EXPERIMENTAL STUDY OF THE DYNAMIC RESPONSE OF A TEN …
132
IV IZCJR 1..150 UILU-ENG-78-2012 c.2 CIVIL ENGINEERING STUDIES -, J STRUCTURAL RESEARCH SERIES NO. 450 EXPERIMENTAL STUDY OF THE DYNAMIC RESPONSE OF A TEN-STORY REINFORCED CONCRETE FRAME WITH A TALL FIRST STORY A Report on a Research Project Sponsored by THE NATIONAL SCIENCE FOUNDATION Research Grant EN-V 74-22962 UNIVERSITY OF ILLINOIS at URBANA-CHAMPAIGN URBANA/ILLINOIS AUGUST 1978
Transcript of EXPERIMENTAL STUDY OF THE DYNAMIC RESPONSE OF A TEN …
IV IZCJR 1..150
UILU-ENG-78-2012
-~ c.2 CIVIL ENGINEERING STUDIES
-, J
STRUCTURAL RESEARCH SERIES NO. 450
EXPERIMENTAL STUDY OF THE DYNAMIC RESPONSE OF A TEN-STORY REINFORCED CONCRETE FRAME
WITH A TALL FIRST STORY
A Report on a Research Project Sponsored by THE NATIONAL SCIENCE FOUNDATION Research Grant EN-V 74-22962
UNIVERSITY OF ILLINOIS at URBANA-CHAMPAIGN URBANA/ILLINOIS AUGUST 1978
ii BIBLIOGRAPHIC DATA 11. Refon No. [2. SHEET U LU-ENG-78-2012 4. Title and Subtitle
EXPERIMENTAL STUDY OF THE DYNAMIC RESPONSE OF A TEN-STORY REINFORCED CONCRETE FRAt1E WITH A TALL FIRST STORY
3. Recipient's Accession No.
5. Report Date
August 1978 6.
7. Author(s)
T. J. Healey & Mete A. Sozen 8. Performin~ Or.!~anization Rept.
No. SI-{S 450 9. Performing Organization Name and Address
University of Illinois at Urbana-Champaign 10. Project/Task/Work Unit No.
Urbana, Illinois 61801
12. Sponsoring Organization Name and Address
National Science Foundation
15. Supplementary Notes
16. Abstracts
11. Contract/Grant No. NSF ENV-74-22962
13. Type of Report & Period Covered
14.
This report documents the experimental work and presents the response data obtained in three earthquake simulation tests of a ten-story reinforced concrete frame. Changes in the dynamic properties of the test structure, such as apparent frequencies and equivalent damping, are discussed. Observed maximum lateral displacements are compared with those obtained from modal spectral analysis.
17. Key Words and Document Analysis. 170. Descriptors
Response spectrum, mode shape, modal spectral analysis, displacements, accelerations, story shear, overturning moment, Fourier amplitude spectrum, frequency, reinforcement, nonlinear
17b. Identifiers/Open-Ended Terms
. ~
~ :' '_' '>oJ ..... .:;,.:.._
17c. COSATI Field/Group
18. Availability Statement
Release Unlimited FORM NTI5-35 (REV. 10-73) ENDORSED BY ANSI AND UNESCO.
19. Security Class (This Report)
·UNrl.ASSIFIED 20. Security Class (This
Page UNCLASSIFIED
THIS FORM MAY BE REPRODUCED
21. No. of Pages 122
22. Price
USCOMM- DC 8265- P 74
Chapter
2
3
4
5
6
iii
TABLE OF CONTENTS
I NTRODUCTI ON • • . • . •
1.1 Object and Scope 1.2 Acknowledgment
TEST STRUCTURE . . • . .
2. 1
2.2
Description of Test Structure and Test Setup. . . . . . . .
Reinforcing Arrangement
TEST PROCEDURE
OBSERVED RESPONSE ..
4.1 Introductory Remarks •.• 4.2 Earthquake Simulation Tests.
DISCUSSION OF OBSERVED RESPONSE
5. 1 Introductory Remarks .•.•.• 5.2 Apparent Frequencies of the Test
Structure • . • . • . . • • • . 5.3 Measured Energy Dissipation Indices. 5.4 Response during the Design Earthquake. 5.5 General Features of Response .•.
SUt1MARY
6.1 Object and Scope •..••• 6.2 Test Structure 6.3 Test Procedure . . .• . • 6.4 Behavior of the Test Structure ..
LIST OF REFERENCES
APPENDIX
A
B
DESCRIPTION OF EXPERIMENTAL WORK
A. 1 ~1a teri a 1 Properti es • A.2 Construction •. A.3 Instrumentation. A.4 Data Reduction •. NOTATION
Page
1 1
3
3 5
10
12
12 13
17
17
17 21 22 24
28
28 28 29 29
32
105
105 107 108 110
119
~ !j
Table
2. 1
3. 1
4. 1
4.2
4.3
4.4
5. 1
5.2
5.3
5.4
A. 1
A.2
A.3
A.4
iv
LIST OF TABLES
Flexural Reinforcing Schedule .•
Sequence of Test Procedure
Spectrum Intensities for Observed Base t10ti ons . . . . • . • • . •
Observed Maximum Single-Amplitude Horizontal Accelerations ••.•
Observed Maximum Single-Amplitude Horizontal Displacements •.•.
Observed Maximum Single-Amplitude Story Shears and Base Overturning Moment ..
Measured Frequencies of the Test Structure .
Page
33
34
35
35.
36
36
37
Maximum Amplification Ratio and Apparent Resonance from the Steady-State Tests . . . . . . . . . . 37
Measured Equivalent Damping Factor from the Free-Vibration Tests .•..•..
Calculated First Mode Frequencies of the Test Structure ...••..•....
Measured Properties of Concrete Control Specimens ...•.• . . • . • . . .
Measured Properties of Flexural Reinforcement.
r~easured Dimensions of the Test Structure ..
Chronology for Test Structure •..•...
38
38
112
. 113
114
115
Fi gure
2. 1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
v
LIST OF FIGURES
Page
Test Structure. . . . . . . .. . . . . . . . . . . . . . 39
Reinforcement Detail and Dimensions of the Test Structure. • . • .
Test Setup
Photograph of Test Setup. •
Design Spectrum ••..••••
Mode Shapes Used for Force Calculations.
Design Beam Moments and Strength Provided in the Beams •..•..•
Distribution of Column Design Shear Forces.
40
41
42
43
44
45
46
2.9 Design Axial Forces and Moments for Exterior Columns. • • •. • ••••.•.•.•. 47
2.10 Design Axial Forces and t10ments for Interior Columns . . . . · · · · 48
2.11 Interaction Diagram for Columns . · · · · 49
2.12 Distribution of Moments in the Columns from a Softened-Exterior-Column Analysis . 50
2.13 Typical Joint Detail in the Test Structure. · · · 51
3. 1 Free Vibration Test Setup · · · · 52
4. 1 Linear Response Spectrum, Run One · · · · · · . . 53
4.2 Linear Response Spectrum, Run One . . . · · · · · 54
4.3 Linear Response Spectrum, Run Two • 55
4.4 Linear Response Spectrum, Run Two . 56
4.5 Linear Response Spectrum, Run Three • 57
4.6 Linear Response Spectrum, Run Three . · · · 58
vi
Figure
4.7 Observed Horizontal Accelerations, Run One.
4.8 Observed Horizontal Accelerations, Run One.
4.9 Observed Horizontal Accelerations, Run Two ..
4.10 Observed Horizontal Accelerations, Run Two.
4. 11 Observed Horizontal Accelerations, Run Three.
4.12 Observed Horizontal Accelerations, Run Three ••
4. 13 Observed Base Overturning Moment and Horizontal Displacements, Run One.
4.14 Observed Horizontal Displacements, Run One.
4.15 Observed Base Overturning Moment and Horizontal Displacements, Run Two.
4.16
4.17
Observed Horizontal Displacements, Run Two.
Observed Base Overturning Moment and Horizontal Displacements, Run Three
4.18 Observed Horizontal Displacements, Run Three •••
4.19 Observed Story Shears, Run One
4.20
4.21
Observed Story Shears, Run One
Observed Story Shears, Run Two
4.22 Observed Story Shears, Run Two
4.23
4.24
4.25
4.26
Observed Story Shears, Run Three ..
Observed Story Shears, Run Three.
Maximu~ Observed Base Acceleration Versus Spectrum Intensity, 8 = 20% .•••••.
Crack Patterns Observed Before Testing.
4027 Crack Patterns Observed After Run One.
4.28 Crack Patterns Observed After Run Two •
4,,29 Crack Patterns Observed After Run Three ••
Page
• • 59 .
· • 60
· . 61
· . . 62
• • 63
· 64
• • 65
· • 66
• . 67
• • 0 68
• • 69
· 70
· 71
· 72
· 73
· 74
· 75
• . 76
· • 77
• • 78
• • • 79
• • 80
· 81
vii Figure Page
4.30 Spalling at the Outside of an Exterior Column,
4.31
5. 1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Run Two •...••.•••••..•
Spalling at the Outside of an Exterior Column, Run Three. • . • . . • . . . . • •
Fourier Amplitude Spectra, Run One •.
Fourier Amplitude Spectra, Run One.
Fourier Amplitude Spectra, Run Two.
Fourier Amplitude Spectra, Run Two ••
Fourier Amplitude Spectra, Run Three.
Fourier Amplitude Spectra, Run Three.
Observed Free-Vibration Responses with Fourier Amplitude Spectra ..•.•• . . . . . . . . .
Observed Free-Vibration Responses with Fourier Amplitude Spectra •••
Amplification Ratio Versus Input Frequency, Steady State Tests ••.•••.••..
. . . . . .
. '. . 5.10 Apparent First-Mode Frequency Versus One-Half the
r1aximun Observed Double Amplitude Tenth Level
5.11
5. 12
5.13
5. 14
5.15
Displacement. . • • • • . . . . . .. •
Comparison of Design Response Spectrum with Obtained Response Spectrum, Run One ...•
Comparison of Maximum Observed Displacements with Calculated Values, Run One ••.••.
Maximum Observed Displacements, Lateral Forces, Story Shears and Overturning Moments, Run One.
Comparison of Maximum Observed Story Shears and Overturning Moment with Calculated Values, Run One • • • • • • • . . . . . . . •
Maximum Observed Single-Amplitude Tenth-Level Displacement Versus Spectrum Intensity, B = 20% •••• • • • • • • • • • • • • • •
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
viii Figure Page
5.16 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Shear, Run Two. · · · · · · · · · · · · · · · 99
5.17 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Overturning Moment, Run Two . · · · · · · · · 100
5.18 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Shear, Run Three. · · · · · · · · · · · · · · 101
5. 19 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Overturning Moment, Run Three . · · · · · · · 102
5.20 Maximum Observed Base Shear Versus r~aximum Tenth Level Displacement . . · · · · · · · · · · · · · · · 103
5.21 r'1aximum Base Shear Versus Collapse Hechanism for a Triangular Lateral Loading Condition · .. · · 104
A. 1 t~easured S tress-Stra in Relation for Concrete . · · · · · 1.16
A.2 Measured Stress-Strain Relation for Reinforcing Steel . . . . . · · · · · · · · · .. · · 117
A.3 Instrumentation Layout for the Test Structure . . . . 118
1.1 Object and Scope
1
CHAPTER 1
INTRODUCTION
The primary objective of this test was to study the nonlinear dynamic
behavior of a small-scale ten-story three-bay reinforced concrete structure
with a tall first story. Actually both the first story and the tenth
story were 20% longer than each of the other stories of the structure.
The test procedure included a series of strong base motions simulating
a scaled version of the north-south component of the El Centro earthquake
of 1940. Reinforcement was selected with guidance from a linear dynamic
analysis using a specific design spectrum.
This report documents the experimental work and presents the accelera
tion and displacement data obtained in three earthquake-simulation tests.
Changes in the dynamic properties of the test structure, such as apparent
frequencies and equivalent damping, are discussed. Observed maximum
lateral displacements are compared with those obtained from modal spectral
analysis.
1.2 Acknowledgment
This investigation is part of a continuing study of the effects of
earthquake motions on reinforced concrete systems being carried out at
the Structural Research Laboratory of the Department of Civil Engineering
of the University of Illinois. The work was sponsored by the National
Science Foundation under Grant NSF-ENV-74-22962
The writers wish to thank D. Abrams, B. Algan, H. Cecen, J. Moehle,
D. Schipper, and B. Volkert, research assistants in the Department of
Civil Engineering for their generous advice and assistance. Acknowledgment
2
is also due to R. Fernandes for his help in constructing the test struc
ture.
Appreciation is due to Professor V. J. MacDonald and Mr. G. Lafenhagen
for their able management of the earthquake simulation and data-acquisition
systems, and to Mr. O. Ray and his staff for fabrication of the hardware
and assistance in casting the specimen. Thanks to t~rs. P. Lane for typing
this report, and to Mr. R. Winburn and his staff for drafting the figures.
The writers are indebted to the members of the panel of consultants
for their advice and criticism. The panel included M. H. Eligator,
Weiskopf and Pickworth; A. E. Fiorato, Portland Cement Association; W. D.
Holmes, Rutherford and Chekene; R. G. Johnston, Brandow and Johnston;
J. Lefter, Vetrans Administration; W. P. Moore, Jr., Walter P. Moore and
Associates; and A. Walser, Sargent and Lundy.
The IBM 360/75 and CYBER 175 computer systems of the Digital Computation
Labora to ry of the Un i vers i ty of 111 i noi s wer.e used for the computa ti ons and
data reduction in this report.
This report was prepared in connection with T. J. Healey's graduate
program toward an M.S. degree in Civil Engineering in the Graduate School
of the University of Illinois, Urbana.
3
CHAPTER 2
TEST STRUCTURE
2.1 Description of Test Structure and Test Setup
The test structure was a small scale ten-story building comprising
two frames working in parallel to carry a total mass of 4540 kg 'distributed
equally to each level (Fig. 2.1). The frames were cast horizontally out
of the same batch of concrete. The compressive strength of the concrete was
40 MPa at time of test. The yield stress for the longitudinal reinforce
ment was 350 MPa.
( a ) 0 i me n s ion s
The overall nominal dimensions of the frames are shown in Fig. 2.2.
The measured dimensions are summarized in Table A.3.
The story heights from center line to center line of the beams were
229 mm for the second level through the ninth level, and 279 mm for the
tenth level. The first level height from the top of the base girder to
the centerline of the first level beam was 279 mm. The columns were 58 mm
deep by 38 mm wide.
Each of the three spans from center line of column to center line
of column was 305 mm. The cross section of the beams was 38 by 38 mm.
( b) T es t Se tup
The test structure was tested using the University of Illinois
Earthquake Simulator (Figures 2.3 and 2.4. A detailed discussion of the
simulator is given by Sozen and Otani (1970).
Before the frames were placed on the test platform, the masses were
stacked on the platform with adjustable wooden blocks in between each mass.
In this way, as the masses were stacked, their positions could be adjusted
so that the center of gravity of a mass was at each of the story levels.
4
The frames were then placed on the test platform parallel to each
other on opposite sides of the masses. They were positioned so that the
major axis of the test structure was parallel to the direction of the input
motion (Figures 2.3 and 2.4). The frames were bolted to the platform
through vertical holes in the base girder.
The masses were then connected to the frame. The process began at
the tenth level and continued in descending order, one level at a time,
to the first level. The wooden blocks were not removed during this pro
cedure and were kept in place until the day of the test. The structure
did not carry dead load until then. The connection of the masses to the
frame was designed so that the reactions at the joints were determinate.
Each story mass was supported by two steel channel cross beams. The
cross beams were positioned so that the weight of the mass would be
carried to the centerline of the exterior bay of each frame. Pinned to
each end of the cross beams were a pair of channels which distributed the
reaction equally to an exterior and an interior column (Figures 2.1 and
2.3). Thus, each joint in the frame was designed to carry one eighth
of the weight of the story mass transferred to the joint through a pin
connection.
To provide stability of the test structure about its weak axis and
to provide torsional stiffness about its vertical axis, steel plate
hinges were provided between masses at each level (Fig. 2.1). The light
hinges were well lubricated to minimize restraint in the direction parallel
to the input motion.
