T"",....,..-,..+,--,-,-,--,~--,-,-+ 0
0.000 1.000 2.000 3.000 4.000
DUCTILITY
(a) Girders
0.00 2.00 4.00 6.006 r'-'-J........L~-c---.l...-.L-t---'---L-L.J.....L-.L-LJ-L+-'-..L...l.....L..;L..L..L-.L...L..!- 6
l.Hl-e-iHl BUCHAREST~ Be..,.., 1. x BUCHAREST~ H LUSTER.. .... "' .... 1. x HOLLISTER
~
W 4-r-------<tf~r------!-------+- 4>W-.J
>0::::otn 2--r--~~----l!Jf_:;_-----+------+- 2
-...
COLUMNS
2.000 4.000
DUCTILITY
(b) Columns
6.000
Fig. 75 Curvature Ductility Demand, Increased PGA
124
0.000 0.005 0.010 0.015 0.0206 +,-..l--L.L.L.I....l.-'«lod-'-L...l.-.l...l--L.J..1...4-JL1-J....l.-.l..L.L.I....l.-I-'-'-L.-.l...l--L.J..1...'--j-- 6
GIRDERS
, ,, ,'tJ
~ BUCHAREST.. B 'HHI 1.3 x BUCHAREST-...- HOLLI TER............ 1.3 x HOLLISTER
-.1W 4+------I------+---'O....-"'<----j~~--_t_4
>W-.1
>-0::::: /o /to 2-+------1--_i:--..;+----<l:-'-,-+--~--+-2
,,
o+'-"""""-rT"...,.....,....,-!--rr-.-r-rT"..-r-rh--rr-rr.,.-,-r-r-l--,-,...,.,....,-,-"r+a0.000 0.005 0.010 0.015 0.020
ROTATION
(a) Girders
0.0606
0.040
<>-<HHHl BUCHARESTBaa .. .., 1. X BUCHAREST~ H LUSTERa.>. ........ 1. X HOLLISTER
0.0200.0006
-IW 4+----'1~-_+_-------\------_+_4
>W---l
>cr.otn 2-r--~~'=:::"-+------r-------+-2-,
COLUMNSo-t-,-,-r---r---r-.,......,-...,..--,--!-.,......,-...,..--,---r-"""",--"'-"'-+-,.......,...--r---c-,--,-,--,-,-J- 0
0.000 0.020 0.040 0.060
ROTATION(b) Columns
Fig. 76 Maximum ,Rotation Demand, Increased PGA
125
,I.. ---------- 500.00,,,,I1I,,
--~---------- 0.00,,,IIII1I
----1----------- -500.00IIIII,III
II,1IIII
I__1 -- _,,
IIIIII
0.00
500.00
-500.00
-10 -5 0 5 101000. 00 ....f-1....Ll...LL..L..L-L.L+,.L.L..l...I-L.WLl...J--+,...L.l...L..L...L.L..L.L-'--T.I.-I-l.....L...J'-'-'--'-'-r 1000.0a
1.3 x: BUCHAREST:, ,,, ,I II ,I ,I I
---------~- --------~- -I ,I ,I II ,, ,,,,,
0::::<.(w:::c(f)
>0::::of-(f)
- 1000.aa -h....,...,.".....rrl--rr..,....-rrrnr+-r...-r-rrr-r-rrl....,....-r.,..-r,--,-rt- - 1000.00-10 -5 a 5 10
DISPLACEMENT (IN.)
(a) Bucharest
-50C.00
500.00
0.00
5o-5 10-t-JLLLLLLLLLf-,L-'-.L.L.L..L.L..L-L+-.L..L..L-L..L-L..L-L-Lf,...L..l.-l.-J.-l.-J.--LJ--L..f- 1000. 00
1.3 x: Hollister :I II II II ,I II I, I I
---------~----------~ - ---~----------I I II ,I II II II II ,I I, I, I
---------4--------- - -----,----------I II I, J, I
I II II II II II I----------1------- - -------r----------I II I, 1
I I1 ,
I II II II I
0.00
500.00
-500.00
-101000.00
0::::«w:::c(f)
w(f)<.(m
- 1a00. 00 --h--r-r..."..,..,.....rrrnrr-l.....,.-,-rf-,..,..-rrrr-rr-m"'.....,.-,-r-r--rr-+- - 1aOJ.00-10 -5 0 5 10
DISPLACE~1ENT (IN.)
(b) Hol~ister
Fig. 77 Base Shear vs. Interstory Disp., Increased PGA
126
127
REFERENCES
1. CSMIP, "Strong Motion Records From the WhittierCalifornia Earthquake of 1 October 1987," Report OSMS 87-OS, Office of Strong Motion Studies, Division of Minesand Geology, California Department of Conservation,1987.
2. USGS, "Strong-Motion Data From the October 1, 1987,Whittier Narrows Earthquake, Open-File Report 87-616,U.S. Geological Survey, Menlo Park, CA 94025.
3. International Conference of Building Officials, UniformBuilding Code, Whittier, CA 1973.
4. Mahin, S. A. and Lin, J., "Construction of InelasticResponse Spectra forSingle-Degree-of-Freedom Systems,"Report No. UCB/EERC-83/17, Earthquake EngineeringResearch Center, University of California, Berkeley, CA1983.
5. Wilson, B. L. and Habibullah, A., "SAP90, A Series ofComputer Programs for the Static and Dynamic FiniteElement Analysis of Structures," Computers. andStructures, Inc., Berkeley, CA 1989.
6. Habibullah, A., IIETABS, Three Dimensional Analysis ofBuilding Systems," Computers and Structures, Inc.,Berkeley, CA 1989.
7. Habibullah, A. and wilson, E. L., IISAPSTL, A SteelStress Check Postprocessor for SAP90," Computers andStructures, Inc., Berkeley, CA 1989.
8. Manual of Steel Construction, Allowable Stress Design,Ninth Edition, American Institute of Steel Construction,Chicago, IL 1989.
9. Sudhakar, Arun, II ULARC, Computer Program for SmallDisplacement Elasto Plastic Analysis of Plane Steel andReinforced Concrete Frames, "Report No. CE/299-561,Department of Civil Engineering, University ofCalifornia, Berkeley, CA 1972.
