By Jack P. t·loeh 1e and A. Sozen
174
UILU-ENG-78-2014 EARTHQUAKE-SH1ULATION TESTS OF A TEN-STORY REINFORCED CONCRETE FRAr-1E WITH A DISCONTINUED FIRST-LEVEL BEAM By Jack P. t·loeh 1e and t4ete A. Sozen University of Illinois Urbana, Illinois August, 1978 1\
Transcript of By Jack P. t·loeh 1e and A. Sozen
UILU-ENG-78-2014
EARTHQUAKE-SH1ULATION TESTS OF A TEN-STORY REINFORCEDCONCRETE FRAr-1E WITH A DISCONTINUED FIRST-LEVEL BEAM
By
Jack P. t·loeh1eand
t4ete A. Sozen
University of IllinoisUrbana, Illinois
August, 1978
1\
BIBLIOGRAPHIC DATA 11. Reporr No.SHEET UILU-ENG-78-20l44. Title and Subtitle
EARTHQUAKE-SmULATIOtI TESTS OF A TEN-STORY REINFORCEDCONCRETE FRAt1E WITH A DISCorlTINUED FIRST-LEVEL BEAr~
7. Author(s) Jack P. Moehle and t1ete A. Sozen
9. Performing Organization Name and Address
University of Illinois at Urbana-ChanpaignUrbana, Illinois 61801
12. Sponsoring Organization Name and Address
National Science FoundationWashington, D.C. 20013
15. Supplementary Notes
5. Re·port IJatew< ~ ~
August 19786.
8. Performin~Organization Rept.No. SR::> No. 451
10. Project/Task/Work Unit No.
11. Contract/Grant No.
NSF EliV-7422962
13. Type of Report & PeriodCovered
14.
16. Abstracts
A small-scale, ten-story, reinforced concrete frame structure withrelatively flexible lower stories was subjected successively to simulatedearthquakes of increasing intensity on the University of Illinois EarthquakeSimulator. The test structure comprised two fra~es situated opposite oneanother with strong axes parallel to a horizontal base motion and with storymasses spanning betv.Jeen. The franes had relatively "tall" first and laststories and a discontinued first floor-level, exterior,span beam. Earthquakesimulation tests were complemented by free-vibration tests and steady-statesinusoidal tests at a series of frequencies bounding the apparent funda~ental
frequency. This report documents the experimental work, presents data(including time-response histories), and discusses the observed dynamic responsein relation to stiffness, strength, and energy-dissipative capacity.
17. Key Words and Document Analysis. 170. Descriptors
Damping, dyna~ics, earthquake-simulation response, free-vibration, framedstructure, multistory structure, spectral-modal analysis, steady-statesinusoidal tests, stiffness, strength
17b~ Identifiers/Open-Ended Terms
17c. COSATI Field/Group
18. Availability Statement
Release Unlimited
FOR.... NTI5-3!l (REI/. 10'731 ENDORSED BY ANSI AND UNESCO.,
19•. Security Class (ThisReport)
t1NrIA"SI~lF:J)20. Securiry Class (This
PageUNCI.ASSI F IEJ)
THIS FORM MAY BE REPRODUCED
21. No. of Pages
(71-
useo......• De 8Z05·P74
iii
TABLE OF CONTENTS
1
11
3
347
15
15161718
19
191922
28
28283132
42
42424344
48
Page
. . .
. . . . . . . . . .., . . .
. '. .
• • • • • • • • • • • • 0 •
Introductory Remarks • • • •Apparent Natural FrequenciesMeasures of Damping••• 0 ••••
Response to Simulated Earthquakes.
Test Structure • • • • • • . • . • •Instrumentation and Recording of DataTest Motions ••Testing Sequence
SUr~~1ARY • • • • • • • •
6. 1 Object and Scope ••6.2 Experimental Work6.3 Data and Studies •••••••••6.4 Observed Response Characteristics.
2.1 General Criteria •••••2.2 Design Method•.•••.•••2.3 Determination of Design Forces.
4.1 Introductory Remarks •••••••4.2 Nature of Data Presented.4.3 Test Results ••...
1.1 Object and Scope.1.2 Acknowledgments ••••
INTRODUCTION.
5. DISCUSSION OF TEST RESULTS.••
5. 15.25.35.4
6.
3. DESCRIPTION OF EXPERIMENTAL PROCEDURE .
3. 13.23.33.4
4. OBSERVED RESPONSE • •
2. DESIGN OF THE TEST STRUCTURE.
1.
LIST OF REFERENCES
APPENDIX
A DESCRIPTION OF EXPERIMENTAL WORK. • • • • . • . • . • • • • 135
Chapter
COt1PLEMENTARY DATA • •
Introductory Remarks•••••••Horizontal Response Measurements.Torsional Motions ••••••••Vertical Motions ••••••••
. .
APPENDIX
B
A.1A.2A.3A.4A.5
B.1B.2B.3B.4
iv
Concrete. • • • • •Reinforcing Steel •••Specimen DetailsDynamic Tests ••Data Reduction •••••
. . .
. . .
. . .
. .. . .. . . . . . .
Page
135136136140145
158
158158159159
2.3 Frame Reinforcing Schedule .••••••.••
TABLE
2. 1
2.2
4. 1
v
LIST OF TABLES
Mode Shapes and Characteristic Values Usedin Design. . . . . • . . .- . . . .....
Design Peak Acceleration, Modal Frequencies,Spectral Amplification, Substitute DampingFactor, and Design Spectral AccelerationUsed in Design. • • • • . .••
Response Maxima Observed During the FirstSimulated Earthquake ••••..••••
Page
49
50
51
52
4.2 Response Maxima Observed During the SecondSimulated Earthquake · · · · · · · · · · · · · · · · · · · · 53
4.3 Response Maxima Observed During the ThirdSimulated Earthquake · · · · · · 54
4.4 First Steady-State Test. · · · · 55
4.5 Second Steady-State Test • · · · · 56
4.6 Third Steady-State Test · · · · · · · · · · · · · · · 57
5. 1 Spectrum Intensities 58· ·5. 1 Comparison of Calculated and Measured Response
for the Design Earthquake. · · · · · · · · · · · · · · · · · 58
A.1 Measured Gross Cross-sectional Beam DimensionsNorth Frame · · · · · · · · · · · · · · · · · · · · · · · · 148
A.2 t~easured Gross Cross-sectional Beam DimensionsSouth Frame · · · · · · · · · · · · · · · · · · · · · · · · 149
A.3 Measured Gross Cross-sectional Column DimensionsNorth Frame · · · · · · · · · · · · · · · · · · · · · · · · 150
A.4 ~leasured Gross Cross-sectional Column DimensionsSouth Frame · · · · · · · · · · · · · · · · · · · · · · · · 151
A.5 Summary of Measured Gross Cross-sectional MemberDimensions • • • • • • 0 ••••••
A.6 Measured Story Masses••••.•••.•.•••.
152
153
vi
LIST OF FIGURES
Figure Page
2.2 Test Structure •••••••••
2.3 Smoothed Design Spectrum for a DampingFactor of 0.02 Compared with EstimatedTest Structure Frequencies ••••••
Calculated Modal Shapes for the FirstThree Modes •• • • • • • • • • • • · . . .. . . . .
2. 1
2.4
2.5
2.6
Configuration and Positioning ofTest Frames.
Interpretation of Damage Ratio ••
Test Frame and Idealized Models ••
. . . . . .
. . ... . . .. .
. . . . .
59
60
61
62
63
64
2.7
2.8
Lateral Forces, Story Shears, OverturningMoments, and Displacements Used in Design(First Mode) •••••••••••••••
Lateral Forces, Story Shears, OverturningMoments, and Displacements Used in Design(Second Mode) ••••••••••••••
· . . . . . . .
· . . . . . . .
65
66
2.9 Lateral Forces, Story Shears, OverturningMoments, and Displacements Used in Design(Third Mode) • • • • • • • • 67
Column Axial Forces Including Gravity Loadfor First Mode. • .••••••
2.10
2. 11
Column End Moments for First Mode••• . . . . .. . . 68
69
2.12
2.13
Column End Moments for RSS of First ThreeModes ... . . . • • . . • • . . .. . •
Column Axial Forces Including Gravity Loadfor RSS of First Three Modes
. . . . . . . . . 70
71
Beam End Moments • •2.14
2.15 Laterally Displaced, One-Bay,One-Story Frame. • • • • • • . . . . . . . . . . . . . . .
72
73
vii
Figure
2.16 Nominal Member Cross Sections~ •
Page
• • • • 74
2.17 Column Interaction Diagram.
2.18 Representative Frame Details.
· .. . . .
75
• 76
. . . . . . . . . . . .
• • 80
Free-Vibration Test Setup • ;, •••••••••
Crack Patterns Observed Before Test Run One.
Location and Orientation of Instrumentation.
• 79
• 81
.77
78
. .• • •
· . . . . .· . .
. . .· . .
Crack Patterns Observed After FirstSimulated Earthquake ••••••
2.19 Location of Reinforcement Throughout aFrame. . . . • . • . . . . . • • • •
3. 1
3.2
4. 1
4.2
4.3 Crack Patterns Observed After SecondSimulated Earthquake • • • • • • • . • • • ••••••••• 82
4.4 Crack Patterns Observed After ThirdSimulated Earthquake • • • • • • • • •••••••••• 83
4.5 Free-Vibration Waveforms of Tenth-levelAccelerations, Observed (Broken) andFiltered (Solid) ••••••••••• . . . . . . . . . . · 84
4.6 Fourier Amplitude Spectra of Tenth-LevelAccelerations During Free Vibration•• . . . . . . . . . . • 85
4.7
4.8
First Simulated Earthquake. LinearResponse Spectra • • • • • • • • • •
First Simulated Earthquake. ObservedResponse (Broken) and ComponentsBelow 3.0 Hz (Solid) ••••••••
· . . . . . . . . . .
· . . . . . . .
• 86
• 88
4.9 First Simulated Earthquake..of Displacements •••••
Fourier Amplitude Spectra· . . . . . . . . . . . . • • • • 94
· . . . . . . . . . . . . . . .Fourier Amplitude4.10
4.11
First Simulated Earthquake.Spectra of Accelerations •
Second Simulated Earthquake.Response Spectra • • • • •
Linear· . . . . . . . . .• 95
· . . • . . . 96
4012 Second Simulated Earthquake. Observed Response(Broken) and Components Below 3.0 Hz (Solid) •••••••• 98
· . . . . . . . . . .
· . . . . . . . . . .
Figure
4.13
4. 14
4.15
4.16
viii
Second Simulated Earthquake. FourierAmplitude Spectra of Displacements.
Second Simulated Earthquake. FourierAmplitude Spectra of Accelerations.
Third Simulated Earthquake. LinearResponse Spectra •••••••••
Third Simulated Earthquake. ObservedResponse (Broken) and Components Below3.0 Hz (Solid) ••••••••••••• . . . . . . . . .
Page
104
105
106
108
4.17
4.18
Third Simulated Earthquake. FourierAmplitude Spectra of Displacements.
Third Simulated Earthquake. FourierAmplitude Spectra of Accelerations.
· . . . . . . . . . .
· . . . . . . .
114
115
4.19 First-Mode Resonance Shapes Observed DuringSteady-State Tests. • • . • • • • • • • • • • • • • • • • 116
5.1 Comparison of Apparent Modal Frequencieswith Maximum Tenth-Level DisplacementPreviously Experienced by Test Structure. • • • • • • • • 117
5.2 Comparison of Apparent First-Mode Frequencywith Maximum Tenth-Level DisplacementPreviously Experienced by Test Structure. · . . . . . . . 118
5.3 Comparison of Observed High Frequencieswith First-Mode Frequency •••••••••• 0 ••••• 119
5.4
5.5
5.6
"t·1oda1 11 Amplification Compared withExciting Frequency in Steady-StateTests . . . • • . . .. . • • . . • . .
r~easured Simu1 ated Earthquake Waveforms
Fourier Amplitude Spectra of SimulatedEarthquake Base Accelerations ••••
· . 120
121
• 122
5.7
5.8
Displacements, Lateral Forces, Story Shearsand Story-Level Moments Measured DuringSimulated Earthquakes • • • • • • 0 • • •
Comparison of Measured Displacement Shapes andShapes Calculated for the Substitute StructureMode1 •••••••••••••••• 0 • • •
• • • • • 123
126
ix
Figure Page
5.9 Comparison of Maximum Tenth-Level Displacementand Spectrum Intensity at a Damping Factorof 0.20...............•......... 127
· . . . . . . .130· . . . . . . .
5.10
5.11
5.12
Measured Response Through a Half-CycleIncluding the Maximum Displacement Duringthe First Simulated Earthquake •••••
Comparison of Base Shear and Tenth-LevelDisplacement ••••••••••••
Comparison of Measured Base Shear andCalculated Collapse Base Shears forMechanism Acting Through Various StoryHeights••••.••..•••••••
128
130. . . . . .
. . . . . . .
5.13
5.14
Calculated Collapse Mechanisms and Base Shearsfor a Triangular Load Distributipn •••••
Cumulative Number and Value of DisplacementPeaks During Simulated Earthquakes.
131• • • • • !I'
132
5.15 Comparison of Design Response Spectrumand Spectrum Calculated from FirstSimul ated Earthquake • • • • • • • • 133· . . . . . . .
5.16
A. 1
Comparison of Design Response and MeasuredResponse for Identical Base Motions••••
Envelope of Measured Concrete Stress-StrainRelations and Design Relation•••••
134
154
. . . .
• • • 157
• '160
•• 156
154
155. . .. . .. .
First Simulated Earthquake. Comparison ofLateral Response as Measured on Northand South Test Frames••••••••••
Overall Configuration of Test Setup••
Detail of Mass-to-Frame Connection ••
Measured Mean Stress-Strain Relation andDesign Relation for No. 13 Gage Wire.
Detail of Base-Girder Reinforcement
A.2
A.3
A.4
A.5
B. 1
B.2 First Simulated Earthquake.Vertical Accelerations ••
Transverse and. . . . . . . . • 162
1
1. INTRODUCTION
1.1 Object and Scope
The overall objective of this work was to observe the effect of strong
simulated earthquake motions on a small-scale, ten-story, reinforced
concrete frame structure with relatively flexible lower stories. The
structure was designed according to the substitute structure method [5]*
which is a design method using linear modal spectral analysis. A secondary
objective, then, was to observe the applicability of the method and, hence,
the applicability of modal spectral analysis.
The experimental work included the building and testing of the small-
scale structure. The test structure comprised two reinforced concrete
frames situated opposite one another with strong axes parallel to base
motions and with story-masses spanning between the frames to increase
inertial forces (Fig. 2.2). The test structure was subjected successively
to three simulated earthquake motions of increasing intensity. Free-
vibration and steady-state sinusoidal tests were complementary tests used
to observe effects of the earthquake simulations.
1.2 Acknowledgments
This work is part of a continuing investigation of reinforced concrete
structure response to earthquakes being carried out at the Structural
Research Laboratory of the University of Illinois Civil Engineering Department.
This work was sponsored by the National Science Foundation under grant
ENV-74-22962.
*References are listed alphabetically at the end of the text. Numbersin brackets [ ] are the number of the reference in the reference list.
2
The writers wish to thank project staff members D. Abrams, B. Algan,
H. Cecen and T. Healey for valuable discussion and assistance with data
reduction. Appreciation is due project staff member M. Saiidi for use of
his modal analysis program and to Professor L. Lopez for assistance in the
use of the IIFinite ll structural analysis system.
Professor V. Jo McDonald provided direction for instrumentation and
data reduction facilities. Mr. G. Lafenhagen provided invaluable assistance
in the instrumentation setup and experimental conduct. Mr. O. H. Ray and
his staff helped in fabricating the specimens and hardware used in the test.
The writers are indebted to the members of the panel of consultants
for their advice and criticism. The panel 'included t·t 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, Veterans Administration; W. P. ~1oore, Jr., Walter P. t100re
and Associates; and A. Walser, Sargent and Lundy.
The IBM-360/75 computer system of the Department of Computer Science
was used for data reduction. The Burroughs 6700 at the Civil Engineering
Systems Laboratory was used for structural analysis computation.
This experimental work and report were undertaken as a special project
toward the Master of Science Degree ln Civil Engineering by Jack P. Moehle,
Research Assistant in Civil Engineering, under the direction of M. A. Sozen,
Professor of Civil Engineering.
3
2. DESIGN OF THE TEST STRUCTURE
2.1 General Criteria
The overall configuration of the test structure was governed by
modeling and equipment limitations and by the objective of the test.
As ideally conceived, the test structure consisted of two ten-story,
three-bay, reinforced concrete frames (Fig. 2.1). Bay widths were
305 mm while story heights varied, being 279 mm for the first and tenth
stories and 229 mm for intermediate stories. In addition, one beam was
omitted at one side of each frame as shown in Fig. 2.1. The gross
cross-sectional dimensions of beams were 38 by 38 mm and of columns
were 51 by 38 mm. Situated opposite one another, the frames would be
subjected to a unidirectional simulated earthquake with motion parallel
to the strong axis of the frames. Supported by and spanning between
the two frames were ten story masses, one at each of ten story levels
(Fig. 2.2). The mass at level one, the level with the lIr.Jissing ll beam,
was nomi na11y 302 kg. Masses at all other 1eve1s were 454 kg.
The configuration described in the foregoing was selected for the
purpose of studying experimentally the effect of strong base motion on a
multistory reinforced concrete structure, in particular, a nonsymmetric
structure with increased top and bottom story heights. Nonstructural
masses are used to increase the inertia forces during the test. The use
of ten such masses allows for the convenient determination of response
variation with height. Particular dimensions of the structure were
based on equipment limitations. The humble nature of the structure, being
nearly a stick structure with a single plane of loading, is advantageous
4
from the analytical viewpoint. The structure becomes a simple physical
model of an ana1~tical concept without the embellishments (architectural
or otherwise) found in a full-scale, multistory building. Indeed, the
test structure is meant in no way to be a prototype or model for any
full-scale structure.