2.2 Reinforcing Arrangement
(a) Design Process
5
The test structure was designed using the substitute-structure method
(Shibata, 1976). The objective of this design method is to establish the
minimum strengths which the members of the structure must have so that a
tolerable response is not likely to be exceeded.
The test structure was reinforced to resist lateral loads based
on a design response spectrum. The design concrete strength was 30 MPa
at a strain of .003 with a Young's Modulus (Ec) of 21,000 MPa. The yield
stress of the reinforcing steel, based on the average value obtained from
coupon tests, was taken as 350 MPa (Table A.2).
Response spectrum A (Figure 2.5) (Shibata, 1976) modified to a time
scale 1/2.5 was used for the dynamic analysis of the substitute structure.
The maximum base acceleration for the design earthquake was 0.4g. A
comparison of the assumed and obtained spectra is given in Chapter 5.
The flexural stiffnesses of the substitute frame elements are related
to the stiffnesses of the actual frame elements by the relation
(E1) . = (E1) OJ S1 a 1 ~
(2-1 )
where (E1) ° and (E1) ° are flexural stiffnesses of member i for the s 1 a 1
sUbstitute and actual structure, respectively, and ~ is the selected
tolerable IIdamage ratio" for element i.
The cracked section stiffnesses of each ~ember in the frame, modified
by the appropriate damage ratio, ~, was used in the analysis of the
substitute structure. Since the amount of reinforcement was not known at
6
the initial stage of design, it was assumed that the ratio of cracked-to-
gross-section moment-of-inertia was 1/3 for beams and columns.
The damage ratio was taken as four for beams (~ = 4) and one for
columns (~ = 1) in the substitute-structure. These damage ratios were
chosen with the intent that energy be dissipated primarily in the beams
during the design earthquake.
A linear dynamic response analysis was made to obtain modal periods,
shapes, and forces for the first three modes of the substitute structure.
For this preliminary analysis, the modal damping was taken as 10% for all
three modes. Motion was considered only in one horizontal direction.
Trial design moments at critical sections were obtained as the square
root of the sum of the squares RSS moments for the beams and 1.2 * RSS
moments for the columns. The column RSS moments were amplified by 1.2
to reduce the risk of inelastic action in the columns.
A steel reinforcement arrangement was selected, and another linear
dynamic response analysis was made. Shapes of the first three modes of
the substitute structure for this final trial are shown in Fig. 2.6.
The substitute modal damping factors were obtained from the following
expressions (Shibata) 1976
where L P. = 1 6(E1) .
Sl
S . S1
= 0.2 (1
EP .*8. 1 S1
EP. 1
(r.l . 2 + al
2 Mbi - t1 . Mb . ) a1 1
- (1/~i)1/2) + 0.02
(2.2)
(2.3)
(2.4)
7
where
Sm = IIsmearedll dampi ng factor for mode m
P. 1
= strain energy of member i
Ss i = substitute viscous damping factor for member i
lJ • = damage ratio for member i 1
L = 1 ength of structural member
Mai & Mbi = end moments of substitute-structure element i for
mode m
It was assumed that the design response acceleration for any damping
factor, S, was related to the response for S= 0.02 by the equation (Shibata,
1976)
Response Acceleration for S Response Acceleration fors= .02
8 =--6+ 1 ODS
(2.5)
The modal forces for the first three modes were then modified using
equation (2.5) according to their respective IIsmearedli damping ratio from
equation (2.2).
The RSS of the modal beam moments were used for design. The
design beam moment per level along with the yield strength provided is
shown in Fig. 2.7.
The RSS of the column shear forces were used for design of the spiral
shear reinforcement. The distribution of those forces are shown in Figure
2.8. All beams and columns had more transverse shear reinforcement than
required by the design forces to minimize the risk of primary failure in
shear.
The design axial forces on columns were taken as the dead weight of
the masses + RSS axial forces. The design column moments were taken as
8
the RSS moments amplified by 1.2, except at the base where the RSS moments
were used. The first story RSS moments were not amplified by 1.2 with the
notion that inelastic action is difficult to avoid at the base. The distri
bution of the design axial forces and design moments are shown in Figures
2.9 and 2.10.
An interaction diagram for the columns is shown in Fig. 2.11. The
position of the columns are also plotted on the interaction diagram. All
columns fall within the diagram except the exterior column at the base on
the tension side of the frame.
To investigate the effects of an exterior column yielding, a second
linear dynamic response analysis was made with the same assumed section
stiffnesses as before, with the exception that a damage ratio of two
(~ = 2) was assumed for one exterior column at the first level. For the
most part, the results of this analysis were not different from those of
the original analysis. As would be expected, the moments at the base
shifted from the soft column to the other three columns which had reserve
capacity. The new positions for the base moments for this analysis are
shown by arrows in Fig. 2.11. The distribution of moments from this analysis
is shown in Fig. 2.12.
(b) Reinforcing Steel Distribution
The arrangement of the longitudinal reinforcement is schematically
shown in Figures 2.2 and 2.13 and is given by the schedule in Table 2.1.
The columns at the base and the second level interior columns were
reinforced with three No. 13 gage wires per face for a reinforcement ratio
of 1.32%. All other columns in the frame contained two No. 13 gage wires
per face for a reinforcement ratio of 0.88%.
9
The beams at the first through the seventh levels were reinforced with
three No. 13 gage wires per face for a flexural reinforcement ratio of
1.10%. The beams at the eighth trhough the tenth levels had two No. 13
gage wires per face for a flexural reinforcement ratio of 0.74%.
All beams and columns were reinforced to resist shear forces with
No. 16 gage wire "spirals" (Fig. 2.2 and 2.13). The spirals were continuous
and had a pitch of 3 mm. The joint details are described in Appendix A.
10
CHAPTER 3
TEST PROCEDURE
On the day of the test, the adjustable wooden blocks were removed
from between the masses. At this time all cracks observed on the specimen
were recorded. To locate the cracks, the specimen was coated with "Partek"
Pl-A Fluorescent and black light was applied.
The tightness of all bolts on the test setup was then checked. This
included the connections of the masses to the frames, the specimen base
to the test platform, the instrumentation fixtures, and the A-frame to the
tes t p 1 a tform (Fi g. 2.3).
Hydrocal was then placed at various locations along the connection of
the base of the frame to the test platform. The hydrocal was used as a
check for slip between the test specimen and the platform during the testing.
The following sequence of operations was performed for each test run:
(1) The tightness of bolts fixing the specimen to the platform was
checked.
(2) The tenth level of the structure was given a small initial displace
ment to induce a low·amplitude free vibration. This displacement was
obtained by hanging a small weight from the tenth level over a pulley (Fig.
3.1). Free vibration was initiated by cutting the wire supporting the
weight.
(3) The specimen was subjected to the desired earthquake base motion at
the specified acceleration level.
(4) The specimen was coated with "Partek" P-1A Fluorescent and the new
cracks were marked and recorded.
11
(5) A low-amplitude free-vibration test was made as described in
(2) .
(6) The structure was subjected to a sinusoidal base motion
IIsweepll of the form
(3-1 )
where Xb is the input base motion, Xo is a constant amplitude of the input
base motion, and w is the "sweeping" driving frequency. These tests will
be referred to as II steady-state tests" throughout this report.
This sequence was followed three times throughout the entire testing
procedure. Table 3.1 summarizes the events of the experiment in chronological
order.
The input motion for the three earthquake simulation tests was the
recorded north-south component of the earthquake motion measured at El Centro,
California (1940). The acceleration level was magnified for each test run.
The maximum recorded base acceleration for the first through the third test
was 0.4 g, 0.95 g and 1.42 g, respectively.
The displacement amplitude, X (Eq. 3.1) was chosen so that ideally o
no damage would occur during the ste~dy state tests. The driving frequency
was varied throughout each individual run. The value of the driving frequency
was taken as .8 Hz below the estimated first natural frequency initially, and
gradually increased in increments of .2 Hz up to .8 Hz above the frequency at
which maximum response amplitude was observed.
12
CHAPTER 4
OBSERVED RESPONSE
4. 1 Introductory Remarks
(a) General Comments
The results of the earthquake simulation tests previously described
in Chapter 3 are presented in this chapter. The presentation is based
on instrument signals which were recorded during each earthquake test,
and on observed crack patterns of the structure o For a complete descrip
tion of the data recording procedure, see Appendix A. The process for
marking and recording the crack pattern of the structure is described in
Chapter 3.
(b) Terminology
Certain terms are used throughout this chapter and are defined here
for clarity. Throughout this chapter IItest run" vlill refer to one of
the earthquake simulation tests.
A response spectrum refers to the response of a linear single-degree
of-freedom system subjected to a given base motion for a given level of
damping. In this chapter the base motion is the base acceleration recorded
during a test run. For each test ruh a response spectrum is presented for
various damping levels.
In describing the base motion, it is sometimes advantageous to use
the spectruD intensity as well as the maximum base acceleration. The
spectrum intensity, as defined by Housner, is the area under the velocity
response spectrum from periods of 0.1 to 2.5. The maximum base accelera
tion and the spectrum intensity for various damping levels are given for
13
each test run. To fit the time scale (2.5) of the earthquake motions used
in the tests, Housner's Intensity is redefined to include the area under
the velocity-response curve over the period range 0.04 to 1.0 sec.
Reference is made to response in a given mode. The mode of vibration
refers to the phase relationship of the responses of the ten floor levels.
For instance, by "first mode" it is meant that the responses of all ten
levels are oscillating in the same phase. By "second mode" it is meant
that some of the levels are oscillating in one phase while the remaining levels
are oscillating in another phase.
The histories of the displacements and accelerations at each story
level for each test run are presented. From these records the story level
shear and base overturning moment waveforms were obtained. The story level
shears and base overturning moments are also presented.
It should be mentioned that a frequency-filtered portion of each
waveform is superimposed on the true waveform of all time histories
presented in this chapter. The filtered waveform is shown asa solid
line, while the total record is shown as a broken line. The filtered
waveforms will be discussed in Chapter 5 and are of no consequence in this
chapter.
In all three test runs, the -responses of the north frame and the
south frame at each level were almost identical. Therefore in this chapter,
only the responses associated with the north frame are reported. The north
side was chosen arbitrarily.
4.2 Earthquake Simulation Tests
(a) Condition of the Specimen Prior to Testing
Small cracks in the structure due to shrinkage and handling were
observed prior to test run one. The crack pattern is depicted in Fig. 4.26.
14
As shown in the figure, cracking was negligible with all crack widths ""
being much less than 0.05 mm.
(b) Base Motion
The maximum observed base acceleration for runs one, two and three
was 0.40 g, 0.98 g and 1.42 g, respectively. The measured base accelera
tions are shown in Fig. 4.8 for run one, Fig. 4.10 for run two, and
Fig. 4.12 for run 3. Response spectra for the base motions for each run
are shown in Fig. 4.1 through 4.6. Spectrum intensities are given in
Table 4.1. Fig. 4.25 shows maximum observed base acceleration versus
spectrum intensity (SI 20 ). As seen in the figure, the relationship is
linear. Thus, the base motion can be described equally well using either
parameter.
(c) Accelerations
The response histories for horizontal accelerations at each level
are shown in Fig. 4.7 through 4.12 for each of the three test runs.
The maximum observed horizontal accelerations at each level are summarized
in Table 4.2.
As shown in the figures, the horizontal accelerations seem to have
very little high-frequency components. The acceleration histories were
almost completely in phase consistent with the first mode, for each of the
three test runs.
(d) Displacements
The horizontal displacement records for the three test runs are
presented in Fig. 4.13 through 4.18. The single-amplitude displacement
maxima are listed in Table 4.3.
As would be expected, the horizontal displacement records exhibited
little or no high-frequency components. For each test run, all ten levels
were in phase consistent with the first-mode.
15
(e) Story Shears and Base Overturni ng r10ments
Histories of story shears for each test run are given in Fig. 4.19
through 4.24. The single-amplitude maximum observed story shears are
summarized in Table 4.4.
Not unlike the acceleration records, the story shear records are
first-mode dominated for each of the three test runs.
The base overturning moment records are shown in Fig. 4.13 for run
one, Fig. 4.15 for run two and Fig. 4.17 for run three. The maximum base
moments are summarized in Table 4.4.
The base overturning moment records are shown along with the horizontal
displacement records. As seen in the figures, the base overturning moment
time histories are in phase with the displacement records for each of the
tes t runs.
(f) Crack Patterns
Figure 4.27 depicts the crack pattern after test run one. The
structure incurred little additional cracking during run one with all
observed crack widths being less than or equal to 0.10 mm.
Figure 4.28 shows the crack pattern after test run two. Cracking
observed after run two was extensive. Crack widths at the first level
were measured to be as high as 0.25 mm. Spalling occurred at the base
on the outside of one of the exterior columns. Figure 4.30 shows a
photograph taken of the spa11ing after run two.
Figure 4.29 depicts the crack pattern of the structure after test
run three. The structure suffered additional cracking with crack widths
at the second level measuring 0.38 mm. Spalling occurred at the base of
16
the outside of both exterior columns. A photograph of the spal1ing is
shown in Fig. 4.31.
17
CHAPTER 5
DISCUSSION OF OBSERVED RESPONSE
5. 1 Introductory Remarks
The presentation in this chapter is based on the observed response
of the structure during the earthquake si~ulation tests and on the results
of the free-vibration and steady-state tests. The testing procedure is
described in Chapter 3. The response histories, response maxima, and
response spectra for the earthquake sinulation tests are presented in
Chapter 4. In this chapter an earthquake simulation test will be referred
to as a II run II •
5.2 Apparent Frequencies of the Test Structure
(a) Frequency-Domain Response
To investigate the apparent frequency of the response of the test
structure, the response histories It/ere transformed into the frequency
do~ain. The transformation into the frequency domain was accomplished
by means of the Fourier transform. Fourier amplitude spectra for the
horizontal displacement and acceleration histories for each test run are
given in Fig. 5.1 through 5.6. From these spectra it is seen that the
displacement and, to some extent, acceleration records are dominated by
components in the 0.0 to 3.0 Hz range. The apparent first-mode frequency
co responds to the spike in the Fourier amplitude within this range. The
measured first-mode frequencies were 2.0 Hz, 1.4 Hz and 1.0 Hz for run
one, two and three, respectively.
18
To investigate the contribution of the apparent first mode to the
response of the test structure during the earthquake simulation tests,
the response histories were filtered of components with frequencies
greater than 3.0 Hz. The filtered response histories are presented in
Chapter 4 in Fig. 4.7 through 4.24. As previously described in Chapter
4, the filtered record is shown as a solid line superimposed over the
total record which is shown as a broken line. As might be expected, the
filtered records match the total records well. However, as seen in Fig.
4.9 through 4.12, the contribution of higher modes is detected in the
acceleration histories for both the second and third runs.
The contribution of higher modes on the response of the structure
can be seen in the Fourier amplitude spectra for the acceleration records
only. As shown in Fig. 5.2, the second through fourth level acceleration
records for run one have perceptible contributions at frequencies 7.7 Hz
and 15.0 Hz, which are the apparent second and third-mode frequencies,
respectively. The motion at the first level is strongly influenced by
the base motion.
In run two the second through fourth level acceleration histories
have a high second mode contribution with an apparent frequency of 6.2 Hz
(Fig. 5.4). The acceleration records at levels two, six and seven show a
moderate third-~ode contribution at 12.3 Hz.
In run three (Fig. 5.6) levels two through six and ten had an apparent
second-mode component at 5.4 Hz. A third-mode contribution at 9.6 Hz
can be seen at levels two, three, six and ten. Table 5.1 summarizes the
apparent frequencies of the test structure obtained from the Fourier
amplitude spectra.
19
(b) Free-Vibration Tests
As previously described in Chapter 3, before and after each test
run, the structure was given an initial-displacement free vibration. The
tenth level acceleration response and the Fourier amplitude spectrum for
each free-vibration test are provided in Fig. 5.7 and 5.8. The response
histories were filtered of components with frequencies greater than 4 Hz
so that the first-mode frequency of the structure could be measured.
As shown in Fig. 5.7, prior to run one, the response of the structure
in the free-vibration test exhibits contributions from several modes.