10. Krawinkler, H. and Popov, E. P., "Seismic Behavior ofMoment Connections and Joints, II Journal of theStructural Division, ASCE, Vol. 108, No. ST2, February,1982.
11. Linderman, R. R. and Anderson, J. C., " Steel Beam toBox Column connections," Proceedings, StructuralEngineers Association of California, San Diego, 1989.
Preceding page blank
128
12. Anderson, J. C. and Bertero, V. v., " Uncertainties inEstablishing Design Earthquakes," Journal of theStructural Division, ASCE, Vol. 113, No.8, August,1987.
13. Uang, C. M. and Bertero, V. V., "Implications ofRecorded Earthquake Ground Motions on Seismic Design ofBuilding Structures," Earthquake Engineering ResearchCenter, Report No. UCB/EERC-88/13, University ofCalifornia, Berkeley, November, 1988.
14. Bertero, V. V., "Strength and Deformation Capacities ofBuildings Made Under Extreme Environments," StructuralEngineering and Structural Mechanics, ed. K.S. pister,Prentice Hall, Inc., 1980.
129
EARTHQUAKE ENGINEERING RESEARCH CENTER REPORT SERIES
EERC reports are available from the National Information Service for Earthquake Engineering(NISEE) and from the National Technical InformationService(NTIS). Numbers in parentheses are Accession Numbers assigned by the National Technical Information Service; these are followed by a price code.Contact NTIS, 5285 Port Royal Road, Springfield Virginia, 22161 for more information. Reports without Accession Numbers were not available from NTISat the time of printing. For a current complete list of EERC reports (from EERC 67-1) and availablity information, please contact University of California,EERC, NISEE, 1301 South 46th Street; Richmond, California 94804.
UCB/EERC-81/01 "Control of Seismic Response of Piping Systems and Other Structures by Base Isolation," by Kelly, J.M., January 1981, (PB81 200735)A05.
UCB/EERC-81/02 "OPTNSR- An Interactive Software System for Optimal Design of Statically and Dynamically Loaded Structures with NonlinearResponse," by Bhatti, M.A., Ciampi, V. and Pister, KS., January 1981, (PB81 218 851)A09.
UCB/EERC-81/03 "Analysis of Local Variations in Free Field Seismic Ground Motions," by Chen, J.-c., Lysmer, J. and Seed, H.B., January 1981, (ADA099508)AI3.
UCB/EERC"81/04 "Inelastic Structural Modeling of Braced Offshore Platforms for Seismic Loading," by Zayas, V.A., Shing, P.-S.B., Mahin, S.A. andPopov, E.P., January 1981, INEL4, (PB82 138 777)A07.
UCB/EERC"81/05 "Dynamic Response of Light Equipment in Structures," by Der Kiureghian, A., Sackman, J.L. and Nour-Omid, B., April 1981, (PB81218 497)A04.
UCB/EERC-81/06 "Preliminary Experimental Investigation of a Broad Base Liquid Storage Tank," by Bouwkamp, J.G., Kollegger, J.P. and Stephen, R.M.,May 1981, (PB82 140 385)A03.
UCB/EERC-81/07 "The Seismic Resistant Design of Reinforced Concrete Coupled Structural Walls," by Aktan, A.E. and Bertero, V.V., June 1981, (PB82113358)AII.
UCB/EERC-81/08 "Unassigned: by Unassigned, 1981.
UCB/EERC-81/09 "Experimental Behavior of a Spatial Piping System with Steel Energy Absorbers Subjected to a Simulated Differential Seismic Input," byStiemer, S.F., Godden, W.G. and Kelly, J.M., July 1981, (PB82 201 898)A04.
UCB/EERC-811l0 "Evaluation of Seismic Design Provisions for Masonry in the United States: by Sveinsson, B.I., Mayes, R.L. and McNiven, H.D.,August 1981, (PB82 166 075)A08.
UCB/EERC-81/11 "Two-Dimensional Hybrid Modelling of Soil-Structure Interaction," by Tzong, T.-J., Gupta, S. and Penzien, J., August 1981, (PB82 142118)A04.
UCB/EERC-81/12 "Studies on Effects of Inlills in Seismic Resistant RIC Construction," by Brokken, S. and Bertero, V.V., October 1981, (PB82 166190)A09.
UCB/EERC-81/13 "Linear Models to Predict the Nonlinear Seismic Behavior of a One-Story Steel Frame," by Valdimarsson, H., Shah, A.H. andMcNiven, H.D., September 1981, (PB82 138 793)A07.
UCB/EERC-811l4 "TLUSH: A Computer Program for the Three-Dimensional Dynamic Analysis of Earth Dams," by Kagawa, T., Mejia, L.H., Seed, H.B.and Lysmer, J., September 1981, (PB82 139 940)A06.
UCB/EERC-81115 "Three Dimensional Dynamic Response Analysis of Earth Dams: by Mejia, L.H. and Seed, H.B., September 1981, (PB82 137 274)AI2.
UCB/EERC-81/16 "Experimental Study of Lead and Elastomeric Dampers for Base Isolation Systems," by Kelly, J.M. and Hodder, S.B., October 1981,(PB82 166 182)A05.
UCB/EERC-81/l7 "The Influence of Base Isolation on the Seismic Response of Light Secondary Equipment," by Kelly, J.M., April 1981, (PB82 255266)A04.
UCB/EERC-81/18 "Studies on Evaluation of Shaking Table Response Analysis Procedures," by Blondet, J. M., November 1981, (PB82 197 278)AIO.
UCB/EERC-8 III 9 "DELIGHT.STRUCT: A Computer-Aided Design Environment for Structural Engineering," by Balling, R.J., Pister, K.S. and Polak, E.,December 1981, (PB82 218 496)A07.
UCB/EERC-81/20 "Optimal Design of Seismic-Resistant Planar Steel Frames," by Balling, R.J., Ciampi, V. and Pister, K.S., December 1981, (PB82 220179)A07.
UCB/EERC-82/0 I "Dynamic Behavior of Ground for Seismic Analysis of Lifeline Systems," by Sato, T. and Der Kiureghian, A., January 1982, (PB82 218926)A05.
UCB/EERC·82/02 'Shaking Table Tests of a Tubular Steel Frame Model," by Ghanaat, Y. and Clough, R.W., January 1982, (PB82 220 161)A07.