The base motion to which the test structure was subjected was modeled
after the El Centro-NS, 1940 earthquake. The time· scale of the prototype
earthquake was compressed by a factor of 2.5 and accelerations were
amplified in order to excHe the test structure into the inelastic range.
The reproduced motion at this time compression and for small amplifications
is relatively undistorted from the original motion. A smoothed design
spectrum of the assumed model earthquake [5 J is shown in Fig. 2.3. Also
shown are the estimated modal frequencies of the test structure for the
first three modes (see Sec. 2.3, for determination of modal frequencies).
As seen in Fig. 2.3, the second and third modes are in the range of
high amplification. Thus, the motion chosen would be expected to excite
the higher modes of vibration.
2.2 Design Method
The design method used in determining design forces was the substitute
structure method [5 J. This method features a linear dynamic analysis
whiCh recognizes nonlinear energy dissipation in a reinforced concrete
structure. Minimum structural strength requirements are set so that a
tolerable set of designer-specified lateral displacements is not likely to
be exceeded in the event of a base motion corresponding to the design
spectrum.
5
Design via the substitute structure ~ethod can be described under
three basic steps.
(1) Given an expected class of earthquake motion, define a smoothed
acceleration response spectrum for a linear, single-degree-of-freedom
system. This design spectrum should be chosen so as to approximate the
calculated response spectrum at a damping factor of 0.10 since this value
is typical of values derived from the substitute structure model. An
acceptable expression [5] relating response at any damping to response
at damping of 0.02 is
Response at damping factor of 6Response at damping factor of 0.02
8= -="6-+--=--::-'10::-::0'-6 (2.1)
Approximate response accelerations can then be determined for any damping.
(2) Define the· substitute structure. Flexural stiffness of
substitute structure members is defined as
(El) ai(E1)s; =---'-
].liwhere
(El) . = substitute cross-sectional stiffness of member iS1
(El)ai = actual cross-sectional stiffness of member i
based on the cracked section
].1. = selected damage ratio of member i1
The damage ratio is seen in Fig. 2.4 to be the ratio of initial cracked
section stiffness to the minimum effective stiffness obtained for a
reinforced concrete member. The damage ratio becomes a measure of
inelastic energy dissipation. It is comparable with ductility only in
that a large damage ratio requires a large ductility. The damage assigned
toa member is largely a matter of choice. However, since practical
6
experience emphasizes the desirability of maintaining a stiff spine
throughout the height of the structure, a damage ratio of one is normally
assigned to columns. Damage ratios assigned to beams depend on the amount
of inelastic action considered to be acceptable.
(3) Determine modal frequencies, shapes, and forces from a linear
analysis of the substitute structure. Member forces can be determined at
at damping factor of 0.02 from which, using an assumed damping factor in
Eq. 2.1, modified member forces can be calculated. These modified member
forces permit calculation of the substitute structure damping factor as
P. * SsiS = L
1m i L: P.
i 1
where~
1 + 10 (1 - (1/ 11 ;) )Ssi = 50
L. 2 2 t1bi )P. = 6(EI) . (Mai + t'1bi M .1 a1Sl
where
S = substitute structure damping for mode mmP. = strain energy of member i1
Ssi = substitute damping of member i
L. = length of member i1M. and t-1bi = end moments of member i for mode ma1
(2.3)
(2.4)
(2.5)
Equation 2.4 is an expression based on dynamic tests and provides an
estimate of the viscous damping required to simulate observed hysteretic
behavior in reinforced concrete [ 1]. Equation 2.3 assumes that each
member contributes to the overall structural damping in accordance with
its strain energy.
7
Having obtained the substitute structure damping factor, new modal
forces can be obtained, again using Eq. 2.1. One iteration is normally
sufficient given the approximate nature of Eq. 2.4.
Having determined member forces for distinct modes, design forces
are based on the root-sum-square (RSS) combination modified by a base
shear factor as
(2.6)
where
F. = design force in member i1
Firss = root-sum-square force in member i
v = root-sum-square base shearrssVabs = absolute sum of the base shear for any two modes.
It is then suggested that design column moments be additionally factored
by 1.2 in order to further reduce the risk of inelastic action.
2.3 Determination of Design Forces
Design of the test structure followed rather closely the substitute
structure method. However, owing to the experimental nature of this work
and to previous experience with similar structures, certain exceptions
to the method were made. As made, these exceptions will be noted and
the reasoning behind the deviations will be presented. Substitute
structure modeling and design calculations are described below.
(a) Model for Analysis
The model used for static analysis of the structure is depicted
in Fig. 2.5b. The structure was considered a stick structure with
lateral forces concentrated at floor levels and gravity forces distributed
equally to beam-column joints at a given level. Columns were assumed to
8
be rigidly fixed at the base. Rigid zones were assumed at member ends,
the zones being the size of beam-column joints in the actual structure.
Axial deformations were considered only for columns. Member flexural
stiffnesses were based on cracked sections modified by a chosen damage
ratio.
The assigned damage ratios were one for columns and four for beams.
This distribution of damage ratios was selected with the intent that
energy be dissipated in the beams and that columns remain in the elastic
range. The specific value of four for beams was based upon the satis
factory upper bound of displacements that resulted in the analysis.
Member cross-sectional stiffnesses for the model were based on
material properties, either known or assumed, and on assumed cross
sectional member dimensions. No strength reduction factors were used. As
determined from coupon tests, Youngs' modulus and yield stress for steel
were 200,000 MPa and 358 MPa, respectively. Assumed concrete modulus was
21,000 MPa. Concrete strength was taken as 35 MPa at a strain of 0.003.
Nominal cross-sectional dimensions for columns and beams were as shown in
Fi g. 2.16.
(b) Method of Dynamic Analysis
Modal analysis of the model was performed using a computer program
developed by M. Saiidi at the University of Illinois. As used for this
analysis, the structural stiffness matrix was constructed by considering
only beam and column flexural deformations and column axial deformations.
The matrix was then condensed to a ten-degree-of-freedom system with
masses lumped at story levels (Fig. 2.5c). After condensation, the ten
freedoms were lateral motions at each of ten floor levels parallel to the
strong axis of the frames. No vertical or rotational inertias were considered.
9
Modal vectors, frequencies, and participation factors obtained from
the analysis are listed in Table 2.1. Modal shapes are plotted in Fig.
2.6.
Lateral forces were determined using the above modal quantities
and a smoothed design spectrum [5]. A design peak acceleration of 0.4 g
was chosen. A design acceleration amplification spectrum for the model
earthquake (El Centro-NS, 1940, time-scale compressed by 2.5) is shown in
Fig. 2.3. Design spectral accelerations for each mode and for a damping
factor of S are calculated asm
where
am = design spectral acceleration for mode m at damping of Sm
ad = design peak acceleration (=0.4 g)
(SA) = spectral amplification for mode mat damping of 0.02.m
(2.7)
Design lateral forces are then calculated as
F. = ¢. * t1. * P * a (2.8)Jm Jm J m m
where
F. = lateral force at level j for mode mJrn¢jm = modal vector at level j for mode m
Mj = mass at level j
Pm = participation factor for mode m
for beams,
10
(c) Member Design Forces
computations to determine member forces were carried out on FINITE
at the University of Illinois [3 J. The structure was modelled as shown
in Fig. 2.5b. As a first trial, lateral forces F. were applied to theJmmodel with 8m assumed at 10% for all modes. With member end moments
determined for these externally applied forces, new damping factors were
calculated. Using Eq. 2.3
1 + 10 (1 - (l)~Q - _--;:-::--_--:.4 = o. 12jJsi - 50
for columns, 8 . = 0.02.Sl
The "smeared" substitute structure damping, 8 , was then determinedm
using Eq. 2.4 and 2.5. Numerical values of design peak acceleration,
modal frequency, spectral amplification, substitute damping factor, and
design spectral acceleration for the first three modes and for first and
second trial calculations are shown in Table 2.2.
Using the new damping factors, the model was again analysed. New
Values for lateral forces, story shears, overturning moments (not including
resisting moment from gravity load), and displacements were obtained for
each of two frames in the test structure. These are plotted for the first
three modes in Fig. 2.7, 2.8, and 2.9.
Column end moments and axial forces for the first mode and for the
root-sum-square of the first three modes are plotted for each story and
each column in Fig. 2.10 to Fig. 2.13.
Beam end moments for the substitute structure were essentially
constant at a given floor level despite the frame irregularity. ~1ean
beam end moments are plotted for the first mode and for the root-sum
square of the first three modes in Fig. 2.14.
11
Having determined member forces for distinct modes, the substitute
structure method stipulates that design forces will be root-sum-square
(RSS) forces modified by a base shear factor (Eq. 2.6) and that column
end moments be additionally factored by 1.2. However, the experimental
nature of this design work was better satisfied by deleting the base
shear factor and working solely with RSS forces and factored column end
moments. In so doing, the design became less conservative, with increased
likelihood that design moments would be realized or surpassed in the
actual test. Such unconservative proportioning is, of course, undesirable
for an actual structure but is desirable for an experimental structure
through which the limits of a design method are being tested. Unfactored
RSS column end moments, column axial forces, and beam end moments are
shown in Fig. 2.10, 2.12, and 2.14.
Use of the column end moment factor as prescribed by the substitute
structure method was modified without misconstruing the intent of the
requirement. The intent of the column end moment factor is best illus
trated by a one-story, one-bay frame as shown in Fig. 2.15a. If the frame
is a laterally displaced as shown in Fig. 2.15b, equal end moments will
exist in both the column and beam at the top level (Fig. 2.15c). If
both are designed for the same moment, yielding may occur at either section.
However, if the column design end moment is increased by a factor of 1.2,
yielding will occur in the beam only. The situation at the base of the
frame in Fig. 2.15a is somewhat different. If yielding occurs, it will
necessarily occur in the column. Factoring of this base end moment
becomes the equivalent of applying a general load factor or strength
reduction factor.
12
Application of the column end moment factor of 1.2 to the test
structure is analogous to its application to the simple structure of
Fig. 2.15a. The factor was applied throughout the height of the structure
with the exception of base column end moments. In keeping with the
convention that no strength reduction or general load factors be employed,
these column base moments were left unfactored. Final design column
end moments are those of Fig. 2.12 factored at every level, except the
base, by 1.2.
(d) Reinforcement
Longitudinal reinforcement requirements for members were based on
design forces as presented in Sec. 2.3(c). Proportioning for these
requirements was aimed at avoiding frequent or extreme changes in member
stiffness and at providing a system that could be readily constructed.
The most convenient arrangement of longitudinal reinforcement from
the analytical and constructional viewpoint is one that has equal steel
throughout the structure. As can be seen from member end moment distri
butions (Fig. 2.12 and 2.14), such an arrangement results in either
overdesign or underdesign of the structure. Gross underdesign is undesir
able because the structure will be unlikely to withstand the design base
motion satisfactorily. Overdesign is undesirable in that it is uneconomical
and results in a structure significantly different from the substitute
structure model. For these reasons, longitudinal reinforcement was varied
to conform to the distribution of design moments.
Figure 2.14b is a plot of design beam end moments. Provided yield
moment with two and three bars per face is plotted in that figure to the
same scale as beam end moments. Nominal cross-sections of beams are
shown in Fig. 2.16a and 2.16b.
13
Column design end forces are plotted versus provided strength in
the interaction diagram of Fig. 2.17. Nominal cross sections of columns
are shown in Fig. 2.16c and 2.16d.
The tension condition controls the design of the column section.
The design forces for one exterior column in tension falls considerably
outside the interaction diagram (Fig. 2.17). This was accepted on the
basis that base shear not carried by the yielding column would be carried
by other columns of the first story-level. The trend in redistribution of
moments after this column yielded was investigated by assigning a damage
ratio of two to the column. The changes in moment for column base end
moments are indicated in Fig. 2.17 where arrows indicate the extent of
redistribution for each column. Under actual conditions, column B
(Fig. 2.17) is already near yield and would be expected to maintain its
yield capacity as columns C and 0 would be expected to pick up more moment.
A failure mechanism is not expected to result from the design forces.
A typical beam-column detail is shown in Fig. 2.18. Shown in addition
to the longitudinal steel is helical transverse reinforcement. This
reinforcement was the same throughout the structure and was designed with
a factor of safety of three to resist the worst possible shear assuming
that shear strength of concrete was zero. A spiral beam-column joint
reinforcement can also be seen in Fig. 2.18. This reinforcement was used
with the intent of confining the joint core. Tubing in beam-column joint
centers was used to prevent deterioration of the joint caused by support
of the story masses at these joints. No special calculations were made
for either of the joint core reinforcements.
14
The location throughout the frame of all types of steel is shown
schematically in Fig. 2.19. A frame reinforcing schedule for longitudinal
steel is presented in Table 2.3.
15
3. DESCRIPTION OF EXPERIMENTAL PROCEDURE
3.1 Test Structure
The overall configuration of the test structure is shown in Fig. 2.2.
Distinctive characteristics, the effects of which were being tested,
included increased first and last story heights as compared with inter
mediate stories and the omission of one first level beam in each of the
two reinforced concrete frames which composed the structure. Ten story
masses were supported between the two frames, one mass centered at each
floor level. In keeping with the omission of a beam in each frame, the
first story mass was close to two thirds the mass at other floors
(Table A.6).
Construction of the test structure was begun with the two reinforced
concrete frames. The frames were cast monolithically with base girders
and in a horizontal position. The concrete was a small aggregate type.
All longitudinal steel for columns and beams (No. 13 gage wire) was
continuous with the exception of cutoffs in longitudinal column steel as
allowed in design (see Chapter 2 for reinforcement details). Anchorage
and development of steel was provided where necessary. Following a
curing period, the frames were fixed to the test platform of the earthquake
simulator in a vertical position and with the strong axis of the frames
parallel to the line of motion of the test platform. The ten story masses
were then connected between the frames (Fig. 2.2 and A.4). No gravity load
from the story masses was transferred to the frames until the day of the
test.
16
Connections between story masses and frames were designed to
minimize transfer of moments. Each mass was supported by two cross
beams which were in turn supported at each end by a pair of perforated
channels (Fig. A.5). These perforated channels were connected to the
frame by bolts through the center of beam-column joints. This mass
supporting mechanism was such that gravity load was transmitted approxi
mately equally to all columns at a given story level for levels two through
ten. The supporting mechanism was indeterminate at level one (Fig. 2.2).
A bellows system connecting the masses at each level provided increased
stiffness in the transverse direction, thereby restricting out of plane
motion of the test structure (Fig. 2.2).
3.2 Instrumentation and Recording of Data
Two basic types of test data were obtained: (1) displacements
and accelerations of the test structure and (2) visible structural
damage.
Data from the response of the structure included both absolute
accelerations and relative displacements. Accelerations were measured
with accelerometers while displacements were measured with differential
transformers (LVDT's). The location and orientation of these instruments
are shown in Fig. 3.1. Response as' measured was recorded on magnetic
tape. All instruments were calibrated and amplified to maintain suffici
ent sensitivity but to avoid saturating the recorded recores. Both
mechanical and electrical calibrations were made before the test.
Electrical calibrations were again made throughout the test as a check
of temperature effects on the instruments.
17
Information concerning structural damage consisted of the location
of cracks and of crushing or spalling in the concrete. Location of
cracks was facilitated through the use of a fluorescent fluid. The fluid
collected in cracks and reflected IIblack light ll to shovi crack patterns.
These were marked on the frames and recorded on data sheets. Crack sizes
and crushing and spalling information were also recorded.
3.3 Test Motions
Response to three types of motion were measured during the test.
These are described briefly below.
(1) Simulated Earthquake. During a simulated earthquake, the
test structure was subjected to a predetermined base motion (El Centro
1940, North-South component, time scale compressed by a factor of 2.5).
The first earthquake input had an expected peak acceleration of 0.4 g
and was the design earthquake. TVIO subsequent inputs had peak acceler
ations approximately two and three times that of the design earthquake.
All instruments were active during the simulated earthquakes.
(2) Steady-State. The structure was given a sinusoidal base motion
that varied in steps from a frequency below the apparent resonance
frequency of the structure to a frequency above the observed apparent
resonance frequency of the structure. The amplitude of motion was
chosen so as to avoid damaging the structure (approximately 5 mm). All
instruments were in operation during a steady-state test.
(3) Free Vibration. The structure was given a small lateral
displacement (approximately 1 mm) at level ten and then released. The
setup for a free vibration test is shown schematically in Fig. 3.2. A
tenth level accelerometer was the only instrument recording data. The
18
voltage from that accelerometer was amplified so as to be sensitive to
the small accelerations produced.
3.4 Testing Sequence
The test was begun by locating and marking all shrinkage cracks.
This was done both before and after the story ma~ses had been connected
to the frames~ but before any testing had begun. The structure was
then subjected to the motions described in Sec. 3.3 in the following
sequence:
1. Free Vibration
2. Simulated Earthquake
3. Free Vibration
4. Steady~State
Following each simulated earthquake~ structural damage was observed and
recorded. This sequence, together with the observation of structural
damage, formed one test run. Three such test runs were performed. The
only variable from test run to test run was the intensity of the simulated
earthquake.
19
4. OBSERVED RESPONSE
4.1 Introductory Remarks
The test structure was tested according to the procedure described
in Chapter 3. Observations of response consist of or were derived from
relative-displacement and absolute-acceleration waveforms recorded during
the test. These waveforms and corresponding Fourier amplitude spectra
are presented for free vibrations and simulated earthquakes. Spectrum
intensities and response spectra were determined for earthquake base
accelerations, and shear and moment waveforms were derived from earthquake
response records. Displacement amplitudes at several frequencies are
presented for steady-state tests. Crack patterns which developed during
simulated earthquake~ are also presented.