From the Fourier spectrum, the apparent first-mode frequency is 3.2 Hz.
However, another strong modal contribution is seen at 6.7 Hz, which is
much too low to represent a second-mode frequency. This frequency is
attributable to a IItorsional ll mode in which the two parallel frames VJere
vibrating out of phase. Torsional vibration could have arisen as a result
of either a difference in the initial stiffness of the two frames comprising
the test structure,' or a difference in the initial displacements of the
two frames at the start of the test. However, since the apparent torsional
mode \AJas not present in the other free vibration tests as evidenced by
the Fourier amplitude spectra, it may be assumed that the two frames had
initial stiffnesses sufficiently different to cause torsional vibrations.
From Fig. 5.7 and 5.8 the measured first-mode frequencies are 3.2 Hz,
2.9 Hz, 2.3 Hz and 1.9 Hz for tests prior to run one, after run one, after
run two and after run three, respectively. In the same order, the apparent
second-mode frequencies are 15.6 Hz, 10.6 Hz, 8.7 Hz and 7.5 Hz. The
apparent third-mode frequencies are 26.5 Hz, 19.0 Hz, 15.4 Hz and 12.9 Hz.
The measured frequencies obtained from the free vibration tests are summarized
in Table 5.1.
20
(c) Steady State Tests
After each test run, the structure was given a steady-state test as
described in Chapter 3. The structure was subjected to low-amplitude
sinusoidal base excitation. The base excitation was swept through various
frequencies near the expected apparent frequency of the structure. The
results of the tests in the form of amplication ratio versus input
frequency of the base motion, are shown in Fig. 5.9.
The amplification ratio was calculated by normalizing the observed
tenth level amplitude with respect to the input base amplitude and the
first-mode participation. The participation of the first mode was cal
culated from the observed displaced shape of the structure at apparent
resonance. Thus it was assumed that the contribution of higher modes on
the response of the structure within this low frequency range was negligible.
From Fig. 5.9, apparent resonance occurred at 2.1 Hz, 1.7 Hz and 1.4 Hz
during the steady state tests after run one, two and three, respectively.
The results of the steady-state test are summarized in Table 5.2.
Figure S.lO is a plot of the measured first-mode frequency of the
test structure versus one-half the maximum double amplitude displacement
of the test structure during the earthquake sinulation tests. That is,
the frequencies measured after the run are correlated with the maximum
displacement of that particular run. As shown in the figure, the measured
frequencies associated with the free vibration tests were consistently
higher while the measurements from the earthquake simulation tests were
consistently lower.
It should be pointed out that the free-vibration and steady state
tests were conducted at low amplitudes. The maximum tenth-level dis
placements during the free-vibration and steady-state tests were approxi
mately 1mm and 7 mm, respectively. Given that the effective stiffness of
21
a nonlinear structural system is higher at low amplitudes of vibration,
the observed difference in the apparent frequencies for the different
types of tests would be expected. From Table 5.1, a similar trend may
be seen to have occurred for the measured second and third-mode frequencies.
5.3 Measured Energy Dissipation Indices
The response histories for the free-vibration tests were used as an
indication of the capacity of the test structure to dissipate energy
under dynamic loading. Log-decrement measurements were taken of the
filtered portion of each record to obtain equivalent viscous damping
ratios. Following in the chronological order at which the free-vibration
tests were administered (Table 3.1), the measured damping factors
expressed as a percentage of critical damping, are summarized in Table
5.3.
The equivalent damping ratio increased as the test procedure progressed.
As the test structure was subjected to more severe base motions and thus
pushed farther into the inelastic range, apparently the capacity of the
structure to absorb energy at low amplitude was also enhanced. Assuming
that the measure~ents are not reliabile for differentiating between
fractions of a percent, it would appear that the change in damping from
before and after the steady-state tests was negligible. However, an
appreciable increase in equivalent damping for low amplitude displace
ments occurred after each earthquake simulation test.
The trend of an increase in the apparent equivalent damping of the
test structure after each run is also seen in the results from the steady
state tests. As shown in Fig. 5.9, the maximum amplification ratios for
the steady-state tests are 5.7 after run one, 4.1 after run two and 3.8
22
after run three. As described in Chapter 3, the base ~otion in each
steady-state test was the same within the limitations of the earthquake
simulation system. From these results, there appears to have been a
large increase in the energy dissipation capacity of the structure at
moderate amplitudes from one to run two. Results of the steady-state tests
are not interpreted in terms of damping factors because, especially in runs
two and three, the response of the system was perceptibly nonlinear.
5.4 Response During the Design Earthquake
As previously described in Chapter 2, the test structure was designed
for an idealized response spectrum at an effective peak acceleration of
0.4 g. Fig. 5.11 compares the obtained response spectra from the ~easured
base acceleration of run one with the assumed response spectra used for the
design. The assumed acceleration response was less than the obtained
response in the low frequency region. For comparison, a linear dynamic
response analysis was made of the substitute-structure (Chapter 2) using
the obtained response spectrum. Another analysis was made of the test
structure assuming gross-section stiffnesses for the components of the
structure and using the obtained response spectrum.
(a) Displacements
The maximum single-amplitude displacements and one-half the maximum
double-amplitude displacements observed in run one are provided in Fig.
5.12. These maxi~um displacements occurred simultaneously during run one.
The calculated displacements given by the various linear dynamic response
analyses described above, are also shown in Fig. 5.12.
The calculated displacements given by the gross-section analysis
result in a low estimate of both the single-amplitude and one-half
23
double amplitude maximum observed displacements. The substitute
structure analysis based on the assumed design spectrum leads to dis
placements that were exceeded at all levels by the observed single
amplitude displacements and at the first six levels by one-half the
observed double-amplitude displacements. The substitute-structure
analysis based on the response spectrum froD run one indicates displace
ments which were not exceeded in the top five levels by either single
amplitude or one-half double-amplitude observed displacements. However,
the single-amplitude displacements observed at levels one through four
and one-half the double-amplitude displacements observed at levels one
and two were greater than those indicated by this analysis.
The gross-section analysis would be expected to five a poor estimate
of the observed maximum displacements. Although the substitute-structure
analysis indicates displacements that are comparable to those observed,
the displacements indicated were exceeded at the lower stories. Since
the primary objective of the substitute-structure method was to produce
a structure to stay within tolerable displacement limits, these results
suggest that some modifications need to be made to the procedure used for
the selection of reinforcement in the lower-story columns and beams. It
is quite likely that another base motion having the same intensity might
excite the structure into larger displacements.
(b) Forces
As mentioned earlier in this chapter, the response of the structure
seems to have been dominated by the first-mode, especially during the
design earthquake. This is demonstrated in Fig. 5.13 which shows the
displacements, lateral forces, shears and overturning moments at each
level at time 1.42 seconds into run one. The maximum displacements, base
shear and overturning moment occurred simultaneously.
24
Fig. 5.14 shows the observed and the calculated maximum story shears
and overturning moments. Both the sUbstitute-structure analyses resulted
in forces less than the maximum observed. On the other hand, the gross
section analysis indicates forces that are much larger than those observed.
It should be noted that the forces developed in the structure are a
function of the actual strength of the structure. Because of the general
trend of the decisions made in going from design requirements to reinforce
ment, the design forces are likely to be exceeded.
(c) Frequencies
A comparison of the calculated frequencies of the structure with the
observed frequencies, previously discussed in section 5.2, provides insight
into the apparent discrepancy be-tween the observed and calculated forces
in the structure. Table 5.4 summarizes the calculated first-mode fre
quencies. The apparent first-~ode frequency was 2.0 Hz in run 1. The
calculated first mode frequencies are 1.8 Hz and 3.6 Hz for the substitute
structure and gross-section analyses, respectively_ The substitute
structure model was evidently more flexible than the actual test structure
was observed to be. However, the gross-section model is far too stiff,
thus leading to low deflections and very high forces.
5.5 General Features of Response
(a) Displace~ents
The naximu~ observed single-amplitude tenth level displacement versus
spectrum intensity (51 20 ) is shown in Fig. 5.15. As seen in the figure
there is a linear relation between the two.
25
In run one the maximum tenth-level displacement was 23.6 mm or 1%
of the total height of the structure. The maximum inter-story displacement
occurred between the base and the first level, ~easuring 4.8 mm, or 1.7%
of the story height. During run t\,IO the maximun tenth level displacement
was 51.2 mm, or 2.2% of the height of the structure. The maxi~um inter
story displacement was 9 mm, or 3.9% of the story height, occurring between
the second and third level. The maximum tenth level displacement in run
three was 68.1, or 2.9% of the height 6f the structure. The maximum
inter-story displacement occurred between levels two and three and measured
9.9 mm, or 4.3% of the story height.
(b) Forces
Unlike the response of the test structure during run one, for runs
two and three the maximum base shear and overturning moment occurred at
slightly different times. This is attributed to the contribution of higher
modes to the response of the structure. Figures 5.16 and 5.17 show the
displacements, lateral force distribution, story shears and overturning
moments for run two at the ins tances of maxililUm base shear and overturni ng
moment, respectively. Similarly, Fig. 5.18 and 5.19 shows the same
sequences of distribution for run three. Notice that although the maximum
base shear and overturning moment occur at different time instances, in
both run two and three they are less than 0.1 second apart.
As presented in Chapter 4, the maximum base shear and overturning
moment during run two was measured at 31.4 kN-m and 16.5 kN, respectively.
During run three the observed maximums were 30.0 kN-m and 16.2 kN. The
test structure apparently developed slightly less force in the third run
than in the second, even though the maximum base acceleration and spectrum
intensity of run three were approximately 1.5 times as great as those of run
two.
26
(c) Force-Displacement Relation
The maximum base shear versus the maximum tenth-level displacement
observed during the earthquake simulation tests is provided in Fig. 5.20.
The points along the initial slope were obtained from the observed tenth
level displacement and base-shear "peak" at the beginning of run one. As seen
in the figure, the maximum base shear starts to level off at 15 kN with a
displacement of 23.6 mm which occurred early in run one. The data in the
figure suggest that general yielding of the structure was reached in run
one, the "design earthquake."
(d) Limit Strengths of the Test Structure
For the purpose of comparison with the observed maximum base shear,
a limit analysis was made of the test structure. In this analysis it was
assumed that the structure was subjected to a first-mode (triangular)
loading. The beam ultimate moments used in the analysis were obtained
from static tests performed on models of beam-column joints (Kreger, 197&).
The column ultimate moments were calculated assuming an ultimate stress
in the steel of 410 MPa. Assuming various collapse mechanisms, the
ultimate base shear was calculated. Figure 5.21 shows a plot of ultimate
base shear versus collapse mechanism.
From the figure, the observed maximum base shear is 16.5 kN, and the
maximum ultimate base shear corresponding to a first-story mechanism is
18.5 kN. The ~iniDum base shear, corresponding to a mechanism with
yielded fifth level columns and first through fourth level beams, is 12.3 kN.
However, observing the crack pattern of the structure after run two and
three (Fig. 4.28 and 4.29) suggests that all or most of the beams had
yielded in the structure. Thus, the last mechanism shown in Fig. 5.21
with all beams yielding is probably the most reasonable one for the test
structure. The base shear corresponding to this mechanism is 14.4 kN.
t Not published
27
It should be remembered that several simplifying assumptions were made
in the limit analysis. For example, in the analysis it was assumed that
the loading was triangular and constant with time. In fact, during the
earthquake simulation tests the magnitude and distribution of the lateral
loading is constantly changing with time. Also no account was made for
strain rate or strain hardening in the components of the structure.
6.1 Object and Scope
28
CHAPTER 6
SUHMARY
The purpose of this study was to investigate the dynamic behavior of
a ten-story reinforced concrete structure with a tall first story. As
part of the testing procedure, the structure was subjected to strong base
motions simulating the north-south component of the earthquake recorded
at El Centro, California (1940).
The structure was designed on the basis of a linear dynamic analysis
using a smooth design spectrum for the input motion (Shibata, 1976). A
IIsubstitute-structure" model for the analysis incorporated the expected
change in strength of the structure.
6.2 Test Structure
The test structure comprised two small scale ten-story three-bay
frames \'Iorking in parallel to carry a 454 kg mass at each level (Fig. 2.1).
The frames were cast horizontally out of the same batch of concrete. The
compressive strength of the concrete on the day of the test was 40 MPa.
The yield stress for the longitudinal reinforcement was 350 MPao
The story heights from beam centerline-to-centerline were 279 mm for
levels one and ten and 229 mm for levels two through eight. Each of the
tht""'ee bay widths were 305 film from column centerline-to-centerline (Fig.
2.2).
29
The reinforcement was proportioned in relation to an effective peak
acceleration of 0.4 g. The first-level columns and the interior second
level columns had a reinforcement ratio of 1.32%. All other columns in the
structure had a reinforcement ratio of 0.88%. The flexural reinforcement
ratios for the beams were 1.10% at levels one through seven and .74% at
levels eight through ten (Fig. 2.2 and 2.13). The design base shear coefficlent
was 0.24.
6.3 Test Procedure
The test structure was subjected to three earthquake simulation tests.
The input motion for the three tests was a scaled version of the north-south
component of the earthquake recorded at El Centro, California (1940). The
acceleration level was magnified for each test run. The maximum recorded
base acceleration for runs one, two and three were 0.4 g, 0.95 g, and 1.42 g,
respectively.
Before and after each earthquake simulation test, the structure was
given a low-amplitude free vibration. Also after each earthquake simula-
tion test, the structure was subjected to a steady-state test by means of a
sweeping sinusoidal base motion. Table 3.1 summarizes the testing sequence.
6.4 Behavior of the Test Structure
One of the striking features of the observed response of the test
structure was the apparent domination of the first mode. As seen in
Fig. 4.7 through 4.24 the response histories for each particular test run
were in phase, especially in run one. However, the influence of higher
modes can be seen in the acceleration histories of both runs two and three.
30
In general, the apparent natural frequency decreased with the maximum
amplitude of motion previously experienced by the test structure as shown
in Fig. 5.10. However, frequency measurements differ as a function of the
amplitude of motion of the particular test to measure the frequency. The
measured frequencies from the free-vibration tests were consistently higher
while those from the earthquake simulation tests were consistently lower.
A similar trend may be seen to have occurred for the measured second and
third-mode frequencies. Table 5.1 summarizes the measured frequencies of
the structure.
Damping factors obtained from the free-vibration tests using the
logarithmic decrement method, were found to have increased after each
earthquake simulation test. The measured equivalent dam~ing factors are
given in Table 5.3. A similar trend can be seen in the results of the
steady state tests (Fig. 5.9). The amplification ratio at apparent resonance
decreased from test to test, especially from the first to the second test.
The response maxima of the earthquake simulation tests are summarized
in Tables 4.2, 4.3 and 4.4. The maximum tenth-story displacement in the
design earthquake test was 23.6 mm, or 1% of the height of the structure.
The maximum inter-story displacement was 4.8 mm, or 1.7% of the story height,
occurring between the base and the first level.
The maximum observed displacements in the design earthquake test
along with maximum displacements indicated by various linear dynamic
response analyses are shown in Fig. 5.12. The linear analyses included
a substitute-structure model based on both the assumed and obtained response
spectra. An lI el as tic" analysis was made of the structure using the gross
section stiffness for the components of the structure. The displacements
31
indicated by the elastic analysis are appreciably lower than those observed.
Although the substitute-structure analysis indicates displacements compar
able to those observed, the calculated displacements at the lower four
stories were exceeded during the design earthquake.
The maximum observed base shear during the first run was 15.6 kN,
or 0.35 W, where W is the weight of the test structure. The elastic
analysis (based on response to measured base motion at a damping factor
of 0.1) described above indicates a maximum base shear of 24 kN, or 0.54 w. As might be expected, the elastic analysis indicated displacements much
lower and forces much higher than those observed.
The maximum observed base shear versus the maximum tenth-level
displacement in the earthquake simulation test is presented in Fig. 5.20.
The plot suggests that general yielding of the structure was reached
during the "design earthquake. 1I However, the crack pattern in the structure
after run one (Fig. 4.27) showed little visible damage to the structure.