UCB/EERC-82/03 "Behavior of a Piping System under Seismic Excitation: Experimental Investigations of a Spatial Piping System supported by Mechanical Shock Arrestors," by Schneider, S., Lee, H.-M. and Godden, W. G., May 1982, (PB83 172 544)A09.
UCB/EERC-82/04 "New Approaches for the Dynamic Analysis of Large Structural Systems," by Wilson, E.L., June 1982, (PB83 148 080)A05.
UCB/EERC-82/05 "Model Study of Effects of Damage on the Vibration Properties of Steel Offshore Platforms: by Shahrivar, F. and Bouwkamp, J.G.,June 1982, (PB83 148 742)A10.
UCB/EERC-82/06 "States of the Art and Pratice in the Optimum Seismic Design and Analytical Response Prediction of RIC Frame Wall Structures," byAktan, A.E. and Bertero, V.V., July 1982, (PB83 147 736)A05.
UCB/EERC-82/07 "Further Study of the Earthquake Response of a Broad Cylindrical Liquid-Storage Tank Model," by Manos, G.C. and Clough; R.W.,July 1982, (PB83 147 744)AII.
UCB/EERC-82/08 "An Evaluation of the Design and Analytical Seismic Response of a Seven Story Reinforced Concrete Frame," by Charney, F.A. andBertero, V.V., July 1982, (PB83 157 628)A09.
UCB/EERC-82/09 -Fluid-Structure Interactions: Added Mass Computations for Incompressible Fluid," by Kuo, J.S.-H., August 1982, (PB83 156 281)A07.
UCB/EERC-82/10 "Joint-Opening Nonlinear Mechanism: Interface Smeared Crack Model," by Kuo, J.S.-H., August 1982, (PB83 149 195)A05.
130
UCB/EERC-82/11 "Dynamic Response Analysis of Techi Dam: by Clough, R.W., Stephen, R.M. and Kuo, J.S.-H., August 1982, (PB83 147 496)A06.
UCB/EERC-82/12 "Prediction of the Seismic Response of RIC Frame-Coupled Wall Structures: by Aktan, A.E., Bertero, V.V. and Piazzo, M., August1982, (PB83 149 203)A09.
UCB/EERC-82/13 -Preliminary Report on the Smart I Strong Motion Array in Taiwan: by Bolt, B.A., Loh, e.H., Penzien, J. and Tsai, Y.B., August1982, (PB83 159 400)AIO.
UCB/EERC-82/14 "Seismic Behavior of an Eccentrically X-Braced Steel Structure,- by Yang, M.S., September 1982, (PB83 260 778)AI2.
UCB/EERC-82/15 -The Performance of Stairways in Earthquakes: by Roha, e., Axley, J.W. and Bertero, V.V., September 1982, (PB83 157 693)A07.
UCB/EERC-82/16 "The Behavior of Submerged Multiple Bodies in Earthquakes: by Liao, W.-G., September 1982, (PB83 158 709)A07.
UCB/EERC-82/17 -Effects.of Concrete Types and Loading Conditions on Local Bond-Slip Relationships," by Cowell, A.D., Popov, E.P. and Bertero, V.V.,September 1982, (PB83 153 577)A04.
UCB/EERC-82/18 -Mechanical Behavior of Shear Wall Vertical Boundary Members: An Experimental Investigation," by Wagner, M.T. and Bertero, V.V.,October 1982, (PB83 159 764)A05.
UCB/EERC-82/19 -Experimental Studies of Multi-support Seismic Loading on Piping Systems: by Kelly, J.M. and Cowell, A.D., November 1982, (PB90262 684)A07.
UCB/EERC-82/20 "Generalized Plastic Hinge Concepts for 3D Beam-Column Elements: by Chen, P. F.-S. and Powell, G.H., November 1982, (PB83 247981)A13.
UCB/EERC-82/21 "ANSR-II: General Computer Program for Nonlinear Structural Analysis: by Oughourlian, e.V. and Powell, G.H., November 1982,(PB83 251 330)AI2.
UCB/EERC-82/22 "Solution Strategies for Statically Loaded Nonlinear Structures: by Simons, J.W. and Powell, G.H., November 1982, (PB83 197970)A06.
UCB/EERC-82/23
UCB/EERC-82/24
UCB/EERC-82/25
UCB/EERC-82/26
UCB/EERC-82/27
UCB/EERC-83/0 I
UCB/EERC-83102
UCB/EERC-83/03
UCB/EERC-83/04
UCB/EERC-83/05
UCB/EERC-83106
UCB/EERC-83107
UCB/EERC·83/08
UCB/EERC-83/09
UCB/EERC-83/10
UCB/EERC-83/11
UCB/EERC-83/12
UCB/EERC-83/13
UCB/EERC-83/14
UCB/EERC-83/15
UCB/EERC·83/16
UCB/EERC-83/17
UCB/EERC-83/18
UCB/EERC-831l9
"Analytical Model of Deformed Bar Anchorages under Generalized Excitations: by Ciampi, V., Eligehausen, R., Bertero, V.V. andPopov, E.P., November 1982, (PB83 169 532)A06.
"A Mathematical Model for the Response of Masonry Walls to Dynamic Excitations," by Sucuoglu, H., Mengi, Y. and McNiven, H.D.,November 1982, (PB83 169 011)A07.
"Earthquake Response Considerations of Broad Liquid Storage Tanks: by Cambra, F.J., November 1982, (PB83 251 215)A09.
·Computational Models for Cyclic Plasticity, Rate Dependence and Creep," by Mosaddad, B. and Powell, G.H., November 1982, (PB83245 829)A08.
"Inelastic Analysis of Piping and Tubular Structures: by Mahasuverachai, M. and Powell, G.H., November 1982, (PB83 249 987)A07.
"The Economic Feasibility of Seismic Rehabilitation of Buildings by Base Isolation: by Kelly, J.M., January 1983, (PB83 197 988)A05.
·Seismic Moment Connections for Moment-Resisting Steel Frames.," by Popov, E.P., January 1983, (PB83 195 412)A04.
"Design of Links and Beam-to"Column Connections for Eccentrically Braced Steel Frames: by Popov, E.P. and Malley, J.O., January1983, (PB83 194 811)A04.