Data presented in this chapter refer to the north frame of the test
structure. Recorded waveforms for both frames were almost identical.
(See Appendix B for a comparison).
4.2 Nature of Data Presented
(a) Frequency Content
Fourier analysis was used to determine frequency content of recorded
waveforms. Using the Fourier Transform, a responsewaveformwas repre
sented in terms of its harmonic components. The relative amplitude of
each component is plotted versus the frequency of that component in a
Fourier amplitude spectrum (e.g. Fig. 4.9).
The Fourier Transform is also suitable for filtering certain
frequencies from the original waveform. In this chapter, all waveforms
are plotted for the original and filtered response. A typical waveform
20
is plotted in Fig. 4.8 where the broken curve represents measured response
and the solid curve represents filtered response. All filtered response
waveforms contain only those harmonic components below 3.0 Hz.
A definition is appropriate at this time as to terms used to designate
those frequencies (or narrow ranges of frequencies) at which peaks on the
Fourier amplitude spectra occur. The lowest of these frequencies is defined
as the first-mode frequency, the next as the second-mode frequency, and
so on. These modal frequencies can be associated tentatively with phase
relationships among the floor level motions. As can be observed generally
on acceleration waveforms (Fig. 4.8) at any instant this first mode can be
associated with a condition that all levels are in phase, the second mode
has one node, and so on. It cannot be assumed that the phase relations
are constant with time for any mode.
(b) Free Vibrations
Free vibrations were imparted to the test structure by laterally
displacing and then releasing the tenth level (Fig. 3.2). Acceleration
waveforms measured at the tenth level and Fourier amplitude spectra
determined for the first three seconds of free vibration are plotted
(Fig. 4.5 and Fig. 4.6).
(c) Simulated Earthquakes
Base motions were modelled after El Centro-NS, 1940. Time scales
were compressed by a factor of 2.5 and acceleration amplitudes were
magnified to achieve the desired motion. Spectrum intensity [ 2 ] at
a damping factor of 0.20 is used to represent the intensity of the base
motion. To be consistent with time-scaling of the base motion, spectrum
intensities were calculated between 0.04 and 1.0 Hz. Response spectra at
various damping factors were also determined for the base motion (e.g.
Fig. 4.7).
21
As noted earlier, response waveforms are reported only for the north
frame. Typical acceleration and displacement waveforms are plotted in
Fig. 4.8. Shear and moment waveforms were derived from the acceleration
and displacement waveforms and structural configuration. The P-delta
moment, typically less than two percent of the total base moment, was
included. Typical story shears are also plotted in Fig. 4.8. Base level
moment is plotted with displacement waveforms in that figure. Maxima
and minima of all waveforms were determined automatically during the data
reduction process.
Fourier amplitude spectra were determined for relative displacement
and absolute acceleration response waveforms (e.g. Fig. 4.9 and 4.10).
(d) Steady-State Tests
Base motion for steady-state tests consisted of an approximately
sinusoidal displacement at nearly constant amplitude. The frequency of
input motion varied in steps and ranged from below to above the observed
apparent first-mode resonance frequency of the test structure. This
frequency is defined as that for which the ratio of tenth-level relative
displacement amplitude to base displacement amplitude was a maximum. All
displacement amplitudes were measured when the test structure was in an
apparent steady-state condition.
Observations reported consist of base motion frequency, base displace
ment amplitude, and the relative displacement amplitude at a level for
each frequency step. In addition, relative displacement amplitude at each
story level is reported for the apparent resonance frequency. In order to
automate frequency and amplitude measurements and to insure that vibration
frequencies higher than the base motion frequency be excluded from the
22
measurements, the waveforms were filtered. Data obtained, then, refer to
the filtered waveforms. Filtered and original waveforms appeared identical
at all but the lowest input frequencies. For those input frequencies at
which higher frequencies interfered substantially with the principal
input frequency, no data are presented.
(e) Crack Patterns
Crack patterns were observed before the test'and after each of three
simulated earthquakes. These are reported typically as in Fig. 4.3.
In crack pattern figures, frame-member depths are drawn to a larger scale
than are lengths.
It is important to note that crack patterns could not be observed in
beam spans in external bays because of the mass connections (Fig. A.5).
Therefore. only shrinkage cracks are presented for these spans.
4.3 Test Results
(a) Test Run One
Crack patterns before the first test run are presented in Fig. 4.1.
All crack widths were small (less than 0.05 mm).
A free-vibration waveform determined before the first simulated
earthquake is included in Fig. 4.5. The Fourier amplitude spectrum of
that waveform is plotted in Fig. 4.6'. The three lowest modal frequencies
were estimated to be 4.5, 14, and 25 Hz. Because of the higher initial
first-mode frequency, the filtered waveform (Fig. 4.5) includes all
component frequencies below 5.0 Hz as opposed to the upper limit of 3.0 Hz
used in all other waveforms.
Two negative peaks of high magnitude can be seen at 0.5 sec. of the
first free vibration (Fig. 4.5). Peaks are to be expected because the
way by which free vibration is imparted (Fig. 3.2) excites the second mode.
23
However, the large magnitude of these peaks as compared with those of
other free vibrations suggests an error in the recording system.
Characteristics of the first simulated earthquake are summarized
below.
1. Base Motion
(a) Peak acceleration was 0.36 g at 0.88 sec. with majority
of large acceleration peaks occurring during the first
2.5 sec. (Fig. 4.8).
(b) Spectrum intensity for a damping factor of 0.20 was 185 mm.
(c) Response spectra (Fig. 4.7).
2. Response Motion
(a) Displacement and acceleration waveforms (Fig. 4.8) and
response maxima (Table 4.1).
(b) Fourier amplitude spectra (Fig. 4.9 and 4.10).
(c) Base moment waveform and story shear waveforms (Fig. 4.8)
and maxima (Table 4.1).
3. Crack Patterns (Fig. 4.2).
Simulated earthquake response waveforms reveal three intervals of
relatively high-level response. These occurred during 0.5 to 3.0, 5.0
to 7.5, and 10.5 to 12.5 sec. intervals. Response (especially during
these intervals) was dominated by the first mode as is particularly
evident in displacement waveforms (Fig. 4.8) and Fourier amplitude
spectra for displacements (Fig. 4.9). Contributions of higher frequencies
are more evident in acceleration waveforms (Fig. 4.8) and acceleration
Fourier amplitude spectra (Fig. 4.10). In the latter it is also evident a
gradual change from high frequency dominance in the lower floors levels to
first-mode dominance in the upper floor levels.
24
The three lowest modal frequencies of response to the first simulated
earthquake could be estimated from acceleration Fourier amplitude spectra
(Fig. 4.10) to be 2.1, 7.8, and 16 Hz. Nodal points can be located
approximately by these spectra as the floor level where a particular modal
frequency has less influence in the total response. For the second mode,
the node is near the seventh floor level, while for the third, nodes
appear at floor levels four and nine. The modal 'frequencies cited refer
only to peaks on the amplitude Fourier spectra and thus refer to dominant
frequencies rather than to invariant properties of the structure.
Crack patterns were as shown in Fig. 4.2. All column cracks were
very fine (less than 0.05 mm in width) as were beam cracks above floor
level four. Beam crack sizes in the lower floor levels ranged from 0.05
to 0.15 mm, the largest cracks appearing in the two floor levels immediately
above the long column. No crushing or spalling was observed.
After the first simulated earthquake, a free vibration waveform
(Fig. 4.5) was obtained. Estimated modal frequencies were 2.8, 9 and 17
Hz (Fig. 4.6).
The first steady-state test followed with frequencies, base displace
ment amplitudes, and tenth-level displacement amplitudes as tabulated in
]able 4.4. The apparent first-mode resonance frequency was between 1.75
and 1.85 Hz with maximum recorded tenth-level amplification of the base
displacement of 5.87. The normalized mode shape at 1.75 Hz is presented
in Fi g. 4. 19.
(b) Test Run Two
Before the second simulated earthquake, a free vibration test
resulted in the waveform and Fourier amplitude spectrum plotted in Fig.
4.5 and 4.6. The modal frequencies are estimated from Fig. 4.6 to be
2.7, 8.8, and 16 Hz. These frequencies are lower than the respective
25
frequencies measured before the first steady-state test, indicating that
minor damage to the structure may have resulted during the steady-state
test.
The second simulated earthquake had the characteristics summarized
below.
1. Base motion
(a) Peak acceleration of 0.83 9 at 0.88 sec. and waveform
(Fig. 4.12) almost identical in shape and frequency content
to that of test run one.
(b) Spectrum intensity at a damping factor of 0.20 was 336 mm.
(c) Response spectra (Fig. 4.11).
2. Response motion
(a) Displacement and acceleration waveforms (Fig. 4.12) and
response maxima (Table 4.2).
(b) Fourier amplitude spectra (Fig. 4.13 and 4.14).
(c) Base moment waveform and story shear waveforms (Fig. 4.12)
and maxima (Table 4.2).
3. Crack patterns (Fig. 4.3).
The general shapes of response waveforms were different from those
determined during the first simulated earthquake. t1aximum response
occurred during two intervals with relatively low-level response occurring
approximately seven seconds into the earthquake duration (Fig. 4.12).
Displacements were again dominated by the first mode. However, acceleration
waveforms reveal a greater dominance by higher frequencies than was
apparent in the first simulated earthquake. Acceleration Fourier amplitude
spectra (Fig. 4.14) also reveal the dominance of the higher frequencies.
26
The lowest apparent frequencies were 1.4,5.5, and 12 Hz (Fig. 4.14).
Nodal points were indicated to be in approximately the same locations as
in the first simulated earthquake.
Crack patterns apparent after the second simulated earthquake are
shown in Fig. 4.3. Cracks wider than 0.05 mm were limited to beams at
column interfaces in the lower five floor levels. Cracks were largest
(up to 0.30 mm) in exterior beam column joints. Minor spalling was
observed (Fig. 4.3).
Response in free vibration after the second simulated earthquake is
plotted in Fig. 4.5 with the Fourier amplitude spectrum in Fig. 4.6.
The first and second mode frequencies were,2.4 and 7.3 Hz. The third-mode
frequency was not apparent (Fig. 4.6).
Test results of the second steady-state test are presented in Table
4.5. The apparent first-mode resonance frequency was near 1.48 Hz with a
maximum measured base displacement amplification of 4.24 at floor level ten.
The displacement shape determined at 1.48 Hz is presented in Fig. 4.19.
(c) Test Run Three
Results from the free-vibration test before the third simulated
earthquake are presented in Fig. 4.5 and 4.6. The two lowest dominant
frequencies were 2.3 and 7.1 Hz.
Characteristics of the third simulated earthquake are summarized
below.
1. Base motion
(a) Peak acceleration of 1.28 g at 0.88 sec. with waveform
shape (Fig. 4.16) and frequency components similar to the
first two simulations.
27
(b) Spectrum intensity at damping factor of 0.20 was 411 mm.
(c) Response spectra (Fig. 4.15)
2. Response motion
(a) Displacement and acceleration waveforms (Fig. 4.16) and
maxima (Table 4.3).
(b) Fourier amplitude spectra (Fig. 4.17 and 4.18).
(c) Base moment waveform and story shear waveforms (Fig. 4.16)
and maxima (Table 4.3).
3. Crack patterns (Fig. 4.4).
Response to the third simulated earthquake indicated a softer
structure. The estimated first three modal frequencies were 1.3, 5.4,
and 10 Hz. Nodal points appeared ~ be at about the same levels as in
earlier simulated earthquakes.
Crack patterns after the third simulated earthquake are sketched in
Fig. 4.4. The worst damage occurred in lower level beams where the
largest crack widths approached 0.40 mm. Measureable cracks (wider than
0.05 mm) extended the height of the structure. More spalling was observed
in the locations indicated in Fig. 4.4.
The waveform of the free vibration after the third simulated earthquake
(Fig. 4.5) was analysed to reveal a first mode frequency of 2. 1 Hz
(Fig. 4.6).
Results of the third steady-state test are tabulated in Table 4.6.
Difficulties with calibrations precluded determination of the tenth level
response and of the deflected shape at resonance. For this reason, relative
displacements are presented in Table 4.6 for level six (rather than level
ten). No resonance shape is presented. The approximate resonance frequency
was 1.30 Hz.
28
5. DISCUSSION OF TEST RESULTS
5.1 Introductory Remarks
Apparent characteristics of response of the test structure are summarized
and discussed in this chapter. The effects of damage and of response ampli
tude on dominant frequencies and apparent damping are noted. Response to
simulated earthquakes is compared and response maxima in the "design"
earthquake are then compared with those calculated for the linear substi-
tute model.
5.2 Apparent Natural Freguencies
Apparent natural frequencies of the test structure were determined
from free vibration, simulated earthquake, and steady-state tests. Values
of measured frequencies averaged over the duration of each test are plotted
versus response history in Fig. 5.1 and 5.2. Maximum double-amplitude
displacement (absolute sum of adjacent positive and negative displacement
peaks) incurred during or prior to the indicated test is used to represent
response history. Characteristics of measured frequencies are described
below.
(a) Initial Freguencies
The three lowest frequencies were determined from a free vibration of
the test structure before the first simulated earthquake. Values of these
frequencies are plotted in Fig. 5.1 at the zero displacement ordinate.
Also plotted are frequencies calculated for the uncracked structure (based
on gross section of members and concrete modulus of 21,000 MPa). The
measured first, second and third apparent modal frequencies were 94, 97,
and 94 percent of the respective calculated values.
29
Possible sources of discrepancy between measured and calculated
frequency values are basically inadequate modelling and unintentional
damage sustained by the test structure during construction. However,
because the discrepancy is small, it is reasonable to assume that the
"uncracked" model was adequate and that only a small amount of damage
occurred during construction. It should also be noted that the initial
"Uncracked ll frequency of the test structure is an insignificant charac
teristic concerning response to simulated earthquakes.
(b) Variation of Apparent Freguencies
An important characteristic of the test structure was reduction of
apparent frequencies observed during or after simulated earthquakes.
Reduction of frequency values with increasing double-amplitude displacement
can be seen in Fig. 5.1 and 5.2.
Study of change in free-vibration frequencies (Fig. 5.1 and 5.2)
reveals that the largest reduction in frequency occurred during the first
simulated earthquake (70 percent of the total observed reduction). The
large reduction is an expected result since the test structure is trans
formed duri ng the fi rs t tes t run from an II uncracked" to a cracked con
dition. Damage in subsequent simulated earthquakes had a much less profound
effect in reducing frequencies than was observed in the first simulation
(Fig. 5.1 and 5.2).
Response frequencies averaged over simulated earthquake durations
also decreased with increasing double-amplitude displacement (Fig. 5.1
and 5.2). It is impoy·tant to note that the apparent frequency for any
given response history was significantly lower than that for free vibrations
and also that the rate of frequency reduction from test to test was
approximately 20 percent greater. Both of the above points indicate the
30
effect of inelastic "softening" caused by the large displacements that
occur during simulated earthquakes and which cannot be accounted for by
low-amplitude free vibration tests.
Simulated earthquake response waveforms (Fig. 4.8,4.12, and 4.16)
indicate that most of the frequency reduction occurring during a simula
tion occurred during the first two seconds. This is seen not as a
characteristic of the test structure but of the base motion because it is
most intense during the first few seconds. More characteristic of the test
structure is the increasing uncertainty in determining response frequencies
as testing proceeded because of the less harmonic character of response
waveforms. This is especially evident by comparing the first and last
test runs (Figs. 4.8 and 4.16).
The rate of reducti.on in the steady-state apparent first mode resonance
frequency (Fig. 5.2) was about the same as that in simulated earthquakes.
The observed values of apparent first-mode frequency also was close to
those observed in simulated earthquakes despite differences in displacement
amplitudes. The mean displacement amplitude in the simulation test was
at least twice that in the steady-state test. No apparent trend related
the values of frequencies in the two test types (Fig. 5.2).
Some interesting observations can be made by comparing the ratios
of higher frequency values to the fundamental value (Fig. 5.3). For
free vibrations the ratios were about the same as those calculated for
the "uncracked" and the substitute-structure models, which indicates that
damage affected the three lowest frequencies approximately equally.
However, for simulated earthquakes the ratios of higher to fundamental
frequencies increased with increasing base-motion intensity (Fig. 5.3).
31
5.3 Measures of Damping
Damping in the test structure was investigated by assuming that
measured response was that of a linearly-elastic system. By making this
assumption damping could be estimated from free vibration and steady-state
tests using well-known methods. Quantitative estimates of damping for
each test type is described below.
Damping apparent in free vibration tests was determined by applying
the logarithmic-decrement method to the filtered components of tenth-level
acceleration response waveforms (Fig. 4.5). Care was exercised so as not
to include any transients apparent immediately after the test structure
was released. The value determined for the first free-vibration test
(uncracked structure) was 0.02. The corresponding value increased to 0.07
after test run one. Free-vibration tests after runs two and three indicated
values of 0.08 and 0.09. It is apparent from the above results that
damping capacity at small amplitudes (approximately one mm) increased
substantially as a result of damage incurred during the first simulated
earthquake, but only slightly after subsequent simulations.
Damping apparent during steady-state tests was determined by first
constructing frequency response curves (Fig. 5.4). Modal displacement
relative to the base was determined by reducing the relative story-level
response (Table 4.4 to 4.6) to a single-degree-of-freedom response by
normalizing with respect to observed resonance shapes (Fig. 4·.19). Modal
amplification (vertical axis, Fig. 5.4) was then the ratio of normalized
relative displacement amplitude to base displacement amplitude. Although
normalization as described here is not a correct procedure for a nonlinear
system, the extent of nonlinear behavior during steady-state tests can be
32
assumed to be small enough that a reasonable responseampl itude results.