In fact, most residual crack widths were too small to measure (less than
0.05 mm). The crack pattern in the structure after runs two and three
(Fig. 4.28 and 4.29) showed spalling at the exterior base columns and
substantial cracking throughout the structure.
Based on the little apparent damage incurred to the structure and
the ~aximum observed displacements of the structure during run one, the
structure was well behaved during the "design earthquake". However, the
fact that observed displacements at the lower levels of the structure
exceeded the displacements indicated by the substitute-structure analysis
suggests that modifications need to be incorporated into the design process
at the lower levels of the structure.
32
LIST OF REFERENCES
1. Aristizabal-Ochao, J. D., and r~. A. Sozen, IIBehavior of Ten-Story Reinforced Concrete Walls Subjected to Earthquake Motions,1I Civil Engineering Studies, Structural Research Series No. 431, University of Illinois, Urbana, October 1976.
2. Clough, R. W., and J. Penzien, Dynamics of Structures, McGraw-Hill, 1975.
3. Gulkan, P., and ~1. A .. Sozen, "Response and Energy-Dissipation of Reinforced Concrete Frames Subjected to Strong Base Motions,1I Civil Engineering Studies, Structural Research Series No. 377, University of Illinois, Urbana, Hay 1971.
4. Jacobsen, L. S., II Steady Forced Vi bra ti on as I nfl uenced by Dampi ng, II Transactions, ASME, Vol. 52, Part 1, 1930.
5. Lybas, J. M., and M. A. Sozen, IIEffect of Beam Strength and Stiffness on Dynamic Behavior of Reinforced Concrete Coupled Halls,1I Civil Engineering Studies, Structural Research Series No. 444, University of Illinois, Urbana, July 1977.
6. Otani, S., and M. A. Sozen, "Behavior of t1ultistory Reinforced Concrete Frames During Earthquakes,1I Civil Engineering Studies, Structural Research Series No. 392, University of Illinois, Urbana, November 1972.
7. Shibata, A., and M. A. Sozen, "The Substitute-Structure Method for Earthquake-Resistant Design of Reinforced Concrete Frames,1I Civil Engineering Studies, Structural Research Series No. 412, University of Illinois, Urbana, October 1974.
33
Table 2.1 Flexural Reinforcing Schedule
Level Number of No. l3g Wires Per Face
Beams Interior Exterior Columns Columns
10 2 2 2
9 2 " II
8 2 " II
7 3 II II
6 II II II
5 II II II
4 " " II
3 " 2 II
2 II 3 2
1 3 3 3
1 .
2.
3.
4.
5.
6.
7.
8.
9.
10.
11 .
12.
13.
34
Table 3~1
Sequence of Test Procedure
Free Vi bra ti on
Earthquake Motion Run 1
Free Vibration
Steady State Run
Free Vibration
Earthquake Motion Run 2
Free Vi brati on
Steady State Run 2
Free Vibration
Earthquake Motion Run 3
Free Vibration
Steady State Run 3
Free Vi bra ti on
35
Table 4. 1 Spectrum Intensities for Observed Base Motions
Spectrum Intensity, mm * 10-3
Test Run Dam~in9 Factor B
0.0 0.02 0.05 0.1 b 0.20 1 0.598 0.378 0.299 0.241 O. 199
2 1 .061 0.671 0.534 0.433 0.362
3 1.274 0.799 0.634 0.517 0.435
Note: Housner's Intensity over a period range of 0.04 to 1.0 sec.
Table 4.2 Observed Maximum Single-Amplitude Horizontal Accelerations
Story Acce 1 era ti on, g Level Run 1 Run 2 Run 3
10 0.76 1 .24 1.64
9 0.60 0.87 1.06
8 0.51 0.67 0.73
7 0.49 0.59 0.72
6 0.41 0.54 0.78
5 0.40 0.68 0.74
4 0.43 0.81 0.78
3 0.46 0.77 0.77
2 0.50 0.66 1.09
1 0.40 0.59 1 • 21
Base 0.40 0.93 1 .42
36
Table 4.3 Observed Maximum Single~Amplitude Horizontal Displacements
Story Displacement, mm Level Run 1 Run 2 Run 3
10 23.6 51.2 68. 1 9 22.8 48.6 66.3 8 21 .3 46.3 60.9 7 20.7 44.5 57.4 6 18.6 40.6 52.2 5 16.7 33.0 40.0 4 14.4 31.0 38.3
3 12.3 25.7 30.0 2 8.3 16.7 20. 1 1 4.8 9.9 11 .9
Table 4.4 Observed Maximum Single-Amplitude Story Shears and Base Overturning Moment
Story Shear, kN Level Run 1 Run 2 Run 3
10 4.0 506 7.4 9 5.9 9.4 11 .0
8 8. 1 11.8 13.2
7 9.6 13.0 14. 1 6 10.9 13.7 14.3 5 12.3 14.0 14.8
4 13.3 14.9 14.9
3 14.2 15.8 15.4 2 15. 1 15.6 15.2
1 15.6 16.5 16.2 Overturning Moment, kN-M
Base 25.3 31 .4 30.0
37
Table 5. 1
Heasured Frequencies of the Test Structure
Test
Earthquake simulation
Free Vibration
Steady State
Test Sequence
After run 1
After run 2
After run 3
Run Frequency
Hode 1 Hode 2
1 2.0 7.7 2 1 .4 6.2 3 1 . 1 5.4
before run 1 3.2 15.6 after run 1 2.9 10.6 after run 2 2.3 8.7 after run 3 1 .9 7.5
after run 1 2. 1 after run 2 1.7 after run 3 1 .4
Table 5.2
Maximum Amplification Ratio and Apparent Resonance from the Steady-State Tests
t1axi mum Amp 1 i fi ca ti on Ratio
5.7
4.1
3.8
(Hz)
Mode 3
15.0 12.3 9.6
26.5 19.0 15.4 12.9
Apparent Resonance (Hz)
2. 1
1 .7
1 .4
Test Sequence
Before run 1
After run 1
Before run 2
After run 2
Before run 3
After run 3
Analysis Type
38
Table 5.3
Measur~d Equivalent Damping Factor from the Free-Vibration Tests
Damping Factor
'1.9
5.6
5.8
7.8
8.4
10.2
Table 5.4
Calculated First-Mode Frequencies of the Test Structure
First r·1ode Frequency (Hz)
Substitute-structure
Gross-sect; on
E E ~
en
"0 ~Q) -fI) fI) 0
Q) ~ ~-t/) Q) oQ)Q) c: fI) 0 1: ~ E c
fI) 0 0 Q) .- co U :E evo,-en a:::UlJ...
39
~ o~ > +-c: 0 '-
I.L.
-.c
~ CD
>
-C
OJ S-;:, ~ u ;:, S-~ (/')
~ U')
OJ t-
. N
0') or-l.1.-
305 "I'
40
i..r- Symmet r ic About i I
305 305
:~=::::!-J!==~I ---,°0 ° ~~=~-===-i----I°O°
Typical JOintlY °0° Reinforcement: I No.16g Wire
r-~~~~~~~~~t:~
Typical Shear ~ ~ V :0: No. 16g Wire .~ F I Tubing
130.0. Reinforcement: r= ~ 0 V
:c~~~~~~~~=~ood TYPical!
L V °0° a.>(\J_No Typical Flexural v r ______ Reinforcement: ~ ~ I
No. 13g Wire ~
Cut Off For~ ~~~~~~~~::~OOO Interior Column Steel --~~-----------
~ L °DO Cut Off For I
Ext e rio r -+,--/'----,---~:=4_P_---4_4I---~~ Column /V L 0 . ..._------.0
Steel ~ f(') v f(')
[ 1 ~ i I 1102
f(') I I I .L...,_L" --~ II1I \ J
I I I I 1 1 1 1
I I II I
'I ~Conduit\ " 440.0.
i i 1 305 1761
T '" 1372 ~ go I. ul-~---n -F--I e-x-u-~-~-! _--.. ~~~.-+I-"':"';::''':'''''='-----------------'l Re rntorcemenf weld~ To 102 x 51 x 3 Ft
v U') (\J
I
Fig. 2.2 Reinforcement Detail and Dimensions of the Test Structure
(All Dimens ions In Meters)
Steel Reference
Fram.~
Hydraulic
Steel Pedestal
o o
I.· 091 2.29 091 0.91.1 091
Fig. 2.3 Test Setup
r Test Structure
t:i'D, --
"': (\/
.,J:::oo --'
42
. N
or-u..
C'
c: .2 ~
0 II. CD CD 0 0 <t
c1 d txJ C) ~ '-1 ~:) 1·-' ~... (0 r".J 1. 1, 0 '··1 c-\- , P '-·l Gl 1-" t..:l ~. 5 (:) \. J '.0 ~'.\ C) ~_Tj ., rn' \:' i (;)
.•. 1. 10 (.1; HJ I I ) . - ( '~1
\f;i' \\ ~:~. - , ' (,~ \ '
\ ' t)"l I\ • .1 \.::
(<') ()
,-.) '<" i~ ltJ
C,· :.:,:J .....
1;·\ ~ .. !
1,1 J
c';' \_.\ -.j
(!) ~ .. t;)
.f\I
1.0
~o
/
30 20
-..- Frequency, Hz
10 0.1
V
0.2 0.3
Maximum Base Accelerat ion 0.4 g f3 = 10 Cfo
0.4 0.5 0.6
Per iod, sec.---
Fig. 2.5 Design Spectrum
~ w
0.7
44
G) "C 0
::E "C ~
.s:::. l-
Q)
"C 0
::E
"C C 0 (.) CD en
CD "C o
::E
V)
t: a
.r-~ ~
r--~ U
r--~
U
OJ U s-o
u... s-a 4-
-c OJ V)
~
V)
OJ C. ~ .c V')
OJ -c a ::E
\0 . ('\J . 0')
.r-lJ...
.,..
Level
@)
o ®
o ®
®
®
®
®
CD
33
o
I 1 85
47 vstrength Provided
58 I
80 I I
87 vstrength Provided
95 1 125
104 I I
112 1
I III 1
I 98 I
I I I 50 100 150
Moment (N -m) (RSS)
Fig. 2.7 Design Beam Moments and Strength Provided in the Beams
____ ........... ~ ___ ... ~ ........ ~ .:ICiiI..1ll 0IIII::.. ......
+:=0 U'1
Level
® -
®
®
o ®
®
~
®
®
CD
o
170
!.-
340 ~
400 ..
440 .. 500
... 560
600 .... 700
.. 650
930
I J 500 1000
Story Shear Force Exter ior Columns (N)(RSS)
o
410
1170
1200
1390
1130
500 1000
Story Shear Force Interior Columns (N)(RSS)
Fig. 2.8 Distribution of Column Design Shear Forces
~ m
Level
@
®
®
CD
®
® 0)
0)
®
CD
o
0.2
Q3 11.5
--.J. 5 o 5 10 15 o 100 200 300
-4-Tension Compression ------Moment
Axial Force Exterior Columns (kN)
Exterior Columns (N-m)
Fig. 2.9 Design Axial Forces and Moments for Exterior Columns
.po -......J
Level
®
® ®
0
®
®
~
®
®
CD
110.6
1 11.1
1 11.7
12.2
I 2.8
13.3
13.9
I 4.4
o 5 10
Compression ---
Axial Force Interior Columns
37
35
o 100 200 300
Moment Interior Columns (N-m)
Fig. 2.10 Design Axial Forces and Moments for Interior Columns
.,J:::o. ex>
30
20
t c:: .2 fI) fI)
CD 10 ~ - Q.
Z E .¥ 0 _ u
CD 0 ~
0 0 LL
c )(
<X c: 0 fI)
c: CD 10 t-
t
~~ ~ ~ ~~ ,.......~
~~ Ilnl 0111 0 I L'_J • I
2 # 13g Wire Per Face Exterior Columns: Levels ® ....... 0Q1 In ter ior Columns: Levels @]--OQ]
3 # 13g Wire Per Face Ex ter ior Columns: Leve I CD Interior Columns: Levels OJ a ~
CP--.. Key:
~ •
200 <D 300 400
Moment (N-m)
Figo 2.11 Interaction Diagram for Columns
CD Exterior Column +:=0 Level i 1.0
OJ Interior Column Level i
500
Level
@
®
®
0
®
®
®
®
®
CD L 0 100 200 0
Moment Exterior Column (kN-m)
(Softened)
100 200 300
Moment Exterior Column (kN-m)
o 100 200 300
Moment Interior Column (kN-m)
Fig. 2. 12 Distribution of Moments in the Columns from a Softened-Exterior-Co1umn Analysis
01 a
Typica I Top lColumn Detai I
Cutoff Point For Additional Reinforcement
No. 16 g Wire Spirals ~
31.8 0.0.- Pitch = 10 ~
Typical Detail
51
I-·r-----,.--------------~~--~ I
76
No. 13g Wire - See Frome Reinforcing Schedule For Number of Bars Per Face
., •• I
'lJ ;'. -.. , : . ,
'. ! :. :~
38
:'~' .. : :',:' : I •• ••
' .. :.,~': .. ' .-' . :-. :.
:~.'::.' :, Ii.:' :_,'f.' .:?~~
51 t ' "A" ItAII cion M-M
25.5 25.5
Section "8"-"8"
(All Dimensions Are In Millimeters)
Spirals
12.7 0.0. x .56 Thick Tubing
5 CL
Fig. 2.13 Typical Joint Detail in the Test Structure
Fig. 3.1
Wire
Free Vibration I. Weigh t Hung from
W ire to Displace Structure
2. Wire Cut to Re lease Structure
Free Vibration Test Setup
Pulley
45 kg
01 N
53
5000.0
()
2000.0
1000.0
~ 500.0 " . ~
~ 200.0 .... ~
~ 100.0
so. 0
10. 0 '--~-'--~_~~"""---:Iw'-'---.::IoL.---J 1.0 2.0 5.0 10.0 20.0 SO.O
tlWING FFCTOR = 0.00 0.02 0.05 0.10 0.20
Fig. 4.1 Linear Response Spectrum, Run One
tt.OO
3.50
3.00
2.50
(!) . is 2.00 .....
~ 8 1.50
~ 1.00 J\ ~
~ 0.50 ~ !/J ---£. ~ ~
0.00 110 30 20 10 5
I
ISO.
lijO.
120.
I
I
i 100. I
j
i
i ~ 80 •
IJ ., ~ ..J SO. ~
\\ f\
$ l , ~ - to... _____
..... Cl
qo.
20.
o. 11.0 so 20 10 5
0.2 O.Y. 0.6 0.8 1.0 0.2 FAEQUENCY.HZ PERlrD.SEC FfEQl£NCl' • HZ
DfttPING FACTOR = 0.02 0.05 0.10 0.20
Fig. 4.2 Linear Response Spectrum, Run One
D.I! 0.6 0.8 PERlrJO. SEC
i
1.0
01 ...f::a
55
2000.0
1000.0
u ILl 500.0 Cf)
"-.. :E :E
.,: 200.0 t--H trl 100.0 >
so. 0
10.0--~~~~~~~--~~~~
1.0 2.0 s.o 10.0 20.0 so.o
FfEQlENCY, HZ.
OFI1PING FACTOR = 0.00 0.02 0.05 0.10 0.20
Fig. 4.3 Linear Response Spectrum, Run Two
It.oo
3.50
3.00
2.50
C)
~ 2.00 ~
~ ffi ~ 1.50
1.00
0.50
0.00 llO
~
/ ~ 1
~I I
'\ [ 1\ \1\
A ,)l bJ ~ \~I\ ~ -- l\~
160.
lllO.
120.
100.
i ~ 80.
u ~ 60. .... o
\ ~ ~ !'... ,.,,---
'1O.
20.
30 20 10 5 0.2 O.ij
FREQL£NCY. HZ
-~~ ~ -o. --
llO so 20 10 5 0.6 0.8
PER Im tI SEC 1 .. 0
FAEQLENCY tI HZ
DAMPING FACTeA = 0.02 0.05 0.10 0.20
Fig. 4.4 Linear Response Spectrum, Run Two
0.2 O.ij 0.6 0.8 PEA I tm .. SEC
tTl 0)
1.0
57
srnro.o--~~----~~~-----------
2000.0
1000.0
u w 500.0 (f)
"-. x x:
>= 200.0 to--is .-J
100.0 UJ >
50.0
10. 0 ~~-'-----lro.o'----'-~"--J.. __ ~"--~---'
1.0 . 2.0 5.0 10.0 20.0 50.0
FREQUENCY, HZ.