"Numerical Techniques for the Evaluation of Soil-Structure Interaction Effects in the Time Domain," by Bayo, E. and Wilson, E.L.,February 1983, (PB83 245 605)A09.
"A Transducer for Measuring the Internal Forces in the Columns of a Frame-Wall Reinforced Concrete Structure: by Sause, R. andBertero, V. V., May 1983, (PB84 119 494)A06.
"Dynamic Interactions Between Floating Ice and Offshore Structures: by Croteau, P., May 1983, (PB84 119 486)AI6.
"Dynamic Analysis of Multiply Tuned and Arbitrarily Supported Secondary Systems," by Igusa, T. and Der Kiureghian, A., July 1983,(PB84 118 272)AI1.
"A Laboratory Study of Submerged Multi-body Systems in Earthquakes," by Ansari, G.R., June 1983, (PB83 261 842)AI7.
"Effects of Transient Foundation Uplift on Earthquake Response of Structures: by Yim, e.-S. and Chopra, A.K., June 1983, (PB83 261396)A07.
"Optimal Design of Friction-Braced Frames under Seismic Loading," by Austin, M.A. and Pister, K.S., June 1983, (PB84 119 288)A06.
"Shaking Table Study of Single-Story Masonry Houses: Dynamic Performance under Three Component Seismic Input and Recommendations," by Manos, G.e., Clough, R.W. and Mayes, R.L., July 1983, (UCB/EERC-83/11)A08.
"Experimental Error Propagation in Pseudodynamic Testing: by Shiing, P.B. and Mahin, SA, June 1983, (PB84 119 270)A09.
"Experimental and Analytical Predictions of the Mechanical Characteristics of a liS-scale Model of a 7-story RIC Frame-Wall BuildingStructure: by Aktan, A.E., Bertero, V.V., Chowdhury, A.A. and Nagashima, T., June 1983, (PB84 119 213)A07.
"Shaking Table Tests of Large-Panel Precast Concrete Building System Assemblages," by Oliva, M.G. and Clough, R.W., June 1983,(PB86 110 21O/AS)AI1.
"Seismic Behavior of Active Beam Links in Eccentrically Braced Frames," by Hjelmstad, K.D. and Popov, E.P., July 1983, (PB84 119676)A09.
"System Identification of Structures with Joint Rotation: by Dimsdale, J.S., July 1983, (PB84 192 210)A06.
"Construction of Inelastic Response Spectra for Single-Degree-of-Freedom Systems," by Mahin, S. and Lin, J., June 1983, (PB84 208834)A05.
"Interactive Computer Analysis Methods for Predicting the Inelastic Cyclic Behaviour of Structural Sections: by Kaba, S. and Mahin,S., July 1983, (PB84 192 012)A06.
"Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints," by Filippou, F.e., Popov, E.P. and Bertero, V.V.,August 1983, (PB84 192 020)AIO. .
131
UCB/EERC-83/20 "Correlation of Analytical and Experimental Responses of Large-Panel Precast Building Systems," by Oliva, M.G., Clough, R.W., Velkov, M. and Gavrilovic, P., May 1988, (PB90 262 692)A06.
UCB/EERC-83/21 "Mechanical Characteristics of Materials Used in a 115 Scale Model ofa 7-Story Reinforced Concrete Test Structure," by Bertero, V.V.,Aktan, A.E., Harris, H.G. and Chowdhury, A.A., October 1983, (PB84 193 697)A05.
UCB/EERC-83/22 -Hybrid Modelling of Soil-Structure Interaction in Layered Media," by Tzong, T.-J. and Penzien, J., October 1983, (PB84 192 178)A08.
UCB/EERC-83/23 -Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations," by Eligehausen, R., Popov, E.P. and Bertero,V.V., October 1983, (PB84 192 848)A09.
UCB/EERC-83124 "Design Considerations for Shear Links in Eccentrically Braced Frames," by Malley, J.O. and Popov, E.P., November 1983, (PB84 192I86)A07.
UCB/EERC-84/01 -Pseudodynamic Test Method for Seismic Performance Evaluation: Theory and Implementation," by Shing, P.-S.B. and Mahin, S.A.,January 1984, (PB84 190 644)A08.
UCB/EERC-84/02 "Dynamic Response Behavior of Kiang Hong Dian Darn, - by Clough, R.W., Chang, K.-T., Chen, H.-Q. and Stephen, R.M., April 1984,(PB84 209 402)A08.
UCB/EERC-84/03 "Refined Modelling of Reinforced Concrete Columns for Seismic Analysis," by Kaba, SA and Mahin, SA, April 1984, (PB84 234384)A06.
UCB/EERC-84/04 "A New Floor Response Spectrum Method for Seismic Analysis of Multiply Supported Secondary Systems,- by Asfura, A. and DerKiureghian, A., June 1984, (PB84 239 417)A06.
UCB/EERC-84/05 -Earthquake Simulation Tests and Associated Studies of a 115th-scale Model of a 7-Story RIC Frame-Wall Test Structure," by Bertero,V.V., Aktan, A.E., Charney, FA and Sause, R., June 1984, (PB84 239 409)A09.
UCB/EERC-84/06 "Unassigned," by Unassigned, 1984.
UCB/EERC-84/07 -Behavior of Interior and Exterior Flat-Plate Connections subjected to Inelastic Load Reversals," by Zee, H.L. and Moehle, J.P., August1984, (PB86 117 629/AS)A07.
UCB/EERC-84/08 "Experimental Study of the Seismic Behavior of a Two-Story Flat-Plate Structure, - by Moehle, J.P. and Diebold, J.W., August 1984,(PB86 122 553/AS)AI2.
UCB/EERC-84/09 -Phenomenological Modeling of Steel Braces under Cyclic Loading," by Ikeda, K., Mahin, SA and Dermitzakis, S.N., May 1984, (PB86132 198/AS)A08.
UCB/EERC-84/1O -Earthquake Analysis and Response of Concrete Gravity Dams," by Fenves, G. and Chopra, A.K., August 1984, (PB85 193902/AS)A II.
UCB/EERC-84/11 -EAGD-84: A Computer Program for Earthquake Analysis of Concrete Gravity Dams,- by Fenves, G. and Chopra, A.K., August 1984,(PB85 193 613/AS)A05.