Response in the third steady-state test was normalized with respect to
the resonance shape of the second test because no resonance shape was
determined in the third test.
Given the frequency response curves (Fig. 5.4) equivalent viscous
damping could be estimated by the bandwidth method, or by observing the
resonance amplification. Values of damping determined by either method
were on the order of 0.10 to 0.15 for all steady-state tests. r40re precise
estimates need not be given because apparent damping can be attributed
more to hysteretic response than to viscous-type damping. Indeed t the
frequency response curves (Fig. 5.4) only remotely resemble those ,of a
linearly-elastic t viscously-damped system.
Damping apparent in steady-state tests was different from that
observed for free-vibration tests. One difference was that calculated
values were on the order of twice those observed in free vibrations t
possibly because amplitudes of steady-state tests were about five times
those of free vibrations. Another difference was that response amplification
in steady-state tests decreased after the second simulated earthquake
but remained unchanged after the third t indicating that apparent damping
capacity first increased and then remained relatively constant for these
tests. Free vibrations, on the other hand, indicated that damping increased
slowly and steadily after subsequent simulations.
5.4 Response to Simulated Earthquakes
Response characteristics of the test structure subjected to three
simulated earthquakes are discussed and compared. Characteristics for
comparison were base motions, observed damage, displacements, accelerations,
forces, and moments. These are discussed below.
33
(a) Base Motions
Base motions for simulated earthquakes were modelled after the
North-South component of El Centro, 1940, with a time scale compression
of 2.5. Response spectra are plotted in Chapter 4 (Fig. 4.7, 4.11, and
4.15). Peak accelerations and spectrum intensities at various damping factors
are presented for successive earthquake simulations in Table 5.1
Base accelerations and displacements are plotted for comparison in
Fig. 5.5. The three motions were nearly identical with the exception of
magnitude. Fourier amplitude spectra of the base accelerations (Fig. 5.6)
indicate that frequency content was similar for each base motion.
(b) Observed Damage
Cracks observed in the test frames before testing began were all smaller
than 0.05 mm. in width (Fig. 4.1). During the first simulated earthquake,
measurable cracks (wider than 0.05 mm) developed only below the fifth level,
the most severe being immediately above the "long" column (Fig. 4.2).
Measurable cracks were observed through level five after the second simulated
earthquake (Fig. 4.3), and by the third they were measurable throughout the
height of the test structure. Minor spalling developed during the last
two simulations (Fig. 4.3 and 4.4) It was noted that the widest cracks
were in the beams at the column faces.
Permanent deformation parallel to the strong axis of the frames was
apparent after the first and third simulations. The permanent deformation
resulting from these two test runs was 1.5 and 1.0 mm, respectively,
measured at the tenth level. Permanent deformation transverse to the frames
34
was 0.5 mm at level ten after the first simulation. The tenth story
returned to its original position (in the transverse direction) after test
run two and remained there after test run three.
(c) Characteristics of Response Waveforms
Displacement waveforms (Fig. 4.8,4.12 and 4.16) indicate that, as
would be expected, displacements of the test structure were dominated by
first mode response. Higher mode influence was so slight as to be immeasur
able at displacement maxima. Displacement maxima at all story levels
appeared to occur simultaneously.
Acceleration waveforms (Fig. 4.8, 4.12 and 4.16) reveal that higher
modes had a large influence on accelerations. The high frequencies apparent
in base motions (Fig. 5.6) were evident in response waveforms for lower
levels but were less apparent at higher levels, having been "filtered"
by the structure. Response waveforms also indicate that, overall, higher
frequencies had more influence on acceleration response as the earthquake
intensity increased, even though base accelerations did not indicate the
same increase in higher frequencies (Fig. 5.6).
Although mode shapes were not directly measured, nodal points of
apparent second and third modes were readily visible on acceleration
waveforms (Fig. 4.8, 4.12 and 4.16) a.nd Fourier amplitude spectra (Fig.
4.10,4.14 and 4.18). For the second mode, a nodal point was located near
the seventh level. Nodal points for the third mode were located approxi
mately at levels four and nine. The nodal points calculated for the
substitute model were near level seven for the second mode and near levels
five and nine for the third (Fig. 2.6). An interesting point is that loca
tions of nodal points did not appear to change during earthquake simulations.
35
Base-level moment waveforms are plotted at the top of Fig. 4.8, 4.12
and 4.16. As is apparent in the figures, base moment was dominated by
first-mode response. It can also be noted that the base moment was quite
similar in appearance to the tenth level displacement.
Story shear waveforms (Fig. 4.8, 4.12 and 4.16) indicate that higher
frequency shears had a large influence on total story shear at the upper
levels of the test structure. At the lower levels, story shear was
dominated by the fundamental mode. The maxima of story shears (Tables 4.1,
4.2 and 4.3) occurred at approximately the same time in lower story levels.
The maximum base shear was almost totally first-mode in the first simulated
earthquake. However, other peaks in shear waveforms during that simulation
and during the maxima of subsequent simulations indicate that the first mode
contribution to the total shear could be as low as 80 percent (Fig. 4.8,
4.12 and 4.16).
In general, all response waveforms revealed changes as testing
proceeded. In the first simulated earthquake (Fig. 4.8) response appeared
to be nearly harmonic. However, by the third test when the structure was
most heavily damaged, response had lost its harmonic character (Fig. 4.16).
The latter waveforms indicate a softened structure and one with less
clearly defined modal frequencies as compared with that of the first
simulated earthquake.
(d) Response Maxima
Maximum deflections, accelerations, and story-shears are tabulated
for each simulated earthquake in Tables 4.1, 4.2, and 4.3. Deflections,
lateral forces, story shears, and story-level moments occurring at the
instant of maximum base-level moment are plotted in Fig. 5.7.
36
Maximum or nearly-maximum deflections occurred at approximately
the same instant as the maximum base-level moment (Fig. 5.7). Comparison
is made in Fig. 5.8 among maximum double-amplitude shapes observed during
simulated earthquakes, steady-state resonance shapes, and calculated linear
substitute model shape. The measured shapes are all quite similar,
indicating that the fundamental-mode shape was relatively insensitive to
either the amount of damage or amplitude of displacement. Co~paring
measured with calculated shapes, it is apparent that the substitute model
assumed the lower levels of the structure to be more stiff relative to
upper levels than they actually were. This result is consistent with the
observed cracking which was concentrated in the lower stories of the. .
structure. The design model was based on uniformly damaged elements over
the height of the structure and columns fixed at the base.
Another feature of tenth-level displacement maxima is their relation
with spectrum intensity (Fig. 5.9). That figure indicates that the rate of
change in displacement between runs three and two exceeds that between
runs two and one. It is possible that this result indicates that damping
capacity in the third simulation did not increase to the extent that it
increased during the second simulation. It should be noted that this
conclusion is consistent with results obtained in the steady-state tests
(Fig. 5.4).
A characteristic of forces measured at the instant of maximum base
moment is the influence of higher modes (Fig. 5.7). Figure 5.10 depicts
response through a half-cycle of oscillation including the maximum dis
placement during the first simulated earthquake. Higher-mode components
in lateral forces are obvious in that figure. It is esti~ated that higher
mode components could constitute up to 20 percent of the maximum base shear
37
in any test run.
The centroid of lateral forces acting on the test structure at the
instant of maximum base-level moment in the first test run was found to be
at a height of 0.67 H, where H is the height of the structure. This height
increased to approximately 0.8 Hand 0.9 H during subsequent runs.
An important characteristic of the response of a structure to earthquake
motions is the ratio of the maximum base shear to the total weight of the
structure. For the first (or design) earthquake this base shear coefficient
was approximately 0.29. The ratio of the base-shear coefficient to the
maximum base acceleration (in units of g), was 0.76. It can be observed
in Fig. 5.11 that the base-shear coefficient determined from the design
earthquake approached the upper-bound base-shear strength of the test model.
The maximum base shears in the second and third earthquake simulations
increased only slightly as member yi~ld apparently spread throughout the
structure.
The measured magnitude of the maximum base shear can be checked
approximately by calculating a first-mode shear as the sum of the products
at each level of three quantities: (1) displacement, (2) the square of
the apparent first-mode frequency, and (3) the mass. The calculation for
the maximum displacement during each test run is plotted in Fig. 5.11.
The calculated base-shear does not correlate well with the measured maxima
except for run one in which the measured shear was primarily first mode.
This calculation indicates that displacement, frequency, and lateral force
measurements are consistent.
38
Static limits to the strength of the test structure under dynamic
1oadi ng conditi ons can be determined for va ri ous 1oadi ng conditi ons.
Figure 5.13 shows three collapse mechanisms of interest. Ultimate flexural
capacity was assigned to yielding members at member faces as indicated in
the figure. Axial dead load was assumed uniformly distributed among
columns at a level. A triangular loading distributi'on was used to determine
the base shear to cause collapse (Fig. 5.13). The minimum base shear so
required was 12 kN for the mechanism of Fig. 5.l3b. The base shear
required to constitute collapse by mechanisms acting through various
story heights is plotted with the maximum measured base-shear in Fig. 5.12.
As may be concluded from the latter figure, calculated collapse base
shears to not correspond well with the maximum measured base shear. Indeed,
residual crack widths and interstory displacements incurred during test
run three suggest that yielding occurred in upper story levels and that
the test structure was approaching the collapse mechanism of Fig. 5.l3c
rather than the minimum (Fig. 5.l3b). By the mechanism of Fig. 5.l3c, the
calculated collapse base shear was within five percent of the maximum base
shear measured.
Two likely sources of discrepancy between measured and calculated
base shears to form collapse are strain rate and loading distribution.
Strain rate effects are not included in calculated collapse base shears.
The effect, especially in the third test run, could be substantial. The
effect of lateral load distribution could be expected to have an even
greater effect on the collapse strength of the test structure, especially
during test runs two and three when higher modes had a substantial effect
on lateral loads. It should be noted that the first-mode component of
39
base shear is apparently between 12 and 13 kN for all test runs, a range
of values comparable with the minimum collapse base shear of 12 kN
calculated for a triangular distribution.
The magnitude and quantity of displacement excursions of the test
structure is of interest because behavior of reinforced concrete is
dependent on response history. For convenience, tenth level displacement
peaks were divided into intervals of five mm magnitude for all displacements
larger than five mm. The number at such displacement peaks is summarized
cumulatively in the bar chart of Fig. 5.14. Referring to Fig. 5.11, the
threshold of overall nonlinear response can be said to occur at a tenth
level displacement of approximately ten mm. The bar chart (~ig. 5.14)
reveals that for the first simulated earthquake and for this test structure,
approximately 60 percent of the peaks greater than five mm extended into the
nonlinear range of response. In subsequent simulations for this test
structure, it is important to note that most of the displacement response
was less than three times that which was taken to indicate general nonlinear
behavior. However, the maxima were observed to extend approximately five
to six times that value.
(e) Comparison of Measured and Design Response
Design forces and displacements for each of two frames in the test
structure were presented in Chapter 2. Design was based on a linear model,
with substitute member stiffnesses and damping factors, subjected to forces
determined from modal spectral analysis with a design response spectrum
(Fig. 2.3). The design spectrum is compared with that obtained during the
first simulated earthquake in Fig. 5.15. The design spectrum is seen to
have been conservative for frequencies higher than 7 Hz but unconservative
for lower frequencies. Because of the difference between the design and
40
measured base motions, response of the substitute model based upon the
measured spectrum was determined for comparison with measured response.
Calculated and measured displacements, story shears, and story-level
moments are compared in Fig. 5.16.
Displacements calculated for the substitute model compare fairly
well with the maxima measured during the first (or design) simulated
earthquake (Fig. 5.16). Only near the base of the'test structure are
calculated displacements exceeded. The discrepancy at the base can be
attributed to the fact that the design model assumed absolute fixity at
the base and that columns at the base did not yield. Release of either
of these restraints would likely have increased the values of displace
ments calculated for lower story-levels.
Forces calculated for the substitute model were substantially less
than the measured maxima (Fig. 5.16). A likely reason for the discrepancy
is that the test structure was not so severely damaged as had been assumed
in the linear model (measured fundamental frequency was 2.1 Hz versus
1.74 Hz assumed). The stiffer structure would be expected to attract
more forces than the softer structure assumed.
During the design earthquake simulation the maximum tenth-level
displacement was approximately one percent of the total height of the
test structure. The maximum interstory displacement was about two percent
of the inters tory height.
A superficial comparison between measured response and response
calculated for a linear model based on gross member sections is of some
value. A spectral analysis of the model used to calculate "uncracked"
modal frequencies resulted in the response values tabulated in Table 5.2
Also tabulated for comparison are measured response and response calculated
41
for the substitute design model. All values in the table were determined
for the same base motion (the design simulated earthquake). As determined
from values in that table, the gross-section model underestimates deflec
tions by a factor of about 2 and overestimates the base shear by a factor
of about 2.
42
6. SW4MARY
60 1 Object and ScoRe
The primary objective of the experiment was to observe the behavior
during simulated earthquake motions of a ten-story, reinforced concrete
frame structure with relatively flexible lower stories. The small-scale
structure (Fig. 2.1 and 2.2) had IItall ll top and first stories. An
exterior-span beam omitted at the first story-level further reduced lower
story-stiffnesses.
The test structure was subjected successively to three base motions
of increasing intensity. The base motions were scaled versions of one
horizontal component of the record obtained at El Centro (1940).
Observations included response of the test structure (1) to earthquake
simulations, (2) in free vibration, and (3) to steady-state sinusoidal
motion at a series of frequencies bounding the estimated fundamental
frequency.
The object of this report is to document the experimental work,
present data, and discuss the observed dynamic response in relation to
stiffness, strength, and energy-dissipative capacity.
6.2 Experimental Work
One test structure, comprising two reinforced concrete frames, was
built and tested. The frames were situated opposite one another with
strong axes parallel to base motions. Ten story-masses spanned between
the test structure to increase inertial forces (Fig. 2.2). The mass at
each level was proportional to the total length of beams at the level
(nominally 302 kg at level one and 454 kg at other levels).
43
Concrete used in the test frames was a small-aggregate type with a
compressive strength of 38 MPa. Longitudinal steel was No. 13 gage
(diameter = 2.3 mm) wire with a yield stress of 358 MPa. Transverse steel
was No. 16 gage (diameter = 2.0 mm) wire bent in a helical shape.
Reinforcement was selected principally according to the substitute
structure method [J. The method features a linear modal spectral analysis
but accounts for nonlinear response of reinforced concrete structures.
Flexural steel ratios ranged between 0.74 to 1.11 percent for beams and
0.88 to 1.75 percent for columns (Fig. 2.16). Transverse reinforcement was
provided to minimize the likelihood of shear failure in the frame elements
and joints.
The test structure was subjected to simulated earthquakes with target
peak accelerations of 0.4, 0.8, and 1.2 g, the first of which was the
design earthquake. The simulations were modelled after El Centro-NS,
1940 with time scales compressed by a factor of 2.5. In addition to
simulation tests, low-amplitude free-vibration and steady-state tests
were conducted. Steady-state tests were sinusoidal base motions at
various frequencies bounding the apparent fundamental resonance frequency.
Data obtained during tests included displacements and accelerations
at each story level as well as visible structural damage. Displacements
and accelerations were recorded in analog form and were later manipulated
through the use of computers for presentation and analysis.
6.3 Data and Studies
Earthquake response data were organized in a series of time histories.
Shear and moment histories were determined from acceleration and displace
ment histories and structural configuration. Time histories are presented
44
in original form and in a form which excludes components with frequencies
higher than the fundamental frequency. Frequency contents were determined
and are presented in Fourier amplitude spectra. Response maxima are
discussed in comparison with design response and strength of the structure. '
Development of crack patterns and spalling are presented in a series
of figures.
The character of base mati ons is descri bed i'n terms of waveforms,
frequency contents, response spectra, and spectrum intensities.
Response in free-vibration and steady-state tests is presented and
discussed. Estimates of damping were made for each test.
Variation in apparent response frequencies is presented for each
test. The effects on apparent frequencies' of damage and response amplitude
is discussed.
6.4 Observed Response Characteristics
It is important before summarizing the test results to stress that the
test structure was subjected to simulated earthquakes of large intensity
to obtain overall nonlinear behavior. During the simulations, the struc
ture underwent numerous cycles at or beyond displacements where overall
nonlinear behavior occurred. In the last simulation, displacements were
observed at approximately six times that which was assumed to be the
threshold of overall nonlinear behavior. The observations and conclusions
which follow should be interpreted considering the extent of nonlinear
behavior obtained. Furthermore, the "damage" was limited to softening of
various elements resulting from axial, flexural, and bond stresses.
Despite nonlinear behavior, clearly identifiable natural response
frequencies were observed during all tests. At any stage of testing, the
45
apparent frequency varied with the displacement amplitude used in the
determination of that frequency. The higher the displacement, the lower
was the frequency. Nodal points could generally be observed for the
apparent second and third modes.
An important characteristic of apparent frequencies was the decrease
in frequency values with increasing displacement previously experienced.
Frequency values decreased by approximately 50 percent of their initial
values during the first (or design) simulated earthquake. Rate of decrease
was lower in subsequent simulations. It was observed that, for the base
motion used, approximately 70 percent of the frequency reduction in a
test run occurred during the first few seconds when response was maximum.
The amount of damage did not extensively change mode shapes although some
change in shape was observed (Fig. 5.8). The amount of damage also did
not have much effect on the ratios of first-to higher-mode frequencies at
low-amplitude response. However, for response amplitudes on the order of
those occurring during simulations, the first-mode frequency appeared to
decrease more compared with the decrease in high frequencies.