DAHPING FACTOR = 0.02 0.05 0.10 0.20
Fig. 4.5 Linear Response Spectrum, Run Three
8.00
7.00
6.00
5.00
(.!) . l5 ij.OO -I--ffi ~ 3.00 u a: ~ 2.00 ~
1.00
0.00 llO 30
liDO.
350 ..
I
300.
250 ..
~ . ~ 200.
j
~ ~\ ~'
~ ~~ f\ --........... r\~ ~'" l \.. ~~
i ~ 150. ..... Cl
/
/" Ji C ~/ 1c2 V
tOO.
~ ~ - ~~ ,,","- ~ ~ :::.--so.
20 10 5 0.2 o.q
FREQUENCY, HZ 0.6 0.8
PERIOD. SEC 1.0
o. 1lO
...... W 30 20 10 5
0.2 FP8l.£tCr .Hl
DftPlOO FRCT~ - 0.02 0.05 O. to 0.20
Fig. 4.6 Linear Response Spectrum, Run Three
0." 0.6 0.8 PflUm, SEC
t.O
U1 0:>
TENTH LEVEL ACCELERRTIBN. UNIT = G 1.00
0.00
-1.00
NINTH LEVEL ACCELERATION, UNIT = G
-1.00
1.00
T ._ f\ ,. . .f. I I~.k f\ J1.... I\.A.. _., . L........ _ h f1 \. A A .A'\. A. -L • ...L ~_.- ......... -., -"--.. •• -A. /'\. ~ __ _ 0.00 1 M' II II , \l> (\ '" 'r'LL' " "" r \ r. .,... .... A. •• ----..........p............-
'Ib" '" ~ v v, v v ~ ~J' '~v V ~ 'T-~ c;s>-n~ accr - ~ ,.,... ~ \1 ~.
EIGHTH LEVEL RCCELERATI~N. UNIT = G
-1.00
1.00 I-.... ~.A A f\ A 1\ ""- --,.. ••. ' ~ A A A ..... "" • • ..... - - -...-,....... fi" .... - (J1 .. 'J f! V \IV \.{ ~ V V v~ V ».-" GO;? V ~....... t..O 0.00
SEVENTH LEVEL RCCELEARTI~N. UNIT = G
-1.00
1.00 I '. .' ...... .',~A /\ A. 1\,....", .f'"' ........... , A. I'\. ~~"" I'" . "'- __ ........ .- _ ... ~ ......... ,...... ,-.., YV'V"\rV ' ~V~ 'IJ - V .... ...... ... V~ ----0.00
SIXTH LEVEL ACCELERATION. UNIT = G
-1.00
1.00 I . A .1\ f\J'i.. A............. fo.. ~~=- -"' -.... - 'J-~~'-~~ 0
1'-"" ':T\Tv "\.IV .. ~v V "'V' V 0.00
T SEC 0.0 1.0 2.0 3.0 Y.O S.O 6.0 7.0 B.O 9.0 10.0 11.0 12.0 13.0 1lLO 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.7 Observed Horizontal Accelerations, Run One
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
FIFTH LEVEL ACCELERATI~N. UNIT G
1 .~/\(i.. A ...... ~. ;o,.A&",,~ .......... -- '-'_"''''' "(~I_'..I:\/"rv.V~ l.....,..~ v ~~v ... ..,.,... .. --.... 'tIQ' '"
F~URTH LEVEL RCCELERATI~N. UNIT G 1 .J". ;~ •••. ~ A.J.,o. .~ - .,. " ,.L. ~ -c"'~w- - ~. · ~v -....r ~~" FCVty.J.i."".....,.... ... _ '- ..... ~~""'" --
THIRD LEVEL ACCELERATI~N. UNIT G
l ,/. iz... _ ft~.,~ ""'-"~tI~_ /"'\.. ~.,I.~£ t.N-.. ~ J-A...~.~ ............. • ~ __ ~ _-L.L. _____ ,.~ .-. ____ _ 1 -~':J'f 'if 'if,......... _. --.,...,.,. -- ---... .... V-'~ ~ ~ .. n~ ..... ~.--- • .--~--..,
SECOND LEVEL ACCELERATI~N. UNIT G
L. AA:,t"". ....... ~ __ ........ _ ... ! .. ,~" ...... ..h... '""-, ........ ~. ~.~ ................ ~ .• h~.--<L _ I~'~''\7'T'!'¥ ,~,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,-,,,,,,,,-,,~-,P-~., •• ...,
FIRST LEVEL ACCELERATION. UNIT G
I ~~A ~ • '. • .. .aL.. • .. ~!\r~Jzyr~' "s 1j41~l'l"'f t ~~ ..... ",~ v;-....... 1. ... * .... iIAc' s, "o,t r\:!,,.... p\ t* '/~ -.,.. . ~ ,
BASE LEVEL ACCELERATION. UNIT = G
l. A f\ AM. b. .• Jt 1'1.. __ • ~ •• U_""-.M '" _ ........ .A. __ • ___ .~.~ A.A._ • ~ _ ~.~ l '" A ft. A ._. • ~ ____ _ 1 ~"""V'~"""f V--~·- ~T~""'-----'-'---~-'-' ,.- .--~--.. v- - - .-- .~~~~--
0'\ o
T SEC O. a 1. a 2. a 3. a Ii. a s. a 6. a 7. a 8. a 9. a 1 o. a 11. a 12 . a 13. a tl! . a 15. a • • I I I I I I I I I I I I I I I I
Fig. 4.8 Observed Horizontal Accelerations, Run One
TENTH LEVEL OCCELEMT I (1.1. LN I T = G 1.00
0.00
-1.00
NINTH LEVEL Fl:CELEMTI~. LNIT = G
-1.00
1.00
1__~j\. flI. ~ A A A. A ..t\. ~~. .A _ --"- _ . -"-- .Jot<. • .AA.. A. -" .• ~ 0.00 1 ~ llV V '1~. v-~~ -vy Y 'iT- T .....,. ~- ~. - "'Tn to. ., ... ~ v·· ~
EIGHTH LEVEL ACCELEAATION. UNIT a G
-1.00
1.00 I ~ ~ h.~ kL,- ~ . .,.., "'?:n:e...Jl.,...,~ -- -~ ¥' V v"~ -vv~ V » .... I&f' ,... "V i. • ~ ... m ...... 0.00
SEVENTH LEVEL ACCElERATION. UNIT = G
-1.00
1.00
1 ' . ill .. . _ . ..1\ A ~ A ~).A... A.JIk ~ ..A..- ... ~ ___ ~ ~ _._.~ • ...a.... J&.. ___ 0.00 [~V-V-- ..... V ......, V· --V V' .."...- ......... __ . ~ . ..,,-..........---m ........ ~ .. -
SIXTH LEVEL OCCElEA1TI~ .. ~IT a G
-1.00
1.00 I .d·~A .tb. · · A' . f'"" .JtA...... s,.., • ~~ l.a.& _ ~~~. ..- ~ .... ......-- 'I' ""'-r .......... · 0.00
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 1ij.0 i5.0 • • I I I I I I I I I I I I I I I I
Fig. 4.9 Observed Horizontal Accelerations, Run Two
1.00
0.00
- 1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
1.00
0.00
-1.00
_~ ~_ L _____ ~ __ ~ _ __________'_ _________ J __ _ .--- ------, - ---------- r------ ---.----~~~y-~-----.-------.
FlFTH LEVEL ACCELERATION. UNIT = G
~ .. A. J,./\,.....Jrn,.. A &.A _ ~~ ___ . _~ _ _.~. ~."..J.A..l. L..I. J......... r--....-----.·- \fT- '-MT ~- -~ ~ - -~.... T ____ v------- -........,....-- - ~ ~T~---.....
nr ,
FOURTH LEVEL ACCELERATlON. ~IT = G
T t1tA I. .,. ~ , .11 _.I~Ii~...a ~ s-n.. .A41. .~. .J'-... .Js..... . " . .L. _ __ ~'" _ ~ __ ~~_. !!dL. . ___ ~'t.'!....... ~_
"THIRD LEVEL ACCELERATION. UNIT = G
SEC~D LEva OCCELERATION. ~IT = G
FIRST LEVEL ACCELERATION. UNIT a G
1.00 BASE LEVEL ACCELERATI6N. UNIT = G
O 00 1 -A A~~ 11..6 t\. ............... ftAIAM!\ft .. A • eJ.",~. ~ Mo' - .... ~ .... -.... ~ M - h ••• 1 '" A AJ. --- ---.u. i .. 1A_"4Ctu *, .v~.., ,,{fA. .\1F,QCI •• ... _v,. .1 .... ...... 1J.~,~.:r .. ;lf4tVUcrQ L.I~'.W.~
-1.00
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.10 Observed Horizontal Accelerations, Run Two
en N
2.00 1 TENTH LEVEL FCCELEffiTI~. lfjIT ~ G
• r,. ,\ A ~ 0.00 • ..6l\i.J, A·~ ::I~_ A'Jwe·~t rl ('+.'-""$4(. .,.......... .... w.o",M., lwb ¥' '." ,. - i '.-. « ,., »r". rCFtc>
-2.00
NINTH LEVEL ACCELEfJITlrJ.l .. ltIIT = G 2.00 T
~ . !, ~. ' - -"---- ~ ~~- - ~ - ... ~ ----------------
SEVENTH LEVEL ACCELERATION. UNIT • G 2.00
T __A .. ~ ....... _~ . .Ao.- __ __ ~ ~ ___ .• _~ ___ ~ 0.00 1-~ . -. y .....-.~ .. -....r .. --_. - .~ .... ~
-2.00
2.00 I . SIXTH LEVEl FCCELEffiTI~. lfjIT - G
0.00 Wi ~""""""~""'''''' "¥' ~ -s+ • ~. Jp '9 • ' • ...".« bay J. dp':"_
-2.00
O'l W
T SEC 0.0 1.0 2.0 3.0 ~.o 5.0 6.0 7.0 8.0 S.O 10.0 11.0 12.0 13.0 1~.0 15.0 • ., , , , , , , I , , I , I I I I
Fig. 4011 Observed Horizontal Accelerations, Run Three
2.00 1- FIFTH LEVEL RCCELERATION. UNIT :I G
»A O. 00">o:.? ~W,;;n...,. -¥ - ~ "c I « • , r \: hA V,. ) cp. "'" ... ftc • .. -
-2.00
:::: T .~~~~.JI ~~~. b,',."" F=H.~EV~~ ~~:~:~':'IT Q G -2.00 r
2.00 1- THlf{) LEVEL ACCELERATION. UNIT = G
, 1\ A - " ,~ 4 ~ . \-0.00 1l'riW ,crt .. 4'\A"' ,,- ", • .,. Mr \f-c/'f" (dIO-' ·IS·' 'vA,. ..... <-,..' ~ p , • • I· 1" C ;" , »4Qi~" ,
-2.00
2.00 1- SECtl4D LEVEL FO:ELERATJON. UNIT = G
• ~ I'
0.00 ''''''''''T~~I ...... ~ 'IA "'''II \:1';/'&"1*;";, <rl~ 0''*- -..,c; .. reO ....... ,n HI •• ""\ ... ' ... , .. _".» a\ Y •• 'Ii
-2.00
2.00 ~ FJRST LEVEL ACCELERATION. UNIT • G
~ {I. ,.' • \ • ~ ..... ....a .. " • ' A.. '" A+ L. 0.00 ~~I ttY" pi"lt.d-'::;t y u.*t~ ... r ... ,,-+-er+ ...... vI-¥' ...... - •• If"tt .. ~.t.. .. , v ,..-- ., ~ --. 4._ W'T • ". I
-2.00
2.00 ~ BASE LEVEL ACCEl..Eff:lTI~. UNIT = G
ft .1\1\. "d~ __ A.A" 0.00 ~Mr'V if .-~vlfF~ ..... J ........ ~ .. ·.M.).,·~ ............. 6.,. __ ,A-A •Al 1-t',h --- ... -ifWV lVr ~..... "i1r.ri.... • •••
-2.00
Q) ~
leSEe,OiO liD 2 j O 3 j O qjO SiD 6.0 7.0 B.O 9.0 10.0 11.0 12 0 13 0 14 a 15 a I I I I I I I • I • I • . I •
Fig. 4.12 Observed Horizontal Accelerations, Run Three
20.0
0.00
-20.0
20.0
0.00
-20.0
20.0
0.00
-20.0
20.0
0.00
-20.0
20.0
0.00
-20.0
BRSE LEVEL H~HENT, UNIT = KN-H
TENTH LEVEL 01 SPLRCEHENT , UNIT = HH
NINTH LEVEL 01SPLRCEHENT, UNIT = HH
EIGHTH LEVEL OISPLRCEMENT, UNIT = HM
T " ,A A A f\ /\ ~.~ A>-<. f\ /\ !\ 1\ 1\ ~ A/', "- ~ "",f\ 1\ f\. ~ _______ _ /.\ I \ I \ ".... ,.... _._ I \ I \ I \ I \ f \ I \"""""""c/' ~ ...-.~WV V 4C7 r -'.1: \ I \ I \ I \I V\""V'""',V V V V V V d=JVVV J
" ~
SEVENTH LEVEL DISPLACEMENT, UNIT = MH
T Iv. A A 1\ 1\ ~._ ..-... i\ /\ /\ 1\ f\ ~ A..r> "- ~.,... /\ t, ,-, ~ _______ _ r"'>... ~/\I\-... ~ 1 \ I \ I \ I \ I \ I \.~ ~ ...... ~~ V V \07 ro~vvv \J V~VV V V V V J \I
20.0 ]-, SIXTH LEVEL OJSFLRCEHENT. UNIT = HH
o 00 -~ difI A !\f 1\..- ~ i\ f\ !\ !\ f\ f\ Q '" r.. - ~ t\f\ A ,... • o. • V V V V \J ''\I V VVVV V ~ ~.... \IV""'
J \
-20.0 T SEC 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0
, • I I I I I I I I I I I I I I I I
Fig. 4.13 Observed Base Overturning Moment and Horizontal Displacements, Run One
0'1 tTl
20.0 FIFTH LEVEL OrSFLRCEHENT. UNIT = HH
f ",j1 1\ f\ i\ f\~._ r=. 1\ 1\ f\ f'\ A c\ 6 ~.., " _ ~ A"\ A C\ = I Vl/lJ \/V V '~\J VV'J V ~ ~-- 9Qr\TV VI
0.00
" , - 20.0
20.0 1f ~ FOURTH LEVEL OISPLRCEMENT. UNIT = MM
0.00 ~(i. 1\ 1\ {\.... f\ ~ ,........." i\ 1\ /\ /"\ f\" r-.. A"""" ~ ~A C\ \J VV \TV V ''\I V V\J~ \r ~ V ...-..... V V '>07--
- 20.0 20.0 1f THIRD LEVEL OISPLRCEHENT. UNIT = HH
O 00 ~ A 1\ f\ 1\... !\ ~ ,.......... 1\ f\ A " /'\ "-. ~'VVV\)\TV' - -~~ _,../"\6 .. ~VVV~V ~'V-""""""VV""'"
-20.0
20.0 SEC~O LEVEL OISFLRCEMENT. UNIT = HM
0.00
-20.0
:~~: 1f A~..../'= = -./''"'"',-",...,~=~~_= FIRST LEVEL OISPLRCEHENT~U~~ = HH
-20.0
0.50 BASE LEVEL RCCELERRTIeN. UNIT = G
1 . ..Ah ~~,IJ...J(\ ~A~ ~~~f#"'.NoNM""'M",AJ"" J~/'''''ofAr' 0.00
-0.50
0'1 0'1
T SEC 0.0 1.0 2.0 3.0 q.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.14 Observed Horizontal Displacements, Run One
30.0 1 ,', " " BASE LEVEL HCJNENT. UNIT = KN-M
0.00 -~ ....... '"'" /"\ .......... ./"'0.. ....... ..,A.......,...... \, ~"V' """V ~~ V"-
-30.0
o 00 -~ f\cxr?'L f\ !\ f\ f\ 1\ -- A /'- ~ /\ r\. A A
50.0 1 . " . TENTH LEVEL DISPLRCEMENT. UNIT ~ HM
· "VlJ \/ V\} \) ~ <;?----50.0
50.0 I ' .. . NINTH LEVEL DISPLRCEMENT. UNIT = HM
0.00 ~f\ f\ 1\ - r.. /"\. ........... ro.. 0, '" " ...... , . ~ \T\T~~~ V~ ~ <;;;? --
-50.0
50.0 EIGHTH LEVEL DISPLACEHENT. UNIT = MH
1_ .f... 1\ .. ~ !\ f\ f\ f\ 1\ r.. /'0 _____ ro.. /'. A " 0.00 r ~ V V' V V V "'J vv- 'V ~ ""V V'CT .... · \T~----------50.0
50.0 SEVENTH LEVEL DISPLACEMENT. UNIT = MH
a 00 I J\~!\ f\ f\ 1\ 1\ = A -'""' --= ro.. /'.. A '" .... · . \TV \jVVVVV-~ V ~V ....... -50.0
50.0 SIXTH LEVEL DISPLACEMENT, UNIT = HM
0001 .1\/\ ~ f\ !\ I\. f\ /\ _ A /"'0. ~ C\ .r....~ '"' ......