UCB/EERC-84/12 -A Refined Physical Theory Model for Predicting the Seismic Behavior of Braced Steel Frames," by Ikeda, K. and Mahin, S.A., July1984, (PB85 191 450/AS)A09.
UCB/EERC-84/13 -Earthquake Engineering Research at Berkeley - 1984," by EERC, August 1984, (PB85 197 341/AS)AIO.
UCB/EERC-84/14 -Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils," by Seed, H.B., Wong, R.T., Idriss, I.M. and Tokimatsu, K.,September 1984, (PB85 191 468/AS)A04.
UCB/EERC-84/15 "The Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations," by Seed, H.B., Tokimatsu, K., Harder, L.P. and Chung,R.M., October 1984, (PB85 191 732/AS)A04.
UCB/EERC-84/16 -Simplified Procedures for the Evaluation of Settlements in Sands Due to Earthquake Shaking," by Tokimatsu, K. and Seed, H.B.,October 1984, (PB85 197 887/AS)A03.
UCB/EERC-84/17 "Evaluation of Energy Absorption Characteristics of Highway Bridges Under Seismic Conditions - Volume I (PB90 262 627)A16 andVolume II (Appendices) (PB90 262 635)AI3," by Imbsen, R.A. and Penzien, J., September 1986.
UCB/EERC-84/18 "Structure-Foundation Interactions under Dynamic Loads, - by Liu, W.D. and Penzien, J., November 1984, (PB87 124 889/AS)All.
UCB/EERC-84/l9 "Seismic Modelling of Deep Foundations," by Chen, e.-H. and Penzien, J., November 1984, (PB87 124 798/AS)A07.
UCB/EERC-84/20 "Dynamic Response Behavior of Quan Shui Dam," by Clough, R.W., Chang, K.-T., Chen, H.-Q., Stephen, R.M., Ghanaat, Y. and Qi,J.-H., November 1984, (PB86 115177/AS)A07.
UCB/EERC-85/0 1 "Simplified Methods of Analysis for Earthquake Resistant Design of Buildings," by Cruz, E.F. and Chopra, A.K., February 1985, (PB86I 12299/AS)AI 2.
UCB/EERC-85/02 "Estimation of Seismic Wave Coherency and Rupture Velocity using the SMART I Strong-Motion Array Recordings," by Abrahamson,N.A., March 1985, (PB86 214 343)A07.
UCB/EERC-85/03 "Dynamic Properties of a Thirty Story Condominium Tower Building," by Stephen, R.M., Wilson, E.L. and Stander, N., April 1985,(PB86 118965/AS)A06.
UCB/EERC-85/04 "Development of Substructuring Techniques for On-Line Computer Controlled Seismic Performance Testing," by Dermitzakis, S. andMahin, S., February 1985, (PB86 1329411AS)A08.
UCB/EERC-85/05 "A Simple Model for Reinforcing Bar Anchorages under Cyclic Excitations," by Filippou, F.e., March 1985, (PB86 112 919/AS)A05.
UCB/EERC-85/06 "Racking Behavior of Wood-framed Gypsum Panels under Dynamic Load," by Oliva, M.G., June 1985, (PB90 262 643)A04.
UCB/EERC-85/07 "Earthquake Analysis and Response of Concrete Arch Dams," by Fok, K.-L. and Chopra, A.K., June 1985, (PB86 139672/AS)AIO.
UCB/EERC-85/08 "Effect of Inelastic Behavior on the Analysis and Design of Earthquake Resistant Structures," by Lin, J.P. and Mahin, SA., June 1985,(PB86 I35340/AS)A08.
UCB/EERC-85/09 "Earthquake Simulator Testing of a Base-Isolated Bridge Deck," by Kelly, J.M., Buckle, I.G. and Tsai, H.-C., January 1986, (PB87 124152/AS)A06.
132
UCB/EERC-85/10 "Simplified Analysis for Earthquake Resistant Design of Concrete Gravity Dams," by Fenves, G. and Chopra, AX., June 1986, (PB87124 160/AS)A08.
UCB/EERC-85/11 -Dynamic Interaction Effects in Arch Dams: by Clough, R.W., Chang, K.-T., Chen, H.-Q. and Ghanaat, Y., October 1985, (PB86I35027/AS)A05.
UCB/EERC-85/12 -Dynamic Response of Long Valley Dam in the Mammoth Lake Earthquake Series of May 25-27, 1980: by Lai, S. and Seed, H.B.,November 1985, (PB86 142304/AS)A05.
UCB/EERC-85/13 "A Methodology for Computer-Aided Design of Earthquake-Resistant Steel Structures: by Austin, M.A., Pister, K.S. and Mahin, S.A.,December 1985, (PB86 I59480/AS)AIO .
UCB/EERC-85/14 -Response of Tension-Leg Platforms to Vertical Seismic Excitations," by Liou, G.-S., Penzien, J. and Yeung, R.W., December 1985,(PB87 124 87I1AS)A08.
UCB/EERC-85/l5 "Cyclic Loading Tests of Masonry Single Piers: Volume 4 - Additional Tests with Height to Width Ratio of I," by Sveinsson, B.,McNiven, H.D. and Sucuoglu, H., December 1985.
UCB/EERC-87/03
UCB/EERC-86/l1
UCB/EERC-86/01
UCB/EERC-86/07
UCB/EERC-86/02
UCB/EERC-86/03
UCB/EERC-85/16
UCB/EERC-86/04
UCB/EERC-86/08
UCB/EERC-86/09
UCB/EERC-86/05
UCB/EERC-86/06
UCB/EERC-86/1 0
UCB/EERC-86/12
UCB/EERC-87/01
UCB/EERC-87/02
-An Experimental Program for Studying the Dynamic Response of a Steel Frame with a Variety of Infill Partitions," by Yanev, B. andMcNiven, H.D., December 1985, (PB90 262 676)A05.
"A Study of Seismically Resistant Eccentrically Braced Steel Frame Systems: by Kasai, K. and Popov, E.P., January 1986, (PB87 124I78/AS)AI4.
-Design Problems in Soil Liquefaction," by Seed, H.B., February 1986, (PB87 124 186/AS)A03.
-Implications of Recent Earthquakes and Research on Earthquake-Resistant Design and Construction of Buildings," by Bertero, V.V.,March 1986, (PB87 124 194/AS)A05.