The initial "uncracked" frequencies of the test structure were within
approximately five percent of calculated uncracked frequencies. The
frequencies observed during the design earthquake did not correlate well
with those assumed for the design model because of the differences between
the assumed stiffness distribution and that in the test structure. However,
nodal points matched approximately those of the design model. The frequency
ratios calculated for the design model compared well with those observed
for all low-amplitude tests but not for higher-amplitude simulated earth
quakes.
46
The relative influence of different frequencies on response was as
would be inferred from modal spectral analysis. Displacements were
dominated by the fundamental mode while accelerations (and thus lateral
story forces) were influenced by higher-mode frequencies. Base-level
moment was predominantly first mode and in phase with the tenth-level
displacement. The contributions of higher modes were larger in the third
test run than in the first.
As inferred from residual crack widths, flexural yielding during
the design earthquake was limited to the lower four stories. By the third
simulation, measurable cracks spread through the height of the structure
and spalling was noted. Permanent deformation was small during all tests.
An equivalent viscous damping factor for the Ifuncrackedll structure was
found from the amplitude "decrement of free vibration to be approximately
0.02. This value increased substantially during the first simulation to
0.07 and then increased gradually after other simulations. Damping factors
inferred from maximum response amplifications in the higher amplitude
steady-state tests were higher than those in the free-vibration tests.
Maximum amplification in steady-state tests decreased from the first to
second tests but remained relatively constant between the second and third
tests.
Maximum displacements during earthquake simulations increased with
increasing spectrum intensity, apparently at an increasing rate. The
maximum interstory displacement during the first simulation was nearly
two percent of the story height, a condition which would be likely to
lend to serious nonstructural damage in a real building. Interstory
displacements by the end of the third simulation were large enough to
47
suggest yield in all beams of the test structure, an observation which
was confirmed by the residual crack widths.
Maximum base shear during simulations was dominated by the fundamental
mode (the first-mode component accounted for at least 80% of the measured
maxima). The maximum base shear during the design simulation was 29 percent
of the structure weight. Maxima during subsequent simulations were not
much larger in magnitude than that of the first earthquake simulation.
Various calculated collapse mechanisms for a triangular lateral
load distribution were investigated. The mechanism resulting in the
minimum base shear for the assumed load distribtuion indicated a yielding
pattern different from that apparent during the tests. A calculated base
shear for the apparent collapse mechanism was five percent less than the
observed maximum.
Response obtained during the design earthquake simulation was compared
with that determined for the design model using the measured response
spectrum. The design was intended specifically to achieve an upper-bound
set of displacements. Measured displacements were within the upper bounds
except in the lower levels. The shortcoming in the design method could be
attributed to yielding in the first-story columns which was expected from
design forces but which was not considered during the design.
Overall, apparent effects of the relatively flexible lower stories
were excessive interstory displacements in lower levels and greater-than
expected damage in beam-column joints near the top of the IItall ll column
(Fig. 2.1). Overall behavior appeared no more unsymmetric than that which
would be expected for a symmetric structure subjected to the same base
motions.
48
LIST OF REFERENCES
1. Gulkan, P. and M. A. Sozen, "Inelastic Response of Reinforced ConcreteStructures to Earthquake Motions," Journal of the American ConcreteInstitute, V. 71, No. 12, November 1974, pp. 601-609.
2. Housner, G. W., "Behavior of Structures During Earthquakes," Journalof the Engineering Mechanics Division, AS_E, Vol. 85, No. EM4, October1959, pp. 108-129.
3. Lopez, L. A., "FINITE: An approach to Structural Mechanics Systems,"International Journal for Numerical Methods in Engineering, Vol. 11,No.5, 1977, pp. 851-866.
4. Otani, S. and M. A. Sozen, "Behavior of Hultistory Reinforced ConcreteFrames During Earthquakes," Civil Engineering Studies, StructuralResearch Series No. 392, University of Illinois, Urbana, November1972.
5. Shibata, A. and M. A. Sozen, "Substitute Structure Method for SeismicDesign in RIC," Journal of the Structural Division, ASCE, Vol. 102,No. ST1, January 1976, pp. 1-18.
6. Sozen, M. A. and S. Otani, "Performance of the University of IllinoisEarthquake Simulator in Reproducing Scaled Earthquake r~otions,"
Proceedings, U.S.-Japan Seminar on Earthquake Engineering withEmphasis on the Safety of School Buildings, Sendai, September 1970,pp. 278-302.
49
TABLE 2.1
Mode Shapes and Characteristic Values Used in Design
Level First Second ThirdMode Mode ~1ode
10 1.000 1.000 1.000
9 0.941 0.583 0.027
8 0.874 0.176 -0.642
7 0.793 -0.220 -0.900
6 0.699 -0.537 -0.656
5 0.591 -0.740 -0.069
4 0.469 -0.796 0.557
3 0.337 -0.699 0.905
2 0.203 -,0.474 0.803
1 0.079 -0.196 0.374
r10da1Frequency 1. 74 5.24 9.49(Hz)
ModalDamping Factor 0.099 0.094 0.080
t·1oda1 Parti ci-pat; on Factor 1. 33 0.51 0.28
TABL
E2.
2
Des
ign
Peak
Acc
eler
atio
n,M
odal
Fre
quen
cies
,S
pect
ral
Am
plif
icat
ion,
Sub
stit
ute
Dam
ping
Fac
tor,
and
Des
ign
Spe
ctra
lA
ccel
erat
ion
Use
din
Des
ign
Des
ign
Peak
Mod
alS
pect
ral
Sub
stit
ute
Des
ign
Spe
ctra
lT
rial
No.
Mod
eN
o.A
ccel
erat
ion
Freq
uenc
yA
mpl
ific
atio
nDa
mpi
ngA
ccel
erat
ion
(g)
(Hz)
Fac
tor
(g) -
1
11
.74
1.05
0.10
0.21
12
5.24
3.14
0.10
0.63
39.
493.
750.
100.
750
1
0.4
a
1
I1
.74
1.05
0.09
9O~
212
25.
243.
140.
094
0.65
39.
493,
.75
0.08
00.
86
TABL
E2.
3
Fram
eR
einf
orci
ngSc
hedu
le
Num
ber
ofN
o.13
g.W
ires
Per
Face
Sto
ryor
Leve
l 10 9 8 7 6 5 4 3 2 1
Beam
s
2 2 2 3 3
lnte
rio
rC
olum
ns
2 2 4
Ext
erio
rC
olum
ns
2 2 4 4
(J'l
--'
52
TABLE 4.1
Response r1axima Observed Duringthe First Simulated Earthquake
Level Acceleration Displacement Shearor Story (g) (mm) ( KN)
(+) (-) (+) (- ) DA* (+ ) (- )
10 0.59 0.42 16.8 24.4 41.2 1.9 2.7
9 0.48 0.38 16.4 23.4 39.8 3.6 .4.8
8 0.43 0.36 16.0 22.8 38.8 5.2 6.5
7 0.39 0.35 15.2 21.6 36.8 6.7 8.0
6 0.38 0.32 13.4 19.7 33.1 8.0 9.4
5 0.35 0.30 12. 1 17.3 29.4 9.3 10.5
4 0.39 0.28 10.2 14.3 24.5 10.2 11.3
3 0.43 0.26 7.3 12. 1 19.4 10.7 12.2
2 0.40 0.26 4.9 7.4 12.3 10.9 12.6
1 0.34 0.29 2.4 3.8 6.2 11.0 12.8
Base 0.38 0.31
*Maximum absolute sum of any two adjacent positive and negative displacementpeaks.
53
TABLE 4.2
Response Maxima Observed Duringthe Second Simulated Earthquake
Level Acceleration Displacement Shearor Story (g) (mm)
(+) (- ) (+ ) (-) DA* (+ ) (-)
10 0.99 0.89 33.0 43.5 72.8 4.0 4.5
9 0.71 0.69 31. 7 41.6 69.4 7.2 7.5
8 0.58 0.52 31.1 40.6 68.0 9.1 9.5
7 0.51 0.45 28.8 38.3 63.0 9.8 10.8
6 0.63 0.43 26. 1 35.0 57.6 10.9 11.8
5 0.71 . 0.41 22.8 30.5 50.0 11.7 12.7
4 0.77 0.46 18.8 25.2 41.2 12.8 13.5
3 0.74 0.55 14.0 20.4 32.4 13. 1 13.7
2 00 57 0.57 9.0 13.3 20.6 12.5 13.2
1 0.60 0.52 4.3 7.3 10.6 12.7 14.0
Base 0.83 0.54
*Maximum absolute sum of any two adjacent positive and negative displacementpeaks.
54
TABLE 4.3
Response Maxima Observed Duringthe Third Simulated Earthquake
Level Acce1era ti on Displacement Shearor Story (g) (mm) (Kn)
(+) (- ) (+ ) (- ) DA* (+ ) (-)
10 1.25 1.20 49.9 57.6 106.8 5.4 5.7
9 0.85 0.81 47.0 55.2 101.8 8.6 9. 1
8 0.68 0.62 44.5 52.0 96.2 10.6 11. 1
7 0.60 0.58 41. 3 48.6 88.6 11. 5 12.4
6 0.61 0.59 36.5 43.5 79.2 12.4 12.9
5 0.59 0;60 31.6 37.5 67.2 1308 13.2
4 0.59 0.58 24.8 30.7 54.2 13.8 13.5
3 0.78 0.69 18.7 24.7 41.8 12 0 5 13.4
2 1.04 0.70 11 .9 16.0 27.0 12.0 13.4
1 1.07 0.74 5.9 9.0 14.6 11.8 14.3
Base 1.28 0.74
*Maximum absolute sum of any two adjacent positive and negative displacementpeaks.
55
TABLE 4.4
First Steady-State Test
Input Base Tenth Level AmplificationFrequency Displacement Displi'lcement at Tenth Level(Hz) (rom) (rrrn)
1.07 1.00 0.27 0.27
1.28 1.02 0.39 0.39
1.44 1.00 0.83 0.83
1. 52 0.96 1.32 1. 38
1.64 1.01 3.20 3~ 13
1.75 1. 01 50 74 5.71
1.85 0.98 5.73 5.87
1. 90 0.97 5.14 5.28
2.11 0.98 3.52 3.60
2.30 0.97 2.98 3.06
2.48 0.98 2.66 2.73
2.68 0.96 2.39 2.50
56
TABLE 4.5
Second Steady-State Test
Input Base Tenth Level AmplificationFrequency Displacement Displacement at Tenth Level
(Hz) (mm) (mm)
1.02 1. 00 0.43 0.43
1. 27 1.02 1.22 1. 19
1.43 0.97 3.96 4.10
1.48 0.99 4.18 4.24
1.53 0.99 3.88 3.93
1.64 1.03 3.48 3.38
1.83 0;99 2.97 3.01
2.01 0.96 2.61 2.73
2.21 0.95 2.33 2.44
2.41 0.98 2.13 2.18
57
TABLE 4.6
Third Steady-State Test
Input Base Sixth Level Ampl ification.Frequency Displacement Displacement at Sixth Level
(Hz) (mm) (mm)
0.85 0.94 0.39 0.41
1.05 0.94 0.67 0.71
1.19 0.94 2.79 3.0
1.26 0.94 3.24 3.4
1.30 0.93 3.20 3.4
1.36 .0.93 2.99 3.2
1.47 0.94 2.88 3. 1
1.67 0.90 2.38 2.6
1. 79 0.89 2.15 2.4
2.03 0.90 1.84 2.0
58
Table 5.1
Spectrum Intensities
Test Run Peak Spectrum Intensity forAcceleration, Damping Factor of
g 0.00 0.02 0.05 0.10 0.20
1 0.38 545 349 276 223 185
2 0.83 983 627 497 403 336
3 1.28 1170 752 597 487 411
TABLE 5.2
Comparison of Calculated and Measured Responsefor the Design Earthquake
"Gross-Section" Substitute-Structure t-1easured~1odel * Model*
Tenth-Leve1Deflection, mm 10.5 27.8 20.6**
Base Shear,kN 28.0 9.64 12.8
Base-Levelr~oment, kN-m 44.7 14.5 22
*Root-sum-square of first three modes
**Double-amplitude displacement divided by two
59
(All Dimensions In mm)
0'
f:
"
',''..
~'.
~1,v~
North ~,F
~,
rame", :::
914
0'
"
',6
o,,'
":.:.....
- ;;'1--38
1'////1'-' //////1'/1'/1'///// ./
~29~.. 686 ..~229~
II
en(\JC\J
ort)
<Xl
-oco
",
-----Jr-- ~VSouth;' Framey,
"
4
3
3
I
~>---__--=-'3:::..:...7=-2 ~
Column Line-I
Bay No.f-'
(0) S ide View (b) Front View
Fig. 2.1 Configuration and Positioning of Test Frames
CTI
o
I91
4I
..<t
...I I
Bellows~
Co
ncr
ete
Fra
me
229
279
Sto
ryM
asse
s
279
229
I_3
05
.1..
30
5.1
..3
05
..I
)'T
19JIn
lIMT!
!T~T
r~\,
Pin
Con
nect
ions
(0)
Sid
eV
iew
(b)
Fro
nt
Vie
w
Fig.
2.2
Tes
tS
truc
ture
Q)
ff) c m
O'l
--.l
Est
ima
ted
Su
bsti
tute
Str
uct
ure
Fre
qu
en
cie
s
(3=
0.0
2
0.6
T
Q)
Q)
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10.
20.
30.
40.
50.
60.
7
~F
req
uen
cy1
Hz
Peri
od1
sec.
----
-
Fig.
2.3
Smoo
thed
Des
ign
Spec
trum
for
aD
ampi
ngF
acto
rof
0.02
Com
pare
dw
ithE
stim
ated
Tes
tS
truc
ture
Fre
quen
cies
m N
8 A=
8e
yM
-8,
Unc
rack
edS
ectio
n
I.y
M-8
,C
rock
edS
ecti
on
I/
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mR
espo
nse
IL
./'I
/'
/"
III
6/"
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8,S
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or
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8=
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MAC~
......
......
......
......
..~)MB(O)
AI..
L/2
..,•
L/2
__IB
Fig.
2.4
Inte
rpre
tati
ono
fD
amag
eR
atio
en w
Long
Col
umn
43
2
Rig
idZ
on
es
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(\J
(\J
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N-o ex>
,.3
05
•,.
30
5.,
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05
../
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DD
DD
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OD
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Col
umn
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51 38 L.
T
(a)
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ram
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ea
lize
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tati
cA
na
lysi
sM
odel
(c)
Idea
lized
Mod
alA
na
lysi
sM
odel
Fig.
2.5
Tes
tFr
ame
and
Idea
lize
dM
odel
s
IJ
1I
-0.5
00
.5I
II
II
·0.5
00
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941
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9
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(a)
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stM
ode
Sha
pe(b
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econ
dM
ode
Sha
pe(c
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hir
dM
ode
Sha
pe
Fig
.2.
6C
alcu
late
dM
odal
Shap
esfo
rth
eF
irst
Thr
eeM
odes
2.7
0Q
')
U1
23
.5
II
Io
102
0
0.4
5
0.17
,I
II
o2
46
3.74
3.3
6 3.7
0
3.5
7
3.0
7
1.2
2
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I0
24
8 7 49 2356
Bas
e
Leve
l
'0
0.0
33 •
0.2~
0.1
27 -
0.3
't,0
0.2
94 -0
.5'1
8
0.6
26 - 0
.43
8 -0.5
89 - 0
.49
7 -
{a}
La
tera
lF
orce
s(K
N)
(b)
Sto
ryS
hear
s(K
N)
(c)
Ove
rtur
ning
Mom
ents
(KN
-m
)(d
)D
ispl
acem
ents
(mm
)
Fig.
2.7
Lat
eral
For
ces,
Sto
ryS
hear
s,O
vert
urni
ngM
omen
ts,an
dD
ispl
acem
ents
Use
din
Des
ign
(Fi:r
-st
t~ode)
0'\
O'l
,I
I
-20
2
1.24
1.20
1.15
I,
oI
,,
,-I
0I
1.2
5
1.17
9 4
1.35
1.13
7
1.3
0
568 23 80
'.
Leve
l10
0.7
37 ..
0.4
29 - 0
.12
9 -0
.16
2 -0
.39
5..
...-
0.5
44
4t
0.5
85
- 0.5
14
• 0.3
49 - 0
.09
6 ..
(a)
La
tera
lFo
rces
(KN
)(b
)S
tory
She
ars
(KN
)(c
)O
vert
urni
ngM
omen
tsld
)D
ispt
acem
ents
(KN
-m)
(mm
)
Fig.
2.8
Lat
eral
Forc
es,
Sto
rySh
ears
,O
vert
urni
ngM
omen
ts,an
dD
ispl
acem
ents
Use
din
Des
ign
(Sec
ond
Mod
e)
en .......
II
II
-50
5/0
0.68
5
38
55
0
552
/I
I"I
II
-50
510
-20
24
O.! O.
,...
.--
0.2
07
0.2
77
.....-
--0
.62
9
0.6
66
-0
.36
7
0./
/9
O. .....
(a)
La
tera
lF
orce
s(K
N)
(b)
Sto
ryS
hear
s(K
N)
(c)
Ove
rtur
ning
Mom
ents
(KN
-m)
(d)
Dis
plac
emen
ts(m
m)
Fig.