· -- V ~V\J\J"'\}VV"" ~ ~-----50.0
C)
'-J
T SEC 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.15 Observed Base Overturning Moment and Horizontal Displacements, Run Two
so.O
0.00
-so.o 50.0
0.00
-50.0
FIFTH LEVEL DISPLACEMENT, UNIT = HM
1 I\f\~ (\ f\ A f\ A _,.., ""' == /"'. ~- ~~ ~ \ 1\ / \ I~) \ ~, /\ 7~ 7' "-J c;;;r ~ \ 7~'>wif~=r'='
FOURTH LEVEL DISPLACEMENT, UNIT = MM
1_ 1\ f\ ,...,......., !\ A A 1\ /\. ~ r--.. .........--".. ~ I ~ v v V v V 'V v ~ -......... "'--'" .~. ""V7 ~~'T~
SO.O 1" THIRD LEVEL DISPLACEMENT, UNIT ~ MH
O 00 /\ D ~ I\. /\. "'" 1\ /'\. _ "", """' "".-..... .... . '9 V ~\T~V "-l~~ .......,. ~ -=0;;:::;7 'V' '=""'- """"' ......
-50.0
:~~: 1" ~~=~~c/'=- ~ _ SEC6NO :~::MEN~UNIT ~ HM
-50.0
:~~: I ,.....,.,.......,. 'V'=-~= ........ """" ....... ""'~ ~ _ FIRST LE:L OIsrLACEHENT. UNIT ~ MH
-50.0 1.00 BASE LEVEL ACCELERATI~, UNIT = G
O 00 1" . A A~u.d"" .. - .... A.IaM& .. A .. IwI.AA..I' Ul.1 ..... ~ ..... A -IA ...... A,,, .6111 An A _. ~, -.rV~r'1I1{V ~ V· -1IV1jV"" rtrV '" 'II tqnv ~ .V'~""V.ovr if 0' v n.·,v," Q~h'" "'0"
-1.00
0"\ 00
T SEC 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 , • I I I I I I I I I I I I I I I I
Fig. 4.16 Observed Horizontal Displacements, Run Two
30.0 1 · BASE LEVEL HtlttENT. UN IT = KN-H
1\ ,\ " 1\ A.. f\ -'"" ' \ ~ ....--.. _ .L"' ~ ~ e-z
'id'V\J~V V' ... =- ~V I I, " .
0.00
-30.0 60.0 I TENTH LEVEL OlSPLRCENENT. UN1T = HH
T _ /\ A !\ A /\ f'--.... ___ . ../'... /\ L'-.._A __ _ 0.00 I '>d V V v v V '(:;::;7 ""''(7 V ---v~-v- ----
-60.0 " 60.0 NINTH LEVEL OlSPLRCEHENT. UNIT = HH
o 00 I j\ A !\ " /\ r-... -v ,0. /\ r--. /\ -. ,. v V VVV~ '(7 V\JV V -60.0 .... "
60.0 EIGHTH LEVEL OlSPLRCEMENT. UNIT ~ HM I 1\ A (\ " 1\ f"-..,..,. ~ /\ r-.. L\ 0.00 VV\j \J\./V~ V''C7~ ~V' V
-60.0 " . 60.0 SEVENTH LEVEL DISPLACEMENT. UNIT = MH I /\ A f\ I'\ !\ f'--,. ~ ~ /\ " ./\ 0.00 VVV ~~~'C7~~ V
-60.0 ~
60.0 SIXTH LEVEL DISPLRCEMENT. UNIT = HH 1 1\ A f\ A /\ f'--,. =- C'-. /\ " ./\ 0.00 'id~~vc-= ....... "C? 'J~""'" \V
-60.0
0)
~
T SEC 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 B.O 9.0 10.0 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.17 Observed Base Overturning Moment and Horizontal Displacements, Run Three
0.00 r F1FTH LEVEL DISPLACEMENT. UNIT = HM
...Av~C>~ = c-.. /'. c--,. ...0 V 'J V c:::::=;;> ....... """'" '\\J'" ~ ~ ~
GO.D
-60.0
60.0 r F~URTH LEVEL OI5PLRCEHENT'~ UNIT = HH
a 00 1\ ~ !\ r.. /\ f'--.... ,....... ~ /""\. C"", :;/'. . ~~ ~\ J\ 7 ~~\ ~~ ...... ~~ 7 """"" ~ " 7
-60.0
60.0 r THIRD LEVEL DISPLACEMENT. UNIT = HM
0.00 ~.....p..r----... - ,.-...... ........ -=- ......... ~ ~ '""""'""~ ~. \(7"
-60.0
GO.O r A 00 .--~~~~~~~~~--~~~--~~~~~~~~~~~~~~~~--------~~~~~~~~~~~--~~ -6~.0 ~ '7 ,,~......,.~ 7- ~==~ ..... ~ -=-.........
SECOND LEVEL DISPLACEMENT. UNIT = MM
60.0 r F1RST LEVEL OISPLRCEMENT. UNIT HM
000 .............. ~,....-..... ............... • "'C7 -...:0:7 ----- ........ 'C7
-GO.O
:::: r ~~ho~f\.,~t4(Vt .. ..t'bJ\AM~\/Av$v4M1'\'V"""""'.rl/.tb-\l .. JtA"r:"",,:V'.,,:~v:LA:C.:~:l~~ ~:~ .~ ",- ... .. •• .... #' "V-W .. '" ,\I'iV"i "1f1~-
-1.50
'" o
EC 0.0 T.S • I--1.0 2.0 3.0 ILO 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0
I I I I I I I I I I I I I I I
Fig. 4.18 Observed Horizontal Displacements, Run Three
20.0 1 TENTH STfFll SHEm. l.I'IIT - lIN
0.00 ' ~c/o ... J\., ..... ".,...- ..... "'- ........ =-,'-" .. -- -.-,
-20.0
20.0 1 NINTH STfFll SHEm. ltIIT c lIN
o 00 hoP. '" A A f'. • .... &!II~ ~~ ~..,... ..... • ~ A ~ -A... ...., c'tn _ .............. ~~..... ..,.. It 4 • ....,.,.. .........
-20.0
:~~ 1 . _,\nA A i\... A,-...... ......A A A. ...... ......... EIGHTH STllRY SHEm. UNIT • KN
_ -co: ~~~___ %::1' .......... ...,... .. ,--, .... rc=:Ptc:>..,..,.,
-20.0
20.0 1 SEVEtrTH STem' SI£AR. UNIT - lIN .
0.00 --tflAA A A ... A,e............ ....J')AA.6~ ~ ...... --~ ....... , ""-'1 _ <, ~.~"I" .,.,. ... A< .O .... fo .....
-20.0
20.0 1 SIXTH STfFll SHER'I. ltIIT - lIN
~ 1\. 0.00 .. , "1' f\ I\. /\-"'. .~t+ A 1\ 1'\ A ~-W\j \j V~ -r ·~V-V V'C>"'\/' ... .+ ............ ,... --... ~ A ~ -" ... '* ~-
-20.0
........ --'
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 B.O 9.0 10.0 11.0 12.0 13.0 lij.O 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.19 Observed Story Shears, Run One
20.0
0.00
FIFTH STMY SHERR. UNIT = KN I .. dV\ A A. /\ A. • ..., S • ~ i\ A A. ...... A ...., - ..... _ ... _ .. "" A ,.... -"~\f V V V~\.l -..., 'J V~.....,~ · '" 'V V~ <:>'
-20.0
20.0 I F~URTH STeRY St£AR. UNlT ~ KN
o.oo-""~\./'"'-",, .... s A. /\ r\ A A A _ <> _ ..... __ .... A '" '"'i, ~V~ ~ "'" -~ .... ~~-
~ .. -20.0
20.0
0.00
-20.0
20.0
0.00
-20.0
20.0
0.00
-20.0
THIRD ST~RY SHERR, UNIT = KN
L _ ;\A 1\ 1\ i\ 1\ "'""~ ~ i\ i\ J\. /'\. ... .1'\ /'\.. _ _ ~ __ -. _ _ ._~ /\ ~ .-.. _ r~JV VV V V _......... ~ V VV '-' V --~.- 'V'. -~V V ~
~ ," 1\ • SEC~IO STORY St£AR. UNIT = KN
_ f" f\ /\.A -'-4. 1\ 1\ 1\" /\ D b ..... C"> ~_ ~/\ ~...." <k,.l~A n), rv-' ~"\I\JV"V'"'V. - V -~ VV"'" -
FlRST STORY SHEAR, UNIT a KN
1 '~AI\' f\ _ .\ I\.A... • _..A..A. l\ 1\ 1\ " 1\ A -.,......... ~.- f) /'\. _ ~ r\/~ r\/ ~'ti\J\ I \ ] \/ V \~-,. ....,.. V --- -"'-1 \:~~-
0.50 BASE LEVEL RCCELERATION, UNIT - G
O 00 I · A A ~~. '" A '~IAtv..,;. 1\ .. ~Jo.At .. "'Y"' ", ... IL •• ~ .M.' A... .M\ A Ash .-. • ... '" · "11 If "*'11" I V"''' 1 .." •• " • 1', if ...... "...-9 V .... ""if ....- .. n
-0.50
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 , • I I I I I I I I I I I I I I I I
Fig. 4.20 Observed Story Shears, Run One
-.s N
20.0 1 TENTH STIfIY SHEIII. lJIlT • KN
0.00 .. '~b'-.'.& ~ ........ Jr. ........ .... • • + . ' •• -
-20.0
20.0 1 NINTH STIfIY SHEIII. lJIlT • KN
0.00 .. 1-0 ~ .. A Aa~ "- At\ WV ~ .... F ~"' .. Y -- ....... - • .. __ ..... j.·A ... ..... . ~ .........- ..... ~-
-20.0
EIGHTH SreR'Y SHERR. UNIT • KN
20.0 T . A .- -.~ - ~ "L ~ ~ _~ ___ --L..- _~ _~_. _____ ____ .--.
~ ,'-- ~ A eft::::, __ ~ .!.Lt, .... .... O 00 1 o/W '@f" ,.,.~("" ~"<iV --~ • .. - • .. - ••• .. .... . V" y~ '" y
\! - , " .
-20.0
20.0 } SEVENTH STIlRY 5I£RR. UNlT D KN
J\ I! :\ 0.00 ~ ~ .Po.. A. A F\ ~... .A. ~ dz WV ~~ V'40 -~ .... ......., ... _ .............. - -~. ..' ......... ..
-20.0
20.0 f SIXTH STIfIY SHEIII. lJIlT • KN
~ . 0.00 ~A.At. A. 1\ A -en .A.. «"'> ~ ~ . ttl V ~~~VV ....... ~ so v-V ~'V ........ ,...
'. \ -20.0
-.J W
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 1~.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.21 Observed Story Shears, Run Two
20.0
1,'. FIFTH ST"RY SHERR. UNIT = KN
__ .J\ A ~ A A .. A_A..- ~_~ -A ~. ____ ~ I'Ik._. A. .-.. . __ _ 0.00 ~VVU-V- ... \/_u.'-.7 V ~m V '\..r- - ~ ----. --~ V "-V '7
1 ." -20.0
~ . 20.0 1 FOURTH STIlRY SHEAR. UNIT = KN
0.00 1fC:J\ A f\ftt\ 1\ If\ A... A A r-"".....,A...... "-c:>~c JLjc::::3U~ ,..... _ ,...,..
-20.0
20.0 I' ~THIffJ STORY SHERR. UNIT = KN .
o 00 _~ A~ J\ I\. 1\ A ..... .... ..0. ~ ..... -- - ,... . ~ VV V-vy"\! VV .......... ..........~ ........ ~ --
-20 .. 0
:~ 1-<cJ\ /I. rb\ /\ A A /\ A ;.,",~..o.:c:=: : __ -20.0
20.0 I ~ FIRST STeRY St£RR. UNIT = KN
~OO b_~~~~
-20 .. 0
1.00 BASE LEVEL ACcaEPATIeIN. UNIT Ia G
1 Ah~LLA,., ........ ~Ad" ... Ik...A~,.u • ..h ....... _ ...... ~ ...... " .. A" ...... AU" • .a,un.A ._. ' __ ._0 0.00 J -..... V' ~r~f'l'V ,.",-"r" "',JP" .. V iii'" V r'V v 'w,.,. .. , v,· ... II" V· "'r" Viii" 'if' n·· -1.00
-.J ..J:::.
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.22 Observed Story Shears, Run Two
TENTH STff\Y SHEm. ~IT = KN
20.0 I _::~ 1~--~~W~~'~ .. ~~~~~-~'~fl~fc~~~~&L~~~_4~,y., •• ~~~~~~_·~.,~~ __ ~ __ ~ ________ ~, _____ -~.~~~~~«~,~.'~ • .------
NINTH STmy SH~. ~IT 1:1 KN 20.0
I ' II " • ___ &.f'v.--l ~~ ~ --l.... __ ~ •• ~ __ ~~~~~ ___ ~~_ ~_ _---"----~ 0.00 r- r~-'Y ~~. -y - - - ~- .. ~ - - ------r--- ~-~,~-~--.----,,-~~
-20.0
20.0 T EIGHTH STMY SHERR. UNIT 1:1 KN
;'.. n _ .• f. .... -~- - -- .......... ~ -- ~~ ~ ._ ...... ~ ------.- ----
SEVENTH ST6RY stERR, UNIT =a KN 20.0
1 ' . , n • _~ _,,~..... ~! ~ ...-'t... .-A.. _ ~~ _ ~---. __ _____ _ ~ --'- ~ 0.00
1--- -~ \~V ~ -,. y ~~~v r~.....-..- -~ - - ----------...-----..........--- -"'""':" -v-
~ '" -20.0
SIXTH ST~Y SHEfI'. lJUT - KN
0.00 I a ~ ~ · ~".-A.. .f\.. ~'" _.-.... ......... ," """~'k~. 'Y'''' - ~ ~. Av ~ ~
20.0
-20.0
-.J ()1
T SEC 0.0 1.0 2.0 3.0 ~.O 5.0 6.0 7.0 B.O 9.0 10.0 11.0 12.0 13.0 1~.0 15.0 • • I I I I I I I I I - I I I I I I I
Fig. 4.23 Observed Story Shears, Run Three
FIFTH STORY st£RR. UNIT III KN 20.0 T .
~ ~ ~
l\. _..1\. ___ tf\. ..... A ~ .,.~ ~_ ~ ~ ~ -'" -'- _~ ~..............-
FOURTH S1~RY SHERR. ~IT :a KN
1~ A ~ J\ ~ 1\ ~ ________ ~__ --"'" ~._~ 0.00 r ~ -v V V-."W' V ---- - ~ --.yr -~---..... V'
-20.0 20.0 THIfIl STORY StERR. UNIT = KN
O 00 I A rA- /\ ---.. AA~ . ~ ..A" -A ~ .... ~ -. VI" "V\I~vy - ... -..,. ......,...., V
-20.0
20.0 I . SECIlNO STORY St£AR. ltIlT • KN
!\ ~ , ~ ~/\ J\.~ + ~ ----'. n~ e
0.00 ~~ v - ........ .q~ ... ,..........."