-The Use of Load Dependent Vectors for Dynamic and Earthquake Analyses,' by Leger, P., Wilson, E.L. and Clough, R.W., March1986, (PB87 124 202/AS)AI2.
-Two Beam-To-Column Web Connections," by Tsai, K.-c. and Popov, E.P., April 1986, (PB87 124 30IlAS)A04.
"Determination of Penetration Resistance for Coarse-Grained Soils using the Becker Hammer Drill, - by Harder, L.F. and Seed, H.B.,May 1986, (PB87 124 210/AS)A07.
-A Mathematical Model for Predicting the Nonlinear Response of Unreinforced Masonry Walls to In-Plane Earthquake Excitations," byMengi, Y. and McNiven, RD., May 1986, (PB87 124 780/AS)A06.
"The 19 September 1985 Mexico Earthquake: Building Behavior," by Bertero, V.V., July 1986.
-EACD-3D: A Computer Program for Three-Dimensional Earthquake Analysis of Concrete Dams," by Fok, K.-L., Hall, J.F. andChopra, AX., July 1986, (PB87 124 228/AS)A08.
-Earthquake Simulation Tests and Associated Studies of a 0.3-Scale Model of a Six-Story Concentrically Braced Steel Structure,- byUang, C.-M. and Bertero, V,V., December 1986, (PB87 163 564/AS)AI7.
-Mechanical Characteristics of Base Isolation Bearings for a Bridge Deck Model Test: by Kelly, J.M., Buckle, I.G. and Koh, c.-G.,November 1987, (PB90 262 668)A04.
-Effects of Axial Load on Elastomeric Isolation Bearings," by Koh, c.-G. and Kelly, J.M., November 1987.
-The FPS Earthquake Resisting System: Experimental Report," by Zayas, V.A., Low, S.S. and Mahin, S.A., June 1987.
-Earthquake Simulator Tests and Associated Studies of a 0.3-Scale Model of a Six-Story Eccentrically Braced Steel Structure," by Whit-taker, A., Uang, C.-M. and Bertero, V.V., July 1987.
-A Displacement Control and Uplift Restraint Device for Base-Isolated Structures," by Kelly, J.M., Griffith, M.e. and Aiken, 1.D., April1987.
UCB/EERC-87/04 -Earthquake Simulator Testing of a Combined Sliding Bearing and Rubber Bearing Isolation System," by Kelly, J.M. and Chalhoub,M.S., 1987.
UCB/EERC-87/05 -Three-Dimensional Inelastic Analysis of Reinforced Concrete Frame-Wall Structures: by Moazzami, S. and Bertero, V.V., May 1987.
UCB/EERC-87/06 -Experiments on Eccentrically Braced Frames with Composite Floors," by Ricles, J. and Popov, E., June 1987.
UCB/EERC-87/07 "Dynamic Analysis of Seismically Resistant Eccentrically Braced Frames,- by Ricles, J. and Popov, E., June 1987.
UCB/EERC-87/08 "Undrained Cyclic Triaxial Testing of Gravels-The Effect of Membrane Compliance," by Evans, M.D. and Seed, H.B., July 1987.
UCB/EERC-87/09 -Hybrid Solution Tecl]niques for Generalized Pseudo-Dynamic Testing," by Thewalt, C. and Mahin, S.A., July 1987.
UCB/EERC-87/10 "Ultimate Behavior of Butt Welded Splices in Heavy Rolled Steel Sections," by Bruneau, M., Mahin, S.A. and Popov, E.P., September1987.
UCB/EERC-87/11 -Residual Strength of Sand from Dam Failures in the Chilean Earthquake of March 3,1985: by De Alba, P., Seed, RB., Retamal, E.and Seed, R.B., September 1987.
UCB/EERC-87/12 -Inelastic Seismic Response of Structures with Mass or Stiffness Eccentricities in Plan," by Bruneau, M. and Mahin, S.A., September1987, (PB90 262 650)AI4.
UCB/EERC-87/13 -CSTRUCT: An Interactive Computer Environment for the Design and Analysis of Earthquake Resistant Steel Structures," by Austin,M.A., Mahin, S.A. and Pister, K.S., September 1987.
UCB/EERC-87/14 -Experimental Study of Reinforced Concrete Columns Subjected to Multi-Axial Loading," by Low, S.S. and Moehle, J.P., September1987.
UCB/EERC-87/15 "Relationships between Soil Conditions and Earthquake Ground Motions in Mexico City in the Earthquake of Sept. 19,1985," by Seed,RB., Romo, M.P., Sun, J., Jaime, A. and Lysmer, J., October 1987.
UCB/EERC-87/16 "Experimental Study of Seismic Response ofR. C. Setback Buildings," by Shahrooz, B.M. and Moehle, J.P., October 1987.
133
UCBIEERC-88/05
UCB/EERC-88/06
UCB/EERC-88/07
UCBIEERC-88103
UCB/EERC-88/04
UCB/EERC-871l7
UCB/EERC-87118
UCB/EERC-87/19
"The Effect of Slabs on the Flexural Behavior of Beams," by Pantazopoulou, S.J. and Moehle, J.P., October 1987, (PB90 262 700)A07.
"Design Procedure for R"FBI Bearings," by Mostaghel, N. and Kelly, J.M., November 1987, (PB90 262 718)A04.
"Analytical Models for Predicting the Lateral Response of R C Shear Walls: Evaluation of their Reliability," by Vulcano, A. and Bertero, V.V., November 1987.
"Earthquake Response of Torsionally-Coupled Buildings: by Hejal, R. and Chopra, A.K., December 1987.
"Dynamic Reservoir Interaction with Monticello Dam," by Clough, R.W., Ghanaat, Y. and Qiu, X-F., December 1987.
-Strength Evaluation of Coarse-Grained Soils," by Siddiqi, F.H., Seed, R.B., Chan, e.K., Seed, H.B. and Pyke, R.M., December 1987.
"Seismic Behavior of Concentrically Braced Steel Frames," by Khatib, I., Mahin, SA. and Pister, K.S., January 1988.
"Experimental Evaluation of Seismic Isolation of Medium-Rise Structures Subject to Uplift," by Griffith, M.e., Kelly, J.M., Coveney,VA and Koh, C.G., January 1988.