2.9
Lat
eral
For
ces,
Sto
ryS
hear
s,O
vert
urni
ngM
omen
ts,an
dD
ispl
acem
ents
Use
din
Des
ign
(Thi
rdM
ode)
O'l co
23
4
Key
For
Col
urnn
Line
Lo
cati
on
I>
24
9I
II
Io
300
47
52
123
98
r-'1
22
,:>
29
2I
II
,
o3
00
27
,:>
-32
6I
II
I
o3
00
,>
28
8I
II
I
o3
00
2-
54
1-
34
4-
47
5-
3-
7-
6-
8-
9-
Bo
se-
Le
vel 10
-
(0)
Col
umn
Line
One
Mom
ents
(N-
m)
(b)
Col
umn
Line
Two
Mom
ents
(N-m
)(c
)C
olum
nLi
neT
hree
Mom
ents
(N-m
)(d
)C
olum
nLi
neFo
urM
omen
ts(N
-m)
Fig.
2.10
Colu
mn
End
Mom
ents
for
Fir
stM
ode
Leve
l 10
-
0.40
1110
.72
9-
0.70
1111
.52
8-
0.9
21
112
.41
7-
0.9
61
113
.48
6-
0.9
01
11
4.6
6
5-
0.7
51
11
5.9
3
4-
0.5
21
117
.27
3-
0.2
48
.66
0.5
6'Y
1)1
".,
,..,
1 1.11 ..
I,L»)
,m,)m
»L1.
672.
41I
23
4
Key
For
Col
umn
2.2
20
.95
3.49
Lin
eL
oca
tio
n
1 2.78
0.9
04
.66
1 3.3
40
.75
5.9
3
I3.
890.
517.
27
4.4
5'"
0.23
111
8.6
7<.
.0
2-
1-
-0.0
610
.07
5.0
0 Col
umn
2of
5.75
-0.0
6
10
.06
Bo
se-
-0.4
211
.17
II
Io
510
Col
umn
3of
,'"
5.37
~0
.76
II
Io
510
II
,o
510
(a)
Col
umn
Line
One
Axi
al
For
ce(K
N)
(b)
Col
umn
Line
Two
and
Thr
eeA
xia
lF
orce
(KN
)
(c)
Col
umn
lin
eF
our
Axi
al
Fo
rce
(KN
)
Fig.
2.11
Colu
mn
Axi
alFo
rces
Incl
udin
gG
ravi
tyLo
adfo
rF
irst
Mod
e
'-J
:=>
I2
34
Key
For
Col
umn
Line
Loca
tion
3. 38
48
49
48
32
48
Leve
l 10
-
9-
8-
7-
6-
5-
4-
3-
49
2-
51
1-
34
Bas
e-I
>-2
70,
>3
06
,>
-27
4I
>23
3I
II
II
II
II
II
II
II
I0
30
00
30
00
30
00
30
0
(a)
Col
umn
Lin
eO
ne(b
)C
olum
nLi
neTw
o(e
)C
olum
nL
ine
Thr
ee(d
)C
olum
nLi
neF
our
Mom
ents
(N-m
)M
omen
ts(N
-m)
Mom
ents
(N-m
)M
omen
ts(N
-m)
Fig
.2.
12Co
lum
nEn
dM
omen
tsfo
rRS
Sof
Fir
stT
hree
Mod
es
......,-
.....~
-....J ......
23
4
')0
1')
'~
IV
Key
For
Col
umn
Lin
eL
oca
tion
6.2
2
8.81
4.9
9
3.82
10.1
4
7.4
9
2.69
II
Ia
510
0.51
1111
.71
0311
110.
80
06
5
0.46
0.3
0
0.0
9
0.5
7
0.6
3
-0.1
3
3.3
4
2.2
2
2.7
8 3.8
9
1.67
1.11
0.5
6
Co
lum
n3
at
5.3
7:t
0.8
0I
,"
II
Ia
510
11.2
1
II
Ia
510
-0.4
6
1-
80
sl-
Lev
e' 10
-0.
31
~~9
-
0.51
1.71
8-
06
5
7-
0;6
6-
0.57
5-
0.46
1116
.21
4-
0.30
1117
.49
3-
0.10
118
.80
2-
-0.1
3.
110.
14
(a)
Col
umn
Line
One
Axi
al
For
ce(K
N)
(b)
Col
umn
Lin
eTw
oan
dTh
ree
Axi
al
For
ce(K
N)
(c)
Col
umn
Line
Fou
rA
xia
lF
orce
(KN
)
Fig.
2.13
Colu
mn
Axi
alFo
rces
Incl
udin
gG
ravi
tyLo
adfo
rRS
Sof
Fir
stT
hree
Mod
es
......
N
Pro
vide
dR
esis
tanc
e(Y
ield
)3
1.2
II
I
o5
010
0
I
45
.8V
I
I5
4.2
II
-,I
..L
76
.0-,
83
.7I
92
.4I ,
10
'I I
10
8I .\
II'
I
98
.5
~~
20
.5
II
I
o5
0'0
0
--
32
.6.
43
.0
66
.6I ,
78
.5I
90
.2
99
.8I
'06
I
10
6I I
93
.2I
~r
1-
7-
9-
2-
4-
3-
8-
5-
6-
Bo
se-
Leve
l1
0-
(a)
Fir
stM
ode
Mom
ents
(N-
m)
(b)
RS
SM
omen
tsan
4P
rovi
ded
Res
ista
nce
(N-m
)
Fig.
2.14
Beam
End
Mom
ents
<t..
(a)
On
e-B
oy,
On
e-S
tory
Fra
me
(b)
De
flect
ed
Sho
pe
Bos
eM
omen
t
(c)
Mom
ents
onL
eft
Ho
Ifo
fF
ram
e
........ w
Fig.
2.15
Lat
eral
lyD
ispl
aced
,O
ne-B
ay,
One
-Sto
ryFr
ame
74
(All Dimensions In Mill imefers)
19
, (\
•9 '.
eCl
No. 16 Gage
No. 13 Gage
__t7.75
19
~=~" .... ,· ').·,."q:~+t-"':-=-:-:'"""'I' r--ir--- <t
'", .. ." <,., .• I'•0: .~::;:;+~~.: . :.
:... ,..~. ~:.: C;;.:' ~:,: ::::.(, ~ :: ':
(a) Beam With Two BarsPer Face
(b) Beam With Three BarsPer Face
19
ct
I 19 V 5C l.:
~~.....5_CL__
No. 16 Gage
r;;::::;;;;~~;::;~ ...",' ...o.· .': .
· l·, ..... : .· .;'w, .'~:.,"..
25.5
(c) Column With Two BarsPer Face
(d) Column With Four BarsPer Face
Fig. 2.16 Nominal Member Cross Sections
30
1-
ttfi
"1"",9
.,,,,C
i,,,,,L
CDC
olum
ni/
Co
mp
ress
ion
Tw
oN
o.13
Gag
e(1
)C
olum
ni/
Te
nsio
nW
ire
sP
"er
Fa
ceI
20Z ~
.. -en~,
::::J '- s; t-
10•
0•
)(
•<X
:• •
••
••
•• •
•I
••
•..
..-.
!0
Fo
ur
No.
13G
age
Wir
es
Pe
rF
ace
'-J
U"I
o10
02
00
30
04
00
50
0
Fle
xura
lM
om
en
t,kN
-mm
Fig
.2
.17
Col
umn
Inte
racti
on
Dia
gram
76
Spirals
12.70.0. x .56 ThickTubing76
Cutoff Point For AdditionalReinforcement
Typical Top /Column Detai I
No. 16 g Wire Spirals
31,8 0.0. - Pitch =10
TypicalDetai I
,-......--,...,.:;-------_......_--'I\
1)EII
----:;\-+-H-t--tt--++-..L--=--=Begm""--~:--_+t__t+t_ttt_-_ff_II
+t:te:::1j::::U=====:::u:::~l:t~~~~~
No. 13g Wire - See Frome ReinforcingSchedule For Numberof Bars Per Face
38
:tJ :'... \
.. : . ,0 .. :
: .~
25.5
<l Column
25.5
5 CL
Section "~I.!.'A" Section l al_"8 11
(All Dimensions Are In Millimeters)
Fig. 2.18 Representative Frame Details
77ItI
305 __ j 305 305
I
(1)NN
Cut Off For-+--~-Interior 1./
Column· /~Steel -/'r<)
~r<)
~,ODO
:~~~OOOTypical JOintty °0°Reinforcement: I
No.16g Wire
Typical Shear : L V :0:Reinforcemen~ 0 r'r-T b"No. /6g Wire I il ,lO:~~
~I~~~~~~~t:~ood Typical ~U °0° N(X)-o
Typical Flexural ~ ____Reinforcement: / ~ I
No. 13g Wire ~"(5~~~~~~~=~
Cut Off For ~ °0°Exterior ColumnSteel ---.,.......-----11
I[£~~~~~ft~;;t=~o~--......,o
t ~~ Column Flexural\'
Reinforcement Welded '\To 102 x 51 x 3 It -
Fig. 2.19 Location of Reinforcement Throughout a Frame
78
Tenth Level Mass
Typical AccelerometerMeasures Minor Direct ionHorizontal Acceleration
Typical AccelerometerMeasures Major DirectionHorizontal Accelerat ion ....._-
Typical LVDTMeasures Major Direct ionHorizontal Displacement
Typical AccelerometerMeasures Vert ical Accelerat ion
Fig. 3.1 Location and Orientation of Instrumentation
Wir
e
Fre
eV
ibra
tio
nI.
Wei
ght
Hun
gF
rom
Wir
eTo
Dis
plac
eS
tru
ctu
re2
.W
ire
Cu
tT
oR
elea
seS
tru
ctu
re
Fig.
3.2
Fre
e-V
ibra
tion
Tes
tSe
tup
45
kg
Pu
lley
'-l
\.0
80
Fig. 4.1 Crack Patterns Observed Before Test Run One
81
Fig. 4.2 Crack Patterns Observed After First Simulated Earthquake
82
"IndicatesSpoiling
t-
( \
Fig. 4.3 Crack Patterns Observed After Second Simulated Earthquake
83
Fig. 4.4 Crack Patterns Observed After Third Simulated Earthquake
84
0.0tl FREE VlBAATIl'lN 8EF~RE RUN ONE. UNl1 = G
0.00
O.JO
-0.00
•.
UNIT ... G
, &I
\:;:\
.: :
Ii: i! FREE VIBRATIl'lN AFTER RUN l'lNE.II II
~'I i,'" I~ •
--~-- ,.... - ~, , ~~ ===0 s;sau
y \ \~
-0.00
0.00
O.Ollt . FREE VIBRAT10N BEFORE lUI nolCl. lJIIIT • G
{"'\ IS ~
O 00 - ~~ .--"'-. I'm - ~...~l1"'~ ~ ........... ~ == • s==,I Uf v .
-0.04
O.CJllt :" J. , FREE VIBFfITIeJN AFTER RUN TW6. UNI1 '" G
0.00 -~t=\~wC">~'"= ... .t~: ~ ...1
"-0.04 ~
0.04t. fl, FREE VIBRAT10N BEFORE lUI TtflEE.
- ~ ~0.00 "~f='~~................................ -- +;, \'"I,
-0.0l! I
UNIT ... G
• • • "¥W
UNIT = GO. 0I.lI I'. • ffl'E VllmTlIlN AfTER IlJN THREE.
O A - ~ ~~ -<&-..0 -~I ~~ ~ ........ PI, 1.,1 .I
"I,-O.OIl f1. SEC.O~ l+-iO 2_il-0 3
4i_O --1ll j 0
Fig. 4.5 Free-Vibration Wavefor~s of Tenth-level Accelerations,Observed (Broken) and Filtered (Solid)
DYN.
TEST
HF2
-SE
PT13
.19
11-
FREE
VIB
lVlT
lIlN
BEFl
IAE
RUN
I-
OTN
.TE
STH
F2-
SEPT
13.
1911
-FR
EEV
IBR
ATI
ON
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13.
1911
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RUN
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13.
1911
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ken)
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II
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4.8
(con
td.)
Fir
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nse
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ken)
and
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PT.
1977
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HF2
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PT.
1977
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1977
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plac
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OrN
TEST
HF2
-SE
PT.
1977
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HF2
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PT.
1977
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HF2
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PT.
1977
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HF2
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PT.
1977
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N
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11F2
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PT.
1977
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HF2
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PT.
1977
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10.
5.
5.
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HF2
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PT.
1977
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ake.
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uri
erA
mpl
itud
eS
pec
tra
of
Acc
eler
atio
ns
~ m
1.0
0.6
0.8
PEA
lml.S
EC0.
1120
105 0.2
FREQ
UENC
YpHZ
30
/ 1//'
11//,
:if/' lv~
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110
100.
20..
120.
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.
110.
i a-:
80Ci
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1.0
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105 0.2
FREQ
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0
~
OYN
TEST
HF2
-SE
PT.
1977
-RU
N2
-AB
N
OAl1P
ING
FACT
OR;::
0.02
0..0
50.
100.
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NTE
STH
F2-
SEPT
,19
77-
RUN
2-
ABN
OAf1P
ING
FACT
OR=
0.02
0..0
50.
100.
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Fig.
4.11
Seco
ndSi
mul
ated
Ear
thqu
ake.
Lin
ear
Res
pons
eS
pect
ra
97
.)0r....~id>
10. 0 L-.._~--J._----"::~_--L_----":::~--L.._~L-...J.-_~~---A
1.0 2.0 5.0 10.0 20.0 50.0
FREQUENCY.. HZ.
orN lEST HF2 - SEPT .. 1977 - RUN 2 - RBNDAMPING FACTOR = 0.00 0.02 0.05 0.10 0.20
Fig. 4.11 (contd.) Second Simulated Earthquake. Linear Response SpectraI
II
II
II
II
II
II
II
II
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BA
SE
LEV
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Fig
.4.
12Se
cond
Sim
ulat
edE
arth
quak
e.O
bser
ved
Res
pons
e(B
roke
n)an
dC
ompo
nent
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elow
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Hz(S
olid
)
II
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II
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II
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Fig
.4.
12(c
ontd
.)Se
cond
Sim
ulat
edE
arth
quak
e.O
bser
ved
Res
pons
e(B
roke
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nent
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elow
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Hz(S
olid
)
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II
II
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II
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II
II
TENT
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TION
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II
,,
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I,
I
Fig.
4.12
(con
td.)
Seco
ndS
imul
ated
Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3.
0Hz
(Sol
id)
1.0
0
II
II
II
II
II
II
II
II
FIFT
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13
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4.0
15
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IJ
IJ
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JI
IJ
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JI
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Fig.
4.12
(con
td.)
Seco
ndSi
mul
ated
Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3.
0Hz
(Sol
id)
II
II
II
II
II
II
II
I.1
II
I,
,.-
II
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---------:r----------
----
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10
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0.0
0
-10
.0
TENT
HST~RY
SHEA
R.UN
IT,=
KN
NINT
HST~Y
SHEA
R.UN
IT=
KN
I, -EI
GHTH
STeR
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UNIT
=KN
f ,
SEVE
NTH
STeR
YSH
EAR.
UNIT
=KN
SIXT
HST~RY
SHEA
R.UN
IT=
KN
.......
a N
TSE
C0
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.02
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.0I.!
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.06
.07
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11
.01
2.0
13
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4.0
15
.0•
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II
II
II
II
II
II
II
I
Fig.
4.12
(con
td.)
Seco
ndS
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ated
Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3.
0Hz
(Sol
id)
II
If
II
II
II
II
II
II
--'
o wSE
COND
~70RY
SHEA
R.U
NIT
=KN
F~URTH
STOR
YSH
EAR.
UNIT
=KN
FIFT
HST
ORY
SHEA
R.UN
IT=
KN
FIRS
TST
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SHEA
R.UN
IT=
KN
THIR
DST
ORY
SHEA
R.UN
IT=
KN
10.0
0.00
-10
.0
10.0
...-;, "
0.00
-10
.0
10.0
0.00
-10
.0
10.0
0.00
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.0
10.0
0.00
-10
.01.
00BA
SELE
VEL
ACCELERATI~N.
UNIT
=G
O001-"~A.
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-••A!
~.....j
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II
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II
II
II
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I
Fig.
4.12
(con
td.)
Seco
ndSi
mul
ated
Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3
.0Hz
(Sol
id)
1.
llll
ITE
STIl
f2-
SEPT
.19
77-
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l2
-U
N
"1 I
llll
ITE
ST""
2-
SEPT
.19
77-
ftlJ
l2
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Il
1.
5.
10.
IS.
20.
25.
30.
35.
FAE
ll.1H
Z!
I·or10
.15
.20
.25
.30
.35
.FA
Ell.
lHZl
llll
ITE
ST1F
2-
SEPT
.19
77-
ftlJ
l2
-L2
Nll
llI
TEST
""2
-SE
PT.
1977
-lU
I2
-L7
N
0.0
O.
5.
10.
IS.
20.
25.
30.
35.
FIlE
D.
1HZ!
---0
.5
.10
.15
.20
.25
.30
.35
.FA
Ell.
1HZ!
1.O
T•
1•
llll
ITE
STIF
2-
SEPT
.19
77-
ftlJ
l2
-L3
Il
~Jll
llI
TEST
""2
-SE
PT.
1977
-lU
I2
-Ll
lN
--0
0 ~0
.0"I'-~
II
II
II
I0
.0'",.~
II
II
II
IO
.5
.10
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.20
.25
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.35
.FA
Ell.
lHZl
O.
5."
10.
IS.
20.
25.
30.
35.
FAE
ll.1H
Z!
I.O
T.
1•
llll
ITE
ST1F
2-
SEPT
.19
77-
ftlJ
l2
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lNII
llll
ITE
STIl
f2-
SEPT
.19
77-
lUI
2-
L9N
1.
S.
10.
IS.
20.
25.
30.
35
.FA
Ell.
IHlJ
1.
s.10
.IS
.20
.25
.30
.35
.FA
Ell.
1HZ!
llll
ITE
ST1F
2-
SEPT
.19
77-
lUI
2-
L5N
llll
ITE
ST""
2-S
EP
T.