-20.0
20.0 I A " '.. F1RST S'TORY S/£Afl. UNlT • KN .
I ~ /\ .. /\" '!:_ ~.-"". _ • 't'"Hn
0.00 WVVVV~ i -~~~ -20.0
2.00 BASE LEVEL ACCELERRlI~. UNIT III G
O 00 I ' A It ~6 /II.. ..... - •• \14; .. " # """Y''''' ~'., ----v - .... ~ .. A A •• ~., .• , ... A.A _. ..-.WV'" I' ~ ~y 'Y r r"~""Vv'''''' \1/ ...... y ... - V '1"Y'V.,v .... ".~ ..., .... ,.411,.,....,- ... -
-2.00
-....J en
T SEC 0.0 t.O 2.0 3.0 ~.O 5.0 6.0 7.0 8.0 9.0 to.O 11.0 12.0 13.0 14.0 15.0 • • I I I I I I I I I I I I I I I I
Fig. 4.24 Observed Story Shears, Run Three
1.5 I
/ -Ol / c 0 .... 1.0 c t-CD i CD () ()
« / CD I/)
c m / ~
~
E :::J E - 1/ )(
c ~
OIL __________ ~--------~----------~--------~----------~--------~ o 100 200 300 400 500 600
SIlO (mm)
Fig. 4.25 Maximum Observed Base Acceleration Versus Spectrum Intensity, S = 20%
78
~ . ~ J
(Not to Scale)
Fig. 4.26 Crack Patterns Observed Before Testing
79
\ ,
r.--
... ,. , ,
000 DOD DOD ODD .
uDD, .000 DOD DOD n
(Not to Scale)
Fig. 4.27 Crack Patterns Observed After Run One
80
~
I'
~ I
,
" I
, I J ...
,.
~ "\00--/ ,_
, ,
(Not to Scale)
. \\
\\1
Fig. 4.28 Crack Patterns Observed After Run Two
81
~ J
~
.1 ~ ,
'7
I ~ ,
(Not to Scale)
Fig. 4.29 Crack Patterns Observed After Run Three
82
c E ~
r--o
U
So
or-SOJ ~ X
l..LJ
C to
4-o OJ
"'C or-
a M . o:::t
or-L1-
83
0) 0)
>-..c I--
s::: ;:,
0::
s::: E ;:,
r--o
U
So
or-SO)
of-> X
W
s::: co 4-o 0)
""C
til of-> ;:, o 0)
..c of->
of-> co en s:::
1.
F IAS'T LEVEL 0 I SPLACE"ENT fUj I
5. 10. 15. 20. 25. 30.
1.
SECI"IO LEYEl 0 I SPLACE"ENT fUj 1
5. 10. IS. 20. 25. 30.
1.
THIAD LEVEL DISPLACEMfIIT lUI 1
5. 10. 15. 20. 25. 30.
1.
flUATH LEYEL DISPLACEMENT lUI 1
s. 10. 15. 20. 25. 30.
1.
fIfTH LEVEL DISPLACEMEMT NJII 1
s. 10. IS. 20. 25. 30.
Fig. 5.1
I.
SIXTH LEVEL OISPLACE"ENT FtJH I
35. fPEQ. QilJ 5. 10. 15. 20. 25.
1.
SEVENTH LEVEL D ISPLACE"ENT fUI 1
35. fPEQ. IHll 5. 10. 15. 20. 25.
1.
EICHTH LEVEL DISPLACEMENT lUI 1
35. FPED. am 5. 10. IS. 20. 25.
1.
NINTH LEVEL DISPLACEMENT lUI 1
315. RED. om 5. 10. IS. 20. 25.
1.
lENTH LEVEL D ISPLACEMEN'T fUI 1
!is. AG. om S. 10. 15.. 20. 25.
Fourier Amplitude Spectra, Run One
30.
30.
30.
30.
30.
35. fPEQ. IHll
35. fPEQ. om
315. FlIED. am
315. FfB. am
{
1,'1' ! I' -'
35. fPEQ. om
ex:> +=:-
1. 1.
FIRST LEVEL RCCELERAlI liN I\IN 1 SIX1H LEVEL RCCELERRHIIH IlIH 1
5. 10. 15. 20. 25. 30. 35. FP£Q. IHZl 5. 10. 15. 20. 25. 30. 35. FPfll. IHll
1.
SECII140 LEVEL RCCELERAT HIH IlJN 1 SEVEH1H LEVEL RCCELERRHIIH IlJN 1
5. 10. 15. 20. 25. 30. 35. FPfll. IHll O. 5. 10. 15. 20. '25. SO. 35. FPfll. 1HZ)
1.1n- 1.
THIRD LEVEL ACCELERR1IIIH IlJN 1
b EIGH1H LEVEL ACCELERR1IIIH IlIH 1
ex> U1
-I 0.0 Il!"f~ t t due , 0: 't I I I 5. 10. 15. 20. 25. 30. 35. FPfll. IHZl O. 5. 10. 15. 20. 25. SO. 35. FPfll. IHlI
1.1n- 1.
FIIURTH LEVEL ACCELERATIIII4 IlJN 1 HI"lH LEVEL ACCELERRl II'" IlJN 1
5. 10. 15. 20. 25. 30. 35. FPfll. 1HZ) ,',
5. 10. 15. 20. 25. SO. 35. FPfll. IHlI
1. 1.
FIFTH LEVEL ACCELfRAHII" IU4 1 lE"lH LEVEL ACCELERAT III" IU4 1
S. 10. 15. 20. 25. 30. 3S. FREQ. IHll 5. 10. 15. 20. 25. 30. 35. FPfll. IHll
I,r;
Fig. 5.2 Fourier Amplitude Spectra, Run One ,(,'I 'c: ?.I)7
I c ,II ~ $((>'
1.
FIRST LEVEL RCCELE"ATlIlN fUI 2
S. 10. 15. 20. 25.
1.
SECDtlD lEYU ~CCH["."ell .... ,
S. 10. 15. 20. 26.
1.
1HI"D LEVEL "CCELERRT U" PUt 2
S. 10. 15. 20. 2S.
1.
FOU"TH LEYEL "((ELE"RT II'" fUI 2
S. 10. IS. 20. 25.
1.
FIFTH LEVEL ACCELE""TlIItI PUt 2
s. 10. 15. 20. 21.
1.
5 I XTH LEVEL RCCELERAT 111M lUI 2
!Q. !Ii. F?flI. S. 10. 15. 20. 25.
1.
SEVENTH LEVEL RCCELEARTIIIN RUN 2
30. !16. flIEIl. om 5. 10. IS. 20. 25.
1.
EIGHTH LEVEL ACCELERRT 111M fUf 2
30. 35. fIG. 1HZ) S. 10. IS. 20. 25.
I.
HIH1H LEVEL ACCELERA111'" PUt 2
30. 36. FIB. 1HZ) S. 10. 15. 20. 25.
1.
TENTH LEVEL A(CELERR1 UN PUt 2
30. 35. FIG. am S. 10. IS. 20. 25.
Fig. 5.4 Fourier Amplitude Spectra, Run Two
90.
30.
30.
30.
30.
!IS. FP£Q. 1HZ)
35. fIG. 1HZ)
35. fIG. om
36. FIG. IfZJ
36. flIED. om
co -.....J
1.
FIRST LEVEL DISPLACEHENT 11M 3
s. 10. 15. 20. 25.
1.
SEC liND LEVEL 0 ISPLACEHfNT lUI!
S. 10. IS. 20. 25.
1.
THI"O LEYEL DISPLlICEHENT lUI 3
S. 10. IS. 20. 25.
1.
FGU"TH LEYEL DII'LACEMMT fUf 3
s. 10. 15. 20. 2&.
FIFTH LEVU DISPLACE"ENT fUf 3
S. 10. 15. 20. 25.
1.
SIXTH LEVEL DISPLACEHET PW S
30. 315. FIG. om 5. 10. IS. 20. 25 •.
1.
SEVENTH LEVEL OISPLACEHENT 11M 3
so. 35. FIG. om 5. 10. IS. 20. 2&.
t.
1:: rOHTH LEVEL 0 IS'LACEHENT fUf S
so. 36. FIG. om S. 10. IS. 20. 2&.
I.
NINTH LEVEL DIS'LACEHENT IUf 3
30. 3&. FIB. om 5. 10. IS. 20. 2&.
I.
TENTH LEVEL DU'LACEHE"T lUI S
30. 36. flIED. om 5. 10. 15. 20. 2&.
Fig. 5.5 Fourier Amplitude Spectra, Run Three
so.
30.
30.
30.
30.
35. FIG. om
36. FIG. lit!)
SS. FlU. OlD
•• flIED. am
!IS. FIB. IHIl
co CO
1. 1.
F lAST LEVEL ACCELEfllITI 11M FIJI 9 SIXTH LEVEL ACCELERATIIIN FIJI 9
5. 10. IS. 20. ~. ~. ~. fmI. om 5. 10. 15. 20. 25.
1. 1.
SECtlMD LEVEL ACCElEMT 111M FIJI 9 SEVENTH LEVEL RCCELERAT ItlN FIJI 3
~~~ .. +,-. ~ 5. to. 15. 20, 25. 30.- 36:-FiG. om S. 10. 15. 20. 25.
1. 1.
THIRD LEVEL ACCELEMT 111M FIJI 3 EIGHTH LEVEL ACCELEAATItlN FIJI 3
S. 10. 15. 20. 25, -- 30.- ,s.-m. om 5. 10. 15. 20, 25.
1. 1.
FtlURTH LEVEL ACCELERATIIIN FIJI 3 NINTH LEVEL ACCELERAT ItlN FIJI 3
5. 10. 15. 20. 25. 30. 35. FRED. QfZ) 5. 10. IS. 20. 25.
1. t •
. FIFTH LEVEL RCCELUIATIIIN FIJI 3 TENTH LEVEL ACCELERAT III" FIJI 3
5. 10. 16. 20. 25. 30. 35. FlB. QfZ) 5. 10. 16. 20. 25.
Fig. 5.6 Fourier Amplitude Spectra, Run Three
30.
30.
30.
30.
30.
36. FIB. QfZ)
35. FIB. QfZ)
35. FIB. om
36. FRED. IJtZ)
36. Fl£D. IJtZ)
co ~
0.05
~-----JJ5"~U~~WMo~~~~vnL--------0.00 I WI'I
F'AE£ VIM. PRI~ Til lUI t
-0.015
0.015 mmt lEtU ACCf1BIfT IaN, LIIIT • G
0.00 I r"'tl \11"u"wnv".
flIU V JlI'. fCl..LlIW INa NJM 1
-0.05
0.05 T8fTJt LEWl. ACalDIATlaN.· LIIIT • G
0.00 ~ I - t4fftd"i!l.u""v"'~-. M _ we
-0.015
0.0 1.0 Tn£.E.
2.0 '.0
flIU VI ... "'I~ Til NJM 2
".0 S.O
1.
30. 35. fPIEQ. om
1.
25. 30. 3S. fPIEQ. om
I.
5. 10. 15. 20. 25. 30. 35. FJIIEQ. om
Fig. 5.7 Observed Free-Vibration Responses with Fourier Amplitude Spectra
\.0 o
0.05 TENTH lfVEl. ACCEl..EAATI~, UNIT • G 1.
0.00 .... llW··~iJl'\r";jI""'''''''''''''''''''''-''''''' 4 SC
flfi VlBA. FtUlIIlNG PtnI 2
-0.05 20. 25. 10. 3S. fREQ. IMZI 5. 10. 15.
0.05 TENTH LE't'El... ACCEJ...EMTI~. lItIT • G I.
I
0.00 ~ .. , ,. lIMY l. J "\. 'lc~ NJI
fPIE£ V IlIA. PAIl.. 111 fUM 3
~
-0.05 ---t
5. 15. 3S. FPIEQ. om 10. 20. 25. 30.
O.DS T£NTH lfVEl. fD:E1..fJIA'T HI', lItlT • G 1.
0.00~"4''''1; ~:MI"w.¥~"""".""" rt
fl'IEE VIllA. FtUlIIIMG fUM 3
-0.05 litE:, SEC. IS. 20. 25. 5. 10. 30. 3S • FPlEQ. 1HZ)
0.0 1.0 2.0 3.0 16.0 S.O
Fig. 5.8 Observed Free-Vibration Responses with Fourier Amplitude Spectra
6
Run I
5
4 0 +- Run 3 c 0::
£:
:3L-,
" " '\.. U)
0 N
+-C (.)
~
Q.
e 2 «
Ol~----------------~----------------~~----------------*-------------o 2 :3
Input Frequency t f (H z)
Fig. 5.9 Amplification Ratio Versus Input Frequency, Steady State Tests
4~1------~--------~------~------~---------------------------------
3L 0
-N :J:
~ 0 0 C Q)
::J t- O tT Q) "V 1 ~ 0 LL
"1J 0 Q) ~
:J (/)
'V 0 0 Q)
~
I~ 'V
0 Free Vibrat ion 0 Steady State 'V Earthquake Simu lot ion
0 1 I o 10 20 30 40 50 60 70 80
Maximum Double-Amplitude Tenth Level Displacement /2 (mm)
Fig. 5.10 Apparent First-Mode Frequency Versus One-Half the Maximum Observed Double Amplitude Tenth Level Displacement
~ w
Ot
c .2 .... c .... CD
1.0
DeSign~
r -/
/ \
\ , " ~ 0.5 //
// ","-
" , o « " "-,
-....."'" ............... ........ -- . ---- ---------Maximum Base Accelerat ion 0.4 g
~ = 10 "lo
o·~----------~--------------------------------------------~----------~----------~----------~--------~ 40 30 20
--t-Frequency, Hz
10 0.1
0.2 0.3 0.4 0.5 o.S
Period, sec. ~
Fig. 5.11 Comparison of Design Response Spectrum with Obtained Response Spectrum, Run One
0.7
~ .p.
Level 10
9
8
7
6
5
4
:3
2
Base
o
95
o
o \J
o '0
o
o
o
o
00 - -- 1/2 x Observed Double Amplitude --- Observed Single Amplitude
o Gross Sect ion, Observed Spectr um o Substitute Structure, Design Spectrum '0 Substitute Structure, Observed Spectrum
10 20 30
Maximum Displacement (mm)
Fig. 5.12 Comparison of Maximum Observed Displacements with Calculated Values, Run One
LEVEL
10
9
8
7
6
5
It
3
2
1
0.0 20.0 I I
DISPLACEMENTS (MMl
0.0 2.0 I ,
LATERAL FORCES (KN)
0.0 20.0 I I
SHEARS lKNl
0.0 30. a I I
MOMENTS IKN-M)
TEST STRUCTURE MFl - TEST RUN 1 - RESPeJNSE AT 1.42 SECeJNDS
Fig. 5.13 Maximum Observed Displacements, Lateral Forces, Story Shears and Overturning Moments, Run One
\.0 en
Level
10
9
8
7 ~ o \l '--. 0
6 -I o \I '-1 0
5 o \I 0
4 o '0 0
3 o '0 0
2 0
0 'V ... 0
Base o 10 20
Max imum Story Shear (k N)
30 o
o
- Observed o Substitute Structure 1 Design Spectrum '0 Subst i tute St ruct ure, Observed Spectr urn o Gross Section, Observed Spectrum
o
0'0" 0
o '0" 0
o '0" 0
o '0 '\.. 0
10 20 30 40
Maximum Overturning Moment (kN-m)
Fig. 5.14 Comparison of Maximum Observed Story Shears and Overturning Moment with Calculated Values, Run One
\.0 -.......J
70. 0 /
60t- / .r; / ... /J c: t!- 50
/ E Q) E
/ ~-... . - .... 40 / - c e.Q)
E E / lD « Q) 0:> I U
0 / Q) - 30 - 0. 0."