"Cyclic Behavior of Steel Double Angle Connections," by Astaneh-Asl, A. and Nader, M.N., January 1988.
"Re"evaluation of the Slide in the Lower San Fernando Dam in the Earthquake of Feb. 9, 1971," by Seed, H.B., Seed, R.B., Harder,L.F. and Jong, H.-L., April 1988.
-Experimental Evaluation of Seismic Isolation of a Nine·Story Braced Steel Frame Subject to Uplift," by Griffith, M.e., Kelly, J.M. andAiken, I.D., May 1988.
"DRAIN"2DX User Guide., - by Allahabadi, R. and Powell, G.H., March 1988.
-Theoretical and Experimental Studies of Cylindrical Water Tanks in Base-Isolated Structures," by Chalhoub, M.S. and Kelly, J.M.,April 1988.
UCB/EERC-88/08 "Analysis of Near-Source Waves: Separation of Wave Types using Strong Motion Array Recordings: by Darragh, R.B., June 1988.
UCB/EERC-88/09 "Alternatives to Standard Mode Superposition for Analysis of Non-Classically Damped Systems: by Kusainov, A.A. and Clough, R.W.,June 1988.
UCB/EERC-88/l 0 "The Landslide at the Port of Nice on October 16, 1979," by Seed, H.B., Seed, R.B., Schlosser, F., Blondeau, F. and Juran, I., June1988.
UCB/EERC-87/20
UCB/EERC-87/21
UCB/EERC-87/22
UCB/EERC-88/0 I
UCB/EERC-88/02
UCB/EERC-89/13
UCB/EERC-89/09
UCB/EERC-89/03
UCB/EERC-89/IO
"Liquefaction Potential of Sand Deposits Under Low Levels of Excitation," by Carter, D.P. and Seed, H.B., August 1988.
"Nonlinear Analysis of Reinforced Concrete Frames Under Cyclic Load Reversals: by Filippou, F.C. and Issa, A., September 1988.
"Implications of Recorded Earthquake Ground Motions on Seismic Design of Building Structures," by Uang, CoM. and Bertero, V. V.,November 1988.
,An Experimental Study of the Behavior of Dual Steel Systems," by Whittaker, A.S. , Uang, CoM. and Bertero, V.V., September 1988.
"Dynamic Moduli and Damping Ratios for Cohesive Soils," by Sun, J.r., Golesorkhi, R. and Seed, RB., August 1988.
"Reinforced Concrete Flat Plates Under Lateral Load: An Experimental Study Including Biaxial Effects: by Pan, A. and Moehle, J.,October 1988.
"Earthquake Engineering Research at Berkeley" 1988: by EERC, November 1988.
"Use of Energy as a Design Criterion in Earthquake-Resistant Design,- by Uang, CoM. and Bertero, V.V., November 1988.
'Steel Beam-Column Joints in Seismic Moment Resisting Frames," by Tsai, K.-C. and Popov, E.P., November 1988.
'Base Isolation in Japan, 1988: by Kelly, J.M., December 1988.
"Behavior of Long Links in Eccentrically Braced Frames," by Engelhardt, M.D. and Popov, E.P., January 1989.
"Earthquake Simulator Testing of Steel Plate Added Damping and Stiffness Elements," by Whittaker, A., Bertero, V. V., .Alonso, J. andThompson, e., January 1989.
"Implications of Site Effects in the Mexico City Earthquake of Sept. 19, 1985 for Earthquake·Resistant Design Criteria in the San Francisco Bay Area of California," by Seed, H.B. and Sun, J.1., March 1989.
"Earthquake Analysis and Response of Intake,Outlet Towers," by Goyal, A. and Chopra, A.K., July 1989.
"The 1985 Chile Earthquake: An Evaluation of Structural Requirements for Bearing Wall Buildings: by Wallace, J.W. and Moehle,J.P., July 1989.
"Effects of Spatial Variation of Ground Motions on Large Multiply-Supported Structures: by Hao, H., July 1989.
"EADAP - Enhanced Arch Dam Analysis Program: Users's Manual: by Ghanaat, Y. and Clough, R.W., August 1989.
"Seismic Performance of Steel Moment Frames Plastically Designed by Least Squares Stress Fields," by Ohi, K. and Mahin, S.A.,August 1989.
"Feasibility and Performance Studies on Improving the Earthquake Resistance of New and Existing Buildings Using the Friction Pendulum System: by Zayas, V., Low, S., Mahin, SA and Bozzo, 1.., July 1989.
'Measurement and Elimination of Membrane Compliance Effects in Undrained Triaxial Testing: by Nicholson, P.G., Seed, R.B. andAnwar, H., September 1989.
·Static Tilt Behavior of Unanchored Cylindrical Tanks: by Lau, D.T. and ClOUgh, R.W., September 1989.
"ADAP-88: A Computer Program for Nonlinear Earthquake Analysis of Concrete Arch Dams," by Fenves, G.L., Mojtahedi, S. and Reimer, R.B., September 1989.
'Mechanics of Low Shape Factor Elastomeric Seismic Isolation Bearings," by Aiken, I.D., Kelly, J.M. and Tajirian, F.P., November1989.
UCB/EERC-89114 'Preliminary Report on the Seismological and Engineering Aspects of the October 17, 1989 Santa Cruz (Lorna Prieta) Earthquake: byEERC, October 1989.
UCB/EERC-89/Il
UCB/EERC-891l2
UCB/EERC-89/06
UCB/EERC-89/07
UCB/EERC-89/08
UCB/EERC-88111
UCB/EERC-88112
UCB/EERC-88113
UCB/EERC-88114
UCB/EERC-88115
UCB/EERC-88116
UCB/EERC-88/17
UCB/EERC-88118
UCB/EERC-88119
UCB/EERC-88120
UCB/EERC-89/01
UCB/EERC-89/02
UCB/EERC-89/04
UCB/EERC-89/05
UCB/EERC-89/15
UCB/EERC-89/16
UCB/EERC-90/0 I
UCBIEERC-90/02
UCB/EERC-90/03
UCB/EERC-90/04
UCB/EERC-90/05
UCBIEERC-90106
UCB/EERC-90/07
UCBIEERC-90108
UCBIEERC-90109
UCBIEERC-901l0
UCB/EERC-90/11
UCB/EERC-901l2
UCB/EERC-901l3
UCB/EERC-90114
UCBIEERC-901l5
UCBIEERC-901l6
UCB/EERC-901l7
UCBIEERC-901l8
UCB/EERC-901l9
UCBIEERC-90120
UCBIEERC-90/21
UCBIEERC-91/01
UCB/EERC-91/02
UCB/EERC-91/03
UCB/EERC-91104
UCB/EERC-91105
UCBIEERC-91106
UCBIEERC-91107
UCB/EERC-91108
UCBIEERC-91/09
UCB/EERC-91/IO
UCBIEERC-911l1
134
"Experimental Studies of a Single Story Steel Structure Tested with Fixed, Semi-Rigid and F1exible Connections: by Nader, M,N, andAstaneh-AsI, A" August 1989, (PB91 229 211IAS)AIO.