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I2
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S.
10.
IS.
20.
25.
30.
0.0
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1"'""
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II
I1
II
I35
.FA
Ell.
1HZ!
O.
S.
10.
15.
20.
25.
~O.
35.
fRED
.1H
Z!
Fig.
4.13
Seco
ndSi
mul
ated
Ear
thqu
ake.
Fou
rier
Am
plitu
deS
pect
rao
fD
ispl
acem
ents
1.
1.
OTN
TEST
1F2
-SE
PT.
1977
-AU
N2
-A
I"OT
NTE
ST1F
2-
SEPT
.19
77-
AUN
2-
A6N
35.
FRED
.lH
Zl30
.25
.20
.15
.
OTN
TEST
1F2
-SE
PT.
1977
-lU
I2
-A7
N
10.
5.
1.0
35.
FAEQ
.(H
Zl30
.25
.20
.15
.
OTN
TEST
IF2
-SE
PT.
1977
-lU
I2
-A2
N
10.
5.
10.
15.
20
..2
5.30
.35
.FA
EQ.
lHZl
O.5
.10
.15
.20
.25
.30
.35
.FR
ED.
lHZl
I.,
I1.
ll.OT
NTE
STIF
2•
VT
.19
77-
lUI
2-
A3N
OTN
TEST
1F2
-SE
PT.
1977
-lU
I2
-Al
lN
..... 0 CJ1
O.OU
'"W'Irrq
_. ,
1st'
I1O.OUI'I·U~"
II
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5.
10.
15.
20
.25
.30
.35
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Eg.
(HZ!
O.5
.10
.15
.20
.25
.30
.3
5.
FRE
g.(H
Zl
I.,
I1.
III
OTN
TEST
IF2
-SE
PT.
1977
-lU
I2
-_
OTN
TEST
1F2
-SE
PT.
1977
-lU
I2
-AS
H
OTN
TEST
1F2
-SE
PT.
1977
-lU
I2
-A
10N
O.oUI'I~'~·~r"l~~~_.1'
II
35.
FRED
.(H
Z)O
.5
.10
.15
.20
.25
.30
.35
.FA
Eg.
,HZ)
30.
25.
20
.15
.
OTN
TEST
IF2
-SE
PT.
1977
-lU
I2
-A5
N
10.
5.
1.o.o
lllr'iV
1lrIl"r~"'f"'_~"
IO.OV'··~'
TIl~"ee!.M¥""""·
fe.
I'mI
IO
.5
.10
.15
.2
0.
25.
30.
35.
FRE
g.(H
ZlO
.5
.10
.15
.2
0.
25.
30
.3
5.
FRE
g.IH
Zl
1.
Fig.
4.14
Seco
ndSi
mul
ated
Ear
thqu
ake.
Fou
rier
Am
plitu
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PT.
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S-
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ING
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TEST
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PT.
1977
-RU
N9
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N
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ING
FACT
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0.02
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00.
20
Fig
.4.
15T
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Sim
ulat
edE
arth
quak
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inea
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ctra
500.0
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1.0 2.0 5.0 10.0 20.0 50.0
FAEWENCY p HZ.
OYN TEST MF2 - SEPT p 1977 - RUN 3 - ABNDAMPING FACTOR. 0.00 0.02 0.05 0.10 0.20
Fig. 4.15 (contd.) Third Simulated Earthquake. Linear Response Spectra
II
II
II
II
II
II
II
II
NINT
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Fig.
4.16
(con
td.)
Thi
rdSi
mul
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Ear
thqu
ake.
Obs
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nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3.
0Hz
(Sol
id)
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Fig.
4.16
(con
td.)
Thi
rdSi
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Obs
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nse
(Bro
ken)
and
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pone
nts
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II
II
II
II
II
II
II
Fig.
4.16
(con
td.)
Thi
rdSi
mul
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Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Belo
w3.
0Hz
(Sol
id)
II
II
II
II
II
II
II
II
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-'
w
FIFT
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SHEA
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SHEA
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I.(J
10.0
0.00
-10
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0.00
-10
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10.0
0.00
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0.00
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01.
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06.
07.
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II
II
II
II
II
II
II
I
Fig.
4.16
(con
td.)
Thi
rdSi
mul
ated
Ear
thqu
ake.
Obs
erve
dR
espo
nse
(Bro
ken)
and
Com
pone
nts
Bel
ow3.
0Hz
(Sol
id)
1.1
.0
DTN
TEST
HF2
-SE
PT.
1977
-lU
I3
-L
INO
THTE
STH
F2-
SEPT
.19
77-
lUI
3-
LaN
10
.1
5.
20
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5.
30.
35.
FAEQ
.(H
Zl5.
10
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5.
20
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0.
35.
FAEQ
.IH
Zl
OTH
TEST
HF2
-SE
PT.
1977
-lU
I3
-L2
N
DYN
TEST
HF2
-SE
PT.
1977
-lU
I3
-L3
N.....
......
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35.
FAEQ
.IH
Zl3
0.
25
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.15
.
OTH
TEST
HF2
-SE
PT.1
97
7-
lUI
3-
LaN
DYN
TEST
HF2
-SE
PT.
1977
-lU
I3
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N
HI.
5.
1.1. 0.0
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tI
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II
35.·
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20
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30.
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FAEQ
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35.
FAEQ
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30.
30.
25
.
25.
20
.
20
.
15
.
15
.
10
.
10
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.
5.
1.
DYN
TEST
HF2
-SE
PT.
1977
-lU
I3
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NTE
STH
F2-
SEPT
.19
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5.
20
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5.
3D.
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FAEQ
.(H
Zl
1.
1.0
DYN
TEST
HF2
-SE
PT.
1977
-lU
I3
-LS
NOY
HTE
ST11
F2-
SEPT
.19
77-
lUI
3-
LIO
N
5.
10
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5.
20
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5.
30.
0.0
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35.
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lJO
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20
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(HlJ
Fig
.4.
17T
hird
Sim
ulat
edE
arth
quak
e.F
ouri
erA
mpl
itude
Spe
ctra
of
Dis
plac
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ts
1.
1.
llYN
TEST
1f'2
-SE
PT.
1977
-lU
I3
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ST1f
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SEPT
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77-
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35
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5.
10.
15.
20
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35
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OTN
TEST
111'2
-SE
PT.
1977
-IU
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1. o.or"··~·"'~~.o
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II
35
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5.
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lHll
30.
25
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5.
10
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.
0.0
5.
10
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5.
20.
25.
30.
35
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RE
Q.
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5.
10
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5.
20.
25
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0.
35.
FREQ
.IH
Zl
I.
llYN
TEST
If'2
-SE
PT.
1977
-lU
I3
-A
3Il
I•
llYN
TEST
1f'2
-SE
PT.
1977
-lU
I3
-Ae
N
..... ......
U'1
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I5
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0.
15
.20
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.30
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5.
FREQ
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.10
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.20
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5.
30
.35
.FR
EQ.
IHZl
l'j
I1
.
I~llY
NTE
STIf
'2-
SEPT
.19
77-
lUI
3-
_llY
NTE
ST11
1'2-
SEPT
.19
77-
filii
3-
Il9N
llYN
TEST
1f'2
-SE
PT.
1977
-lU
I3
-AS
HOT
NTE
ST11
1'2-
SEPT
.19
77-
AIJ
I3
-A
IOIl
35.
FRE
a.(H
Z)3
0.
25.
20.
IS.
10.
5.
I.
35
.FR
Ea.
IHlJ
30.
25
.20
.1
5.
10
.5
.
I.
Fig
.4
.18
Th
ird
Sim
ula
ted
Ear
thqu
ake.
Fo
uri
erA
mpl
itud
eS
pec
tra
of
Acc
eler
atio
ns
116
Level10 ----..... 1.000 -----1.000
9 0.973 0.972
8 0.943 0.939
7 0.885 0.876
6 0.807
5
4
3
2
80se
(a) First Steady -StateTest
(b) Second Steady-StateTest
Fig. 4.19 First-Mode Resonance Shapes Observed DuringSteady-State Tests
117
Fig. 5.1 Comparison of Apparent Modal Frequencies with MaximumTenth-Level Displacement Previously Experienced by TestStructure
118
I I
5.0 I--
o Free Vibration• Simulated EarthquakeoSteody - State... 4.0 - -%:..
""ucU::lCT 5.0~ -e 0/1.1:
u0'0
0:E 2.0 ..-- • 0 -I
0-co~ 0ii: •
1.0 I-- -
I I I I I r°0~--~2~O----4""O"""---6~O---~80"----...IIOO"""---12.&.O-~
Double - Amplitude Displacement I mm
Fig. 5.2 Comparison of Apparent First-Mode Frequency with MaximumTenth-Level Displacement Previously Experienced by TestStructure
119
I I I I
30 10- Simulated 'FreeEarthquake Vibration
2nd MOdeC .. A3rd Mode I 0
025 I--
N 20~ -:::J:
enQ)
0'u •cQ):::JtT IS I--- -Q)~u.~
Q) •s=0'
:r::10 i---" • -
A
AA
51--- AA
I I 1 I Iool~----.L.'----~2----~3------14~---~5~""
First - Mode Frequency t Hz
Fig. 5.3 Comparison of Observed High Frequencies with First-Mode Frequency
120
5.0
3.0o.....~~-----------------'----_..I-_ ....
2.0
Frequency, Hz
c 4.00-CU....Q. 3.0E~
::
0
" 2.00~
::Second Steady-State
1.0
Fig. 5.4 "Modal" Amplification Compared with Exciting Frequency inSteady-State Tests
II
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II
II
II
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II
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Fig. 5.11 Comparison of Base Shear and 'Tenth-Level Displacement
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20
15 ~Maximum MeasuredBase Shear
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135
APPENDIX A
DESCRIPTION OF EXPERIMENTAL WORK
A.l Concrete
The concrete was a small-aggregate type. The cement was high early
strength. Coarse and fine aggregates were, respectively, Wabash River
sand and fine lake sand. Mix proportions we~e 1.1 : 1.0 : 4.0 (coarse
fine: cement) by dry weight. A water: cement ratio of 0.74 was chosen
based on desired workability and compressive strength. A slump of 70 mm
was obtained.
The control specimens and the test specimen were cast from a single
batch. Age of the test specimen at testing was 47 days. The control
specimens were tested at 49 days. Similar treatment for both control
specimens and test frames was provided during the intervening period.
Control specimens comprised ten 100 by 200 mm cylinders for compression
tests, six 100 by 200 mm cylinders for splitting tests, and eleven
50 by 50 by 200 mm prisms for modulus-of-rupture tests.
The stress-strain relationship was determined from compression
tests on 100 by 200 mm cylinders. Strains were measured over a 125 mm
gage length with a O.OOl-in mechanical dial gage. It was not possible to
measure the descending portion of the stress-strain curve with any
accuracy because of equipment limitations. Figure A.l. shows the bounds
of all the stress-strain curves compared with the relation used in design.
The ultimate compressive strength, f~, had a mean of 38 MPa with a standard
deviation of 2.3 MPa. The secant modulus, Ec ' as determined from a
straight line drawn from the origin through the stress-strain curve at
20 MPa, had a mean value of 21000 MPa.
136
The tensile strength of the concrete was determined by splitting 100
by 200 mm cylinders. The mean tensile strength, f t , was 3.59 MPa with a
standard deviation of 0.38 MPa.
The modulus of rupture, f r , was determined by loading 50 by 50 by
200 mm prisms at the center of alSO mm span. The mean modulus of rupture
was 7.88 t1Pa with a standard deviation of 0.72 f4Pa.
A.2 Reinforcing Steel
Longitudinal steel for beams and columns consisted of No. 13 gage
bright basic annealed wire (Wire Sales Company, Chicago). The wire was
ordered annealed and processed to a yield stress of approximately 400 MPa.
All wire was received in straight 3 m lengths.
Stress-strain properties of the No. 13 gage wire were determined
at a strain rate of 0.005/sec. From ten coupons tested, Young's modulus
was determined to be 200,000 MPa. The mean and standard deviation for
the yield stress were 358 MPa and 5.2 MPa.The mean stress-strain
relation is plotted in Fig. A.2.
Wire for the helical and spiral reinforcement was #16 gage annealed
wire. The wire was received in a roll. It was subsequently straightened
and turned on a lathe into the helical or spiral shape. Considering the
extent of overdesign with regard to shear failure, extensive testing of
the wire was not required. However, the yield stress of the wire was
determined to be approximately 750 MPa.
A.3 Specimen Details
(a) Frame Configuration
One test structure was built. It consisted of two ten-story, three-bay
frames cast monolithically with very stiff base girders. The overall
137
configuration of a frame is shown in Fig. 2.1. Column lines were
regularly spaced. Story heights varied, those at levels one and ten
being approximately 20% taller than those at other levels. In addition,
an exterior-span beam was omitted at the first level in each frame
(Fig. 2.1). Stubs protruding from all beam and column ends were'provided
for development of reinforcing steel.
Nominal gross cross-sectional beam dimensions were 38 by 38 mm,
while those for columns were 51 by 38 mm. Owing to fabrication tolerances,
these dimensions differed slightly from the nominal values. The measured
gross dimensions are presented in Tables A.l through A.5. All depth
dimensions were measured in the plane of the frame. Width dimensions
were measured perpendicular to that plane. A key locating column lines
and East-West direct10ns is given in Fig. 2.1 Nominal beam and column
lengths varied as shown in Fig. 2.1. Measured lengths did not differ
from these values.
Holes were provided in the center of each beam-column joint to
facilitate supporting of a mass at each level (Fig. 2.18). These holes
were reinforced with steel tubing (12.7 mm outside diameter). Holes were
also provided in the base girders (Fig. A.3). Horizontal holes were
provided to facilitate the transporting of the frames from the formwork
to the test platform, while vertical holes were provided for fastening
the test structure to the test platform. Both horizontal and vertical
holes were reinforced with steel tubing (19 and 44 mm outside diameters,
respecti vely).
(b) General Reinforcement Details
Preparation of all steel was initiated by soaking in solvent and
then wiping clean. The longitudinal steel was then cleaned further with
acetoneo This process left the steel free of dirt and oil.
138
The steel reinforcing cages were assembled by tying all reinforcing
elements with a ductile steel wire (0.91 mm diameter). Longitudinal
steel was continuous with the exception of cutoffs in the columns at the
lower levels (Fig. 2.19). No welding was performed except at the base
of the vertical steel where 3.2 mm thick steel plates were welded to
insure embedment into the base girders (Fig. A.3).
The completed cages were removed to a fog room. There they were
sprayed with ten percent hydrochloric acid solution and left for four
days to rust the steel in order to improve bond. The extent of rusting
was such that it had negligible effects on the steel force-strain
properties. All loose rust scales were removed with a wire brush prior
to placement of the cages in the forms.
(:c) Beam and Col umn Reinforcement
The distribution of beam and column reinforcement is given in Table
2.3. Typical details are shown in Fig. 2.16, 2.18, and 2.19. Steel
ratios for columns are computed as the ratio of the total longitudinal
steel to the nominal gross cross-sectional area. For four and eight bars
the steel ratios were 0.88 percent and 1.75 percent. For beams, the
steel ratios are computed as the ratio of the steel area per face to the
nominal effective area of the section (nominal width times nominal depth
to tension steel). Three bars per face gave a steel ratio of 0.74
percent. For two bars, the ratio was 1.11 percent. Nominal beam and
column cross-sections are shown in Fig. 2.16. Following testing, the mean
cover of longitudinal steel was determined to be 6.1 mm for columns and
6.7 mm for beams versus the nominal value of 6.6 mm.
139
Development of the full flexural capacity of all members was of
primary concern in design. Development of this capacity required either
embedment or an adequate development of longitudinal steel. In general,
this was accomplished by having all steel continuous and developed into
protruding stubs at member ends (Fig. 2.18). In the stubs, the steel
was bent to the opposite face of the member. Column steel at the base
was developed 102 mm into the base girder and welded to steel plates
(Fig. A.3). Finally, where bar cutoffs were made in the columns, the
steel was developed 64 rom above floor level centerlines.
Transverse reinforcement consisted of #16 gage wire bent into a
helical shape. The outside dimensions. and pitch are shown i,n Fig. 2.18.
The quantity Avf dis (where A = cross-sectional area of the wire,y v
fy = yield stress, d = effective depth of beam, and s = spacing of
transverse reinforcement) was 9.0 KN (minimum) compared with a maximum
expected shear force of 2.6 KN.
(d) Joint Reinforcement
Two types of beam-column joint reinforcement were used. Number 16
gage spiral reinforcement provided joint confinement. The outside diameter
and pitch were 31.8 and 10.0 mm, respectively. The second type of
reinforcement, a steel tubing, served to reinforce the holes provided for
support of the concrete masses at each level. The locations within a
joint of each reinforcement type are shown in Fig. 2.18 and 2.19.
(e) Base Girder Reinforcement
The base girder was designed as a rigid element of each frame.
Fig. A.3 presents the details of the reinforcement.
140
(f) Concrete Casting and Curing
The test specimen was cast monolithically in a horizontal position.
Formwork consisted of a steel form bed and steel side pieces. Casting
of both frames and of the control specimens was done simultaneously
from a single batch of concrete. Concrete was vibrated with a stud
vibrator. Vibration for the base girders was done by placing the
vibrator inside the formwork. Vibration for the rest of each test
specimen was done by vibration against the reinforcing cage. All
concrete was in place within one and one-half hours of mixing. Finishing
was done approximately one-half hour after placement had been completed.
The specimens were covered with a plastic sheet for 8 hours to help
prevent water loss. After this time) the sheet was removed and all side
pieces of the forms were removed. The specimens were sUbsequently
covered with wet burlap and plastic sheets for a period of 18 days.