0/ C .-
00 0
-E ., :::J > 20 E~ )I(
0 ~
1:[ 0 100 200 300 400 500 600
Spectrum Intensity, S '20 (mm )
Fig. 5.15 Maximum Observed Single-Amplitude Tenth-Level Displacement Versus Spectrum Intensity, f3 = 20%
LEVEL
10
9
a
7
6
5
l!
3
2
1
0.0 50.0 ~ I
DISPLACEMENTS (t1M)
0.0 S.O t I
LATEAAL FORCES (KNl
0.0 20.0 I I
SHEAAS IKNl
0.0 30.0 I I
MOMENTS (KN-Ml
TEST STRUCTURE MFI - TEST RUN 2 - RESPONSE AT 2. 52 SEC~NDS
Fig. 5.16 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Shear, Run Two
\.0 \.0
LEVEL
10
9
6
1
6
5
ij
3
2
1
0.0 50.0
DISPLRCEMENTS (MMl
0.0 5.0 I I
LRTEARL FORCES IKNl
0.0 20.0 I I
SHEAAS IKNl
0.0 30.0 I I
MOMENTS (KN-Ml
TEST STRUCTURE MF 1 - TEST RUN 2 - AESPeJNSE AT 2.46 SECeJNDS Figs. 5.17 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time
of Maximum Base Overturning Moment, Run Two
--' o o
LEVEL
10
9
8
7
6
5
L!
3
2
1
0.0 50.0 I I
DISPLACEMENTS (MM)
0.0 5.0 I I
LATERAL FORCES IKNl
0.0 20.0 I I
SHEARS IKNl
0.0 30.0 • I
MOMENTS (KN-Ml
TEST STRUCTURE MF 1 - TEST RUN 3 - RESPrJNSE AT 2.58 SECONDS
Fig. 5.18 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Shear, Run Three
-..J
o -..J
LEVEL
10
9
8
7
6
5
ij
0.0 50.0 I I
DISPLACEMENTS (MM)
0.0 5.0
LATERAL FORCES IKNl
0.0 20.0
SHEARS IKNl
0.0 30.0 t I
MOMENTS (KN-M)
TEST STRUCTURE MF1 - TEST RUN 3 - RESPONSE AT 2.51 SECONDS
Fig,. 5. 19 Observed Displacements, Lateral Forces, Story Shears and Overturning Moments at Time of Maximum Base Overturning Moment, Run Three
--' o N
Z .liC
"-0 Q)
L: en Q) f/)
c en '"'C Q)
> "-CD f/)
.Q 0
E ::s E )(
0 ~
20
15
/ /0
10 / /
01
5
/ 10
/~ __ --D-
0 Run I 0 Run 2 {j. Run 3
20 30 40 50
Maximum Tenth Level SingleAmplitude Displacement (mm)
60 70
Fig. 5.20 Maximum Observed Base Shear Versus Maximum Tenth Level Displacement
--i
0 w
'8
L 16 ~ ~ObSerVed I '\c
14
-ZO» .3IC .!: 12 -"'0 ... 0 o 0 CD-I
L Calculated
10 .s:::. C/) ...
0 CD::; (/)0» Oc::
8 CDo r T T
CD'" ..... t-0 EO 6 :;: ... -0 ::::>'t-
4
2 .. l ,;., ~ j
0' 6 7 8 9 10 2 3 4 5
Level Below Which Plast ic Hinges Are Located
Fig. 5.21 Maximum Base Shear Versus Collapse Mechanism for a Triangular Lateral Loading Condition
--' o ~
lOS APPENDIX A
DESCRIPTION OF EXPERIMENTAL WORK
A.l Material Properties
(a) Concrete
Small-aggregate concrete was used to cast the test frame. The mix
proportions by dry weight were 1:0.90:3.61 (cement:fine aggregate:course
aggregate). The water-cement ratio \'las 0.80. The cement was high early
strength (Type III), the fine aggregate was fine lake sand and the course
aggregate was Wabash River sand.
~1echanical properties were determined from tests on samples which
were cast simultaneously with the frame specimen. These tests were
performed on the same day that the frame specimen was tested.
Compressive properties were determined by testing cylinders using a
"l20-kip'l universal testing machine. Strains were measured using a 0.025-mm
mechanical dial gage with a l27-mm gage length up to maximum stress. A
representative stress-strain relation is shown in Fig. A.l. Young's
modulus of the concrete was taken as the slope of the secant drawn from
zero to seven MPa.
The tensile properties were determined by splitting tests on l02X204-mm
cylinders. The modulus of rupture was determined by loading SlX5l-rrrn cross
sections at the center of a l52-mm span. The average strength of the
concrete control specimens is summarized in Table A.1.
(b) Steel Reinforcement
(1) Flexural Reinforcement: No. 13 gage plain bright basic
annealed wire was used as flexural reinforcement. The nominal cross
sectional area and diameter are 4.242 mm2 and 2.324 mm, respectively.
106 Twenty random samples of no. 13 gage wire were picked from the same lot
that the flexural reinforcement was taken. The average measured diameter
was 2.326 mm with a standard deviation of .002 mm.
Tension tests were performed on twenty coupons using a 111.5-
kipll MTS testing machine. Strains were determined using an electrical-
resistance clip gage with a .5-in. gage length.
Ten of the coupons were tested at a strain rate of .001/sec., and
the other ten were tested at a strain rate of .005/sec. The results of
these tests are summarized in Table A.2. A typical stress-strain relation
is shown in Fig. A.2.
(2) Transverse Reinforcement: No. 16 gage plain wire was used
for transverse reinforcement in this experiment. The nominal cross-sectional
area and diameter are 1.981 mm2 and 1.588 mm, respectively. Twenty random
samples of No. 16 gage wire were selected from the same lot that the trans-
verse reinforcement was taken. The average measured di ameter was 1.584 mm
with a standard deviation of .006 rnm.
The wire was deformed by a machine into a rectangular helix of
25 x 38 mm for columns, and a 19 x 25 mm rectangular helix for beams. The
helix had a pitch of 10 mm (Fig. 2.13). The average yield stress was found
to be 760 t1Pa.
(3) Joint Reinforcement: For confinement of the concrete at the
joints, 32 rrm 0.0. spirals made of No. 16 gage vJire \\Jere used for joint
reinforcement. The spiral had a pitch of 10 mm. Metal tubing with a 13.11
mm 0.0. was also provided at each joint to prevent deterioration of the
concrete at the connection of the masses to the frame (Fig. 2.13).
(4) Base Girder Reinforcement: Details of the reinforcement for
the base girder are shown in Fig. 2.2. Two #4 rebars grade 60 per face were
used for flexural reinforcement. Number 8 gage wire stirrups spaced at 51
107
mm were used as shear reinforcement. The reinforcement was provided so that
the base girder could resist the maximum overturning forces. Steel
tubing provided vertical hole~ in the base girder to bolt the specimen to
the earthquake simulator.
A.2 Construction
(a) Fabrication of Steel Reinforcing Cages
For protection during shipping, the reinforcing steel was covered with
heavy oil by the supplier. To remove the oil, the wire was soaked in a
petroleum-based solvent. The wire was then cleaned with acetone to remove
any residual film.
The reinforcing cages for both frames of the test specimen were fabri
cated by tying the flexural reinforcement to the transverse spiral
reinforcement with a ductile .912-mm dia. wire. First the column reinforce
ment was assembled with continuous transverse spiral reinforcement. Then the
beam flexural reinforcement was slipped through the column cages and tied
to the transverse spiral beam reinforcement (Fig. 2.13).
The reinforcing cages were then sprinkled with a 10% solution of
hydrochloric acid and placed in a fog room for 35 hours. This process
induced slight rusting of the steel to improve bond with the concrete in
the test specimen. Upon removal from the fog room, the cages
were brushed and rinsed with water to remove excess rust.
The day before the specimen was cast, the reinforcing cages were placed
in the forms. The spiral reinforcement was then placed at the joints. To
provide imbedment at the base of each frame, a 102 x 51 x 3.2-mm steel
plate was welded to the flexural reinforcing of each column 102 ~m below
the top of the base girder.
108 (b) Casting and Curing
The two frames and the control specimens were cast using concrete from
the same batch. The frames were cast monolithically. Proper placement of
the concrete was insured by use of a mechanical stud vibrator. Approximately
one half hour after placement, the concrete was struck off and finished with
a metal trowel. The frames were then covered with plastic sheet.
Approximately ten hours later, the side forms. were carefully removed.
The frames were then covered with wet burlap, and plastic sheet was placed
over the burlap. The frames were left this way for two weeks and allowed
to cure. The plastic and burlap were then removed, and the frames were
stored in the lab. The cylinders and prisms received the same treatment.
Table A.4. gives the chronology for the test frame.
(c) Measured Dimensions
Before the specimen was tested, the length, depth and width of all
beams and columns in the test frame were measured. Within the accuracy of
a tape measure, the length of every beam and column in the test frame was
found to match the nominal length.
After the specimen was tested, the concrete cover was chipped off in
30 locations near joints in the structure. The cover thickness was measured
to determine the depth to the flexural steel in the beams and columns in
the test frame. All measurements taken of the test frame are summarized in
Table A.3.
A.3 Instrumentation
Two types of gages were used to measure the response of the specimen.
Twenty-seven accelerometers were installed to measure accelerations, and 21
linear voltage differential transformers (LVDT) were installed to measure
displacements.
109
For each frame, one accelerometer was fastened to the longitudinal
connections of the weights along the centerlines of the beams at each level
and at the top of the base girder (Fig. A.3). Also an accelerometer was
installed on the centerline of the tenth level mass between the two frames.
These accelerometers were positioned to measure horizontal acceleration
parallel to the imposed direction of motion.
One accelerometer was installed on the top of each frame and posi
tioned to measure vertical acceleration. Two accelerometers were installed
on the tenth level mass. These accelerometers were situated in such a way
as to measure horizontal acceleration perpendicular to the imposed direction
of motion.
Eighteen of the accelerometers were Endevco Model 2262C Accelerometers
with a range of ~ 50 g. The other nine accelerometers were Endevco Model
AQ-116-l5 Accelerometers with a range of ~ l5g. Both models measure
absolute acceleration.
Twenty-one LVOT's were used to measure relative displacements of the
test specimen. Twenty of the gages were mounted on a steel A frame (Fig. A.3)
which had a natural frequency of 48 Hz. These gages were mounted with their
axis parallel to the direction of the imposed motion along the center-line
of the beam of each floor level on both frames. One LVOT was also mounted
on the ram of the earthquake simulator to measure the input motion during
the experiment.
The LVDT's used in this experiment were Schaevitz AC-type differential
transformers. The travel limit for the gages ranged from + 3 in. at the
top floor levels to + 1 in. at the first level.
110 A.4 Data Reduction
The voltage output of the LVDT's and accelerometers was continuously
recorded in an analog format on magnetic tape. Four tape recorders were
used, each having the capability to record thirteen voltage signals and one
audio signal. The input earthquake acceleration waveform was recorded on
one channel of each of the four recording units. In this way the data on all
four tapes could be synchronized.
In order to facilitate conversion from voltage units on the tape to
physical units of the actual test specimen response, calibrations were
performed on both the accelerometers and the linear voltage differential
transformers prior to this experiment. The accelerometers were calibrated
to the earth's gravity (~g) by changing the direction of the axis of the
gage from horizontal to vertical. The LVDT's were calibrated using metal
blocks machined to specific dimensions. The voltage outputs corresponding
to these known physical response levels were recorded on the analog
magnetic tape.
The analog records of the tests were converted into digital records
using the Spiras-65 computer of the Department of Civil Engineering. The
digitization rate was 1000 points per second, and these records were also
placed on magnetic tape. These tapes were then copied on the Burroughs
6700 computer of the Department of Civil Engineering to make them compa
tible with the reading device on the IBM 360-75 computer of the Digital Com
puter Laboratory at the University of Illinois.
A computer program was used to read the calibration factors and zero
levels recorded on the tapes in voltage units. The approximate calibration
factors could then be computed by comparing the known physical response
level to the voltage output for each gage. By reading a portion of the
111
tape immediately prior to the onset of a test, the same computer program
obtained zero levels for each gage.
Another computer program was used to process the data into its final
form for permanent storage on magnetic tape. The previously obtained
calibration factors and zero levels were applied to the data, and the data
was processed into the form of a series of response-time relations.
Various other computer programs were used to plot the response-time
relations, shear force and overturning moment records, Fourier Sepctra,
and Response Spectra for the recorded base accelerations. The overturning
effect of gravity load acting through the lateral displacements of the
specimen was included in calculating the overturning moment relations.
Also, a computer program was utilized to separate certain harmonic components
of the wave forms.
Parameter
Secant t Modulus x 10-3 (Ec) U:1Pa)
Compressive Strength (flc) (r~P a)
Splitting Test (MPa)
Hodu1us of Rupture (MPa)
Table A.l Measured Properties of Concrete Control Specimens*
Number of Tests
6
6
6
11
Mean
22.0
40.2
3.3
7.5
Standard Deviation
2.2
2. 1
0.6
0.7
* Age of the specimens was 34 days
t Measured at 7 MPa in compression test of 102 x 203 - mm cylinder
...... ...... N
Table A.2 Measured Properties of Flexural Reinforcement
Young's St rai n Yield r~odul us x 10-3 Rate Stress (fy)
(MPa) (sec- l ) (MPa)
r~ean Standard Deviation
200.0 .001 350 9.7
.005 360 5.2 --' --' w
Parameter
Column Width (h)*
Beam Depth (t)*
Frame Thickness (b)*
Cover Thickness (d')*
* See figures below
Table A.3 Measured Dimensions of the Test Structure
Size of Nominal t,1ean Standard Sample (rrm) (mm) Deviation (mm)
160 50.8 50.9 0.4
120 38.1 38.1 2.4
280 38.1 39.0 2.2
30 3.4 5.2 1 .5
• • •
h
• • • • L .... , ____ _
Beam Section Column Section
...., ....,
.,J:::.
115
Table A.4
Chronology For Test Structure
Date Reinforcement fabrication 23 t·1ay 1977
Casting 26 Hay 1977
Si de forms struck 26 May 1977
Wet burl ap cover removed 9 June 1977
Lifted off 9 June 1977
Mounted on the earthquake simulator 15 June 1977
Tested 29 June 1977
451
40
35
0 a. ~
25 It) It)
/ --' G) --' .. m +-en 20
0 )(
« 15
4
Strain x 105
Fig. A.l ~1easured Stress-Strain Relation for Concrete
I I 1
4001-- -
3001-- , 0 Q.
:E
U) ., Q) '-...
-. ~ en 200t-. ~
Q) ....... Q) ... en
IOO~ -
O~I--------------~----------------~--------------~------~ o 0.01 0.02 OD3
Steel Strain
Fig. A.2 Measured Stress-Strain Relation for Reinforcing Steel
118
Tenth Level Mass
Typical Accelerometer Measures Minor Direct ion Horizontal Acceleration
Typica.1 Accelerometer Measures Major Direct ion Horizontal Accelerat ion
Typical L VDT Measures Major Direct ion Horizontal Displacement
t:::I---i-.
DO ~DD ----...........DD ~DD ~DD
~ DO
c::J---~
~DD ............... DD ..--.....-DD
Fig. A.3 Instrumentation Layout for the Test Structure
119
APPENDIX B
NOTATION
b = width of a cross section
d' = edge distance from the top of concrete to the top of steel
of a cross section
Ec initial moduls of elasticity of concrete
Es = modulus of elasticity of steel
( E I ) . = act u a 1 s t iff n e s s of memb e r i a1
(E1) .= sUbstitute stiffness of member i Sl
f' = compressive strength of concrete c
f = ultimate stress of steel su f = yield stress of steel y
g = acce 1 era ti on of gravity
h = tota 1 depth of a column cross section
L = length of a structural member
f·1 . ,t1b · = end bending moments of mer.Jber i all
P. = s tra in energy of member i 1
5I = spectrum i ntens i ty
t = time
W = weight of the test structure
Xb = base motion of the steady-state tests
Xo = amplitude of the base motion of the steady-state
S = dar.Jping factor
Sn = damping factor for mode n
Ssi = substitute damping factor for member i
tests.
~ = damage ratio
~. = damage ratio for member i 1
120
w = driving frequency of the base motion of the steady-state tests