"Collapse of the Cypress Street Viaduct as a Result of the Lorna Prieta Earthquake," by Nims, D.K., Miranda, E., Aiken, J.D., Whittaker, A.S. and Bertero, V.V., November 1989, (PB91 217 935/AS)A05.
"Mechanics of High-Shape Factor Elastomeric Seismic Isolation Bearings: by Kelly, J.M., Aiken, I.D. and Tajirian, F.F., March 1990.
"Javid's Paradox: The Influence of Preform on the Modes of Vibrating Beams: by Kelly, J.M., Sackman, J.L and Javid, A., May 1990,(PB91 217 943IAS)A03.
"Earthquake Simulator Testing and Analytical Studies of Two Energy-Absorbing Systems for Multistory Structures: by Aiken, I.D, andKelly, J.M., October 1990.
"Damage to the San Francisco-Oakland Bay Bridge During the October 17, 1989 Earthquake: by Astaneh, A., June 1990.
"Preliminary Report on the Principal Geotechnical Aspects of the October 17, 1989 Lorna Prieta Earthquake: by Seed, R.B., Dickenson, S.E" Riemer, M,F., Bray, J.D., Sitar, N., Mitchell, J.K., Idriss, J.M., Kayen, R.E., Kropp, A" Harder, L.F., Jr. and Power, M,S.,April 1990,
"Models of Critical Regions in Reinforced Concrete Frames Under Seismic Excitations;' by Zulfiqar, N. and Filippou, E, May 1990.
"A Unified Earthquake-Resistant Design Method for Steel Frames Using ARMA Models," by Takewaki, I., Conte, J.P., Mahin, S.A. andPister, K.S., June 1990.
-Soil Conditions and Earthquake Hazard Mitigation in the Marina District of San Francisco: by Mitchell, J.K., Masood, T., Kayen,R.E. and Seed, R.B., May 1990.
"Influence of the Earthquake Ground Motion Process and Structural Properties on Response Characteristics of Simple Structures: byConte, J.P., Pister, K.S. and Mahin, S.A., July 1990.
"Experimental Testing of the Resilient-Friction Base Isolation System: by Clark, P.W. and Kelly, J.M., July 1990.
"Seismic Hazard Analysis: Improved Models, Uncertainties and Sensitivities: by Araya, R. and Der Kiureghian, A., March 1988.
"Effects of Torsion on the Linear and Nonlinear Seismic Response of Structures: by Sedarat, H. and Bertero, V.V., September 1989.
"The Effects of Tectonic Movements on Stresses and Deformations in Earth Embankments: by Bray, J. D., Seed, R. B. and Seed, H. B.,September 1989.
"Inelastic Seismic Response of One-Story, Asymmetric-Plan Systems: by Goel, R.K. and Chopra, A.K., October 1990.
"Dynamic Crack Propagation: A Model for Near-Field Ground Motion.," by Seyyedian, H. and Kelly, J.M., 1990.
"Sensitivity of Long-Period Response Spectra to System Initial Conditions: by Blasquez, R., Ventura, e. and Kelly, J.M., 1990.
"Behavior of Peak Values and Spectral Ordinates of Near-Source Strong Ground-Motion over a Dense Array: by Niazi, M., June 1990.
-Material Characterization of Elastomers used in Earthquake Base Isolation: by PapouJia, K.D. and Kelly, J,M., 1990,
"Cyclic Behavior of Steel Top-and-Bottom Plate Moment Connections," by Harriott, J.D. and Astaneh, A., August 1990, (PB91 229260/AS)A05.
"Seismic Response Evaluation of an Instrumented Six Story Steel Building: by Shen, J.-H. and Astaneh, A., December 1990.
"Observations and Implications of Tests on the Cypress Street Viaduct Test Structure: by Bolio, M., Mahin, S.A., Moehle, J.P.,Stephen, R.M. and Qi, X., December 1990.
"Experimental Evaluation of Nitinol for Energy Dissipation in Structures: by Nims, D.K., Sasaki, K.K. and Kelly, J.M., 1991.
"Displacement Design Approach for Reinforced Concrete Structures Subjected to Earthquakes: by Qi, X. and Moehle, J.P., January1991.
"Shake Table Tests of Long Period Isolation System for Nuclear Faciliiies at Soft Soil Sites: by Kelly, J.M., March 199 I.
"Dynamic and Failure Characteristics of Bridgestone Isolation Bearings: by Kelly, J.M., April 1991.
"Base Sliding Response of Concrete Gravity Dams to Earthquakes: by Chopra, A.K. and Zhang, L, May 1991.
"Computation of Spatially Varying Ground Motion and Foundation-Rock Impedance Matrices for Seismic Analysis of Arch Darns: byZhang, L and Chopra, A.K., May 1991.
"Estimation of Seismic Source Processes Using Strong Motion Array Data: by Chiou, S.-J., July 1991.
"A Response Spectrum Method for Multiple-Support Seismic Excitations: by Der Kiureghian, A. and Neuenhofer, A., August 1991.
"A Preliminary Study on Energy Dissipating Gadding-to-Frame Connection," by Cohen, J.M. and Powell, G.H., September 1991.
"Evaluation of Seismic Performance of a Ten-Story RC Building During the Whittier Narrows Earthquake: by Miranda, E. and Bertero, V.V., October 1991.
"Seismic Performance of an Instrumented Six Story Steel Building: by Anderson, J.e. and Bertero, V.V., November 1991.