Removal of the specimens from the forms immediately followed this period
of curing. This was done by first fixing the specimen to the formwork.
The formwork and the specimen were then lifted with a crane to an upright
position such that the weight of the specimens was supported by its base
and the formbed was supported by the crane. Removal of the bolts fixing
the specimen to the form allowed the form to be separated from the
specimen. All specimens were then sored in the laboratory for an
additional period of 29 days.
A.4 Dynamic Tests
(a) Earthquake Simulator
The dynamic tests of the structure were run on the University of
Illinois Earthquake Simulator. The earthquake simulator is located in
141
the Structural Research Laboratory of the Civil Engineering Department at
the University of Illinois at Urbana-Champaign. Major components of the
system are a hydraulic ram, a power supply, a command center, and a test
platform. The overall configuration of the hydraulic ram and the test
platform is shown in Fig. A.4.
The test platform is 3.66 m square in plan. Four flexure plates
support the test platform so that it has essentially unrestrained free
motion in one horizontal direction. A 330 KN capacity hydraulic ram
drives the test platform. A flexure link connects the hydraulic ram and
the test platform.
Motion of the test platform is controlled by input from the command
center. An appropriate acceleration record is integrated twice and the
resulting displacement record is recorded on magnetic tape. This record
forms the input for a test run. A servomechanism uses the input to
control the hydraulic ram and reproduce the desired motion.
A more detailed description of the earthquake simulator and its
performance can be found in Reference [4] and.[6].
(b) Assembly of the Test Structure
The test structure was assembled on the simulator platform. It
consisted primarily of the two frames and their connections to the platform
and the ten masses with their connecting systems. The entire structural
system can be seen in Fig. 2.2 and A.4. Three stages of construction are
distinguished to be (1) stacking of the ten masses, (2) positioning of
the frames adjacent to the ten stacked masses, and (3) connection of the
masses to the frames.
Construction was begun by stacking ten story-masses on wooden blocks
on the earthquake simulator platform. The mass of each is presented in
142
Table A.6. Each was positioned so that its known center of mass would
coincide with the appropriate story level. Bellows (Fig. 2.2) were
attached to each mass after it was positioned. The two test frames were
then positioned astride the stacked masses and the base girders fixed to
the test platform (Fig. A.4). Fixity was provided by bolting angle
sections across the base girders so as to bear down on them and by pro
viding reaction angles at the end of each base girder (Fig. A.4).
The mass at each story-level was supported by two cross-beams which
protruded from beneath each mass in the transverse direction (Fig. 2.2).
The crossbeams were pinned at either end to perforated channels which
were in turn pinned through frame joints (Fig. A.5). Although the
connections through frame joints cannot be considered frictionless,
they were made only "snug" tight so as to reduce the transfer of moment
between a mass and a joint. In addition, washers were provided (Fig.
A.5) to further reduce moment transfer.
The mass-connecting system for levels two through ten was such that
each frame joint was ideally leaded with one~eighth of the total load
acting at that floor-level. The connection at the first level was
indeterminate (Fig. 2.2).
(c) Instrumentation
Displacements and accelerations were the two types of data directly
obtained in the dynamic tests of the structure. Displacements were
measured with differential transformers (LVDT's) and accelerations with
accelerometers. Locations and orientations of these instruments on the
structure are shown schematically in Fig. 3.1.
143
LVDT's measured relative displacements of each side of the structure,
one at each level on a given frame. These were attached to the perforated
channels of the mass-supporting system, these channels being confined
to move identically with the frame at that level (Fig. A.5). The LVDT's
were mounted to an A-Frame which was rigidly fixed to the test platform
and which served as a rigid reference to the base. The natural frequency
at the A-Frame was approximately 48 Hz. In addition, one LVDT measured
displacements of the hydraulic ram. Mechanical calibrations were per
formed by mechanically moving the rod of the LVDT. Machined aluminum
spacers were used to define the displacement of the rod in each mechanical
calibration. In addition, resistive electrical calibrations were made
throughout the tests.
Accelerations were measured in both horizontal and vertical directions
with two types of accelerometers (Endevco piezoresistive and Endevco
Q-Flex). Location and orientation of all accelerometers is shown
schematically in Fig. 3.1. Accelerometers which measured horizontal
accelerations of each frame in the direction of the input motion were
attached at each level to a perforated channel of the mass-supporting
system (Fig. A.5). Additional accelerometers were mounted one to the base
of each frame and one at the center of the tenth level mass to measure
in-plane motion at that point. Two accelerometers measured torsional
accelerations, that is acceleration out of the plane of the input motion.
These were attached at opposite ends of the tenth level mass (Fig. 3.1).
Finally, two accelerometers measured vertical acceleration. These were
mounted at the top of exterior columns, one at the side with the omitted
144
beam and one at the side with beams at all levels. Mechanical calibra
tion of all accelerometers was done by holding them vertical and then
rotating to a horizontal posHion for an acceleration of one g. All
accelerometers of a given type (piezoresistive or Q-Flex) were mechanically
calibrated simultaneously. Electric calibrations were performed for
accelerometers throughout the tests.
(d) Test Procedure
The tests were conducted in a single day. An outline of the test
procedure insured that the tests would be conducted smoothly and
reliably.
On the morning of the tests, the wooden blocks supporting the masses
were removed, transferring the weight of the masses to the test frames.
All connections were checked to insure a11ignment and to insure the
tightness of connecting bolts. All bolts connecting the frames to the
test platform were retightened to compensate for the creep that had
occurred under the high bearing stress.
Preparation of the earthquake simulator required that the hydraulic
ram be warmed up prior to the test. This was done by operating the ram,
free of the test platform, for one-half hour. After this time, the ram
was connected to the test platform~
Shrinkage cracks in the frames were checked both before and after
the masses had been connected to the frames, but before the first test
run. Cracks were located by spraying the frames with "Partek" Pl-A
Fluorescent (Magnaf1ux Corporation, Chicago, Illinois). The liquid
penetrated the cracks, reflecting under a "b1ack 1ight" to show the
crack patterns. Observed cracks were marked on the structure and
recorded on data sheets.
145
The actual conduct of a test is given below.
(1) The test structure was given a small-amplitude free vibration
by laterally displacing and then releasing the tenth-level mass (Fig.
3.2).
(2) The test structure was subjected to the earthquake input
selected for that test run.
(3) The crack pattern resulting fron the test run was observed,
marked on the structure, and recorded on data sheets. Any spalling or
crushing was also noted.
(4) The test structure was given another small-amplitude free
vibration.
(5) The test structure was subjected to a sinusoidal base motion
starting at a frequency below the apparent resonance frequency and
sweeping in steps to a frequency above the observed apparent resonance
frequency.
The above sequence formed one test run. Three such runs were
performed. Electrical calibrations were made before and after each of
the steps (1), (2), (4), and (5). The voltages from free vibrations,
simulated earthquakes, steady-states, and electrical calibrations were
recorded on magnetic tape. A movie camera and a videotape machine
recorded the motion of the test structure during the test runs.
A.5 Data Reduction
Response measurements in all tests consisted of instrument voltage
responses. These voltage responses were amplified as required and
continuously recorded by four magnetic tape recorders. Each recorded
146
13 voltage signals and one audio signal. One of the 13 voltage signals
was a signal common to all recorders, thereby allowing synchronization
of all response measurements.
In order to put the data in a more usable form, the analog records
were converted to a digital form using the Spiras-65 computer of the
Department of Civil Engineering. Data was digitized at 250 points per
second and the digitized data recorded on magnetic tape.
Using the digital tape, calibrations and zero levels for each test
event were determined using a computer program. Another computer
program was then used to calibrate and zero the digitized voltage
responses and to reorganize the data in terms of a series of time
histories, one for each instrument and test event. One option of this
computer program was used to record the reorganized data on another
magnetic tape. A second option allowed determination of amplitudes and
frequencies for use in the steady-state tests.
A series of computer programs was then used to manipulate the
response-time histories. The functions of these are destribed below.
(a) Story shear and moment histories were determined for simulated
earthquakes at each digitized time instant (250 per second) by considering
horizontal accelerations, displacements, story-masses, and story heights.
The P-delta moment was included. These histories were also recorded on
magneti c tape.
(b) Response-time histories were plotted (Chapter 4). A filtering
option utilizing the Fast Fourier Transform allowed specified harmonic
components of the histories to be filtered from the total response.
(c) Spectrum intensities and response spectra were determined at
various damping factors and the latter plotted (Chapter 4).
147
(d) Fourier amplitude spectra were determined and plotted using the
Fast Fourier Transform. Dominant frequency components were determined
from these (Chapter 4).
(e) Response at any time instance could be determined. Distri
butions of displacements, accelerations, lateral forces, story shears,
and story moments at the specified instant were determined and plotted.
These were used to observe changes in distributions throughout the test
runs.
Tab
leA
.lM
easu
red
Gro
ssC
ross
-sec
tion
alBe
amD
imen
sion
s-
Nor
thFr
ame
Dim
ensi
ons,
mm.
Bay
1Ba
y2
Bay
3
Lev
elD
epth
Wid
thD
epth
Wid
thD
epth
Wid
th
10W
est
39.4
40.1
38.9
39.1
38.1
38.6
Eas
t38
.439
.638
.438
.439
.639
.1
937
.640
.138
.639
.137
.838
.639
.139
.638
.639
.139
.138
.98
37.8
39.9
38.4
38.9
37.1
39.6
37.8
39.4
38.1
39.4
38.6
39.9
737
.138
.937
.839
.137
.340
.1.....
...j:
::o
·38.
139
.938
.138
.637
.839
.9co
638
.139
.937
.639
.938
.639
.936
.839
.137
.639
.437
.639
.6
538
.139
.938
.438
.437
.639
.938
.138
.438
.138
.938
.439
.6
437
.639
.136
.838
.636
.638
.937
.638
.937
.338
.937
.838
.6
337
.339
.437
.838
.438
.638
.637
.338
.438
.138
.937
.640
.4
238
.139
.137
.838
.437
.339
.436
.838
.638
.440
.138
.439
.9
1W
est
37.6
39.9
38.1
38.9
Eas
t38
.438
.437
.139
.6
mea
n37
.939
.338
.039
.038
.039
.4st
d.
dev.
0.67
0.59
0.53
0.49
0.75
0.59
Tab
leA
.2M
easu
red
Gro
ssC
ross
-sec
tion
alBe
amDi~ensions
-So
uth
Fram
e
Dim
ensi
ons,
mm.
Bay
1Ba
y2
Bay
3
Lev
elD
epth
Wid
thD
epth
Wid
thD
epth
Wid
th
10W
est
38.1
38.6
39.1
38.9
38.1
38.4
Eas
t36
.338
.638
.438
.137
.639
.1
939
.939
.138
.638
.139
.438
.638
.438
.639
.439
.438
.439
.4
838
.138
.938
.438
.938
.638
.638
.438
.638
.439
.138
.439
.1
7·3
7.6
38.9
38.9
38.6
37.6
38.4
-I
38.4
38.6
38.1
38.9
38.4
38.6
..r.:.~
638
.138
.637
.638
.438
.438
.438
.638
.638
.138
.938
.438
.6
538
.637
.838
.438
.637
.638
.138
.138
.438
.638
.638
.138
.9
437
.338
.438
.138
.637
.838
.638
.438
.138
.438
.638
.438
.6
338
.639
.139
.138
.138
.138
.638
.638
.637
.839
.637
.838
.9
238
.139
.437
.838
.938
.138
.437
.838
.438
.439
.938
.638
.9
Wes
t37
.338
.939
.138
.4-
-,E
ast
37.8
38.4
37.6
39.1
mea
n38
.138
.638
.438
.838
.238
.7st
d.
dev.
0.71
0.36
0.54
0.48
0.45
0.32
Tab
leA
.3M
easu
red
Gro
ssC
ross
-sec
tion
alC
olum
nD
imen
sion
s-
Nor
thFr
ame
Dim
ensi
ons,
rrm.
Colu
mn
Lin
e1
Colu
mn
Lin
e2
Colu
mnL
ine
3Co
1umn
Lin
e4
--
Sto
ryD
epth
Wid
thD
epth
Wid
thD
epth
Wid
thD
epth
Wid
th
]0to
p50
.839
.451
.138
.650
.338
.450
.838
.9bo
ttom
50.8
39.4
50.3
39.4
50.0
38.9
50.3
38.9
950
.839
.950
.538
.650
.839
.450
.339
.151
.139
.449
.838
.950
.539
.651
.139
.48
50.8
39.4
50.3
39.4
50.8
38.4
50.5
40.4
51.1
38.9
50.8
38.6
50.3
39.1
51.3
39.9
.....7
51.1
38.9
50.5
40.4
49.8
39.9
50.8
38.1
01
051
.139
.450
.538
.950
.539
.150
.839
.6
651
.140
.450
.039
.450
.839
.649
.838
.949
.839
.450
.038
.150
.538
.650
.838
.4
550
.539
.150
.838
.950
.538
.949
.339
.950
.839
.450
.338
.650
.339
.151
.139
.9
450
.339
.950
.538
.949
.838
.649
.839
.651
.339
.150
.338
.451
.338
.150
.839
.4
350
.039
.150
.538
.650
.838
.450
.839
.650
.838
.650
.838
.450
.839
.450
.040
.4
250
.839
.150
.538
.650
.839
.150
.338
.950
.338
.650
.338
.950
.538
.4
1to
p50
.339
.150
.838
.950
.339
.1bo
ttom
50.5
39.1
50.6
39.6
49.~
39.6
51.1
39.6
mea
n50
.739
.'350
.438
.950
.439
.050
.539
.4st
d.
dev.
0.40
0.43
0.33
0.52
0.43
0.51
0.54
0.64
Tab
leA
.4M
easu
red
Gro
ssC
ross
-sec
tion
alC
olum
nD
imen
sion
s-
Sout
hFr
ame
Dim
ensi
ons,
mm.
Colu
mn
Lin
e1
Colu
mn
Lin
e2
Colu
mn
Lin
e3
Col
umn
Lin
e4
Sto
ryD
epth
Wid
thD
epth
Wid
thD
epth
Wid
thD
epth
Wid
th
10to
p50
.838
.150
.039
.450
.538
.451
.138
.6bo
ttom
51.1
39.1
51.1
38~
150
.338
.450
.838
.9
950
.339
.650
.838
.450
.038
.451
.139
.151
.139
.651
.138
.450
.338
.950
.339
.1
850
.838
.650
.838
.450
.838
.650
.838
.951
.138
.150
.838
.450
.338
.950
.538
.6.....
50.5
38.4
38.4
(J"I
750
.838
.438
.150
.050
.8.....
50.8
38.4
51.1
38.6
50.5
38.4
50.8
38.4
650
.338
.450
.838
.950
.538
.650
.838
.151
.339
.151
.138
.150
.838
.450
.838
.6
550
.839
.150
.838
.450
.038
.450
.838
.650
.838
.650
.538
.451
.138
.950
.838
.6
451
.138
.450
.838
.150
.838
.450
.537
.851
.1.
38.4
50.8
38.4
50.8
38.6
51.1
38.9
350
.538
.950
.838
.450
.539
.150
.538
.651
.138
.450
.538
.450
.538
.950
.838
.6
250
.538
.450
.538
.450
.838
.650
.038
.951
.339
.151
.139
.150
.538
.6
1to
p50
.838
.651
.139
.950
.839
.4bo
ttom
50.8
38.1
50.8
38.4
51.1
40.4
51.1
39.4 -
mea
n50
.938
.750
.838
.550
.538
.750
.738
.7st
d.
dey.
0.30
0.46
0.29
0.46
0.33
0.48
0.29
0.37
Tab
leA
.5Su
mm
ary
ofM
easu
red
Gro
ssC
ross
-sec
tion
alM
embe
rD
imen
sion
s
Dim
ensi
ons,
rrm.
Mea
nM
ean
Stan
dard
plus
min
usPa
ram
eter
Nom
inal
Mea
nM
inim
umM
axim
umD
evia
tion
Std
.D
ev.
Std
.D
ev.
Nor
thFr
ame
Colu
mn
Dep
th51
.050
.549
.351
.30.
4150
.950
.1
Colu
mn
Wid
th38
.039
.138
.140
.40.
5439
.638
.6--'
Beam
Dep
th38
.037
.936
.639
.60.
6338
.537
.3U
1N
Beam
Wid
th38
.039
.238
.440
.40.
5839
.838
.6
Sout
hFr
ame
Colu
mn
Dep
th51
.050
.750
.051
.30.
3051
.050
.4
Colu
mn
Wid
th38
.038
.737
.840
.40.
4339
.138
.3
Beam
Dep
th38
.038
.336
.339
.90.
5938
.937
.7
Beam
Wid
th38
.038
.737
.839
.90.
3739
.138
.3
153
Table A.6Measured Story Masses
Level
10987654321
t1ass(Kg)
461464463466464465465462465291
Descript ion of Delilln Curve
fc'O ·c<Ofc ' f o[2(..!2.1 - (S)2} 0 < .c<.o
"0 41'0'
fc ' fo [I-150(.c- Eol] ·o<·c<·o+O.ool
40
30
ClQ.::IE
,;..CD 20..Ui
10
154
-- Measured Envelope--- Desion
2
Strain x 101
3 4
Fig. A.l Envelope of Measured Concrete Stress-StrainRelations and Design Relation
400~
358 '-- ,_-------------------------1300t-
Cl I-- 200,000 MPaQ.
::IE.: 200 i-- - Measured~ --- DesionU;
100
00I I I I I I I
4 8 II! 18 20 1!4 28
Strain x 101
Fig. A.2 Measured Mean Stress-Strain Relation andDesign Relation for No. 13 Gage Wire
.......
CJ1
CJ1
i I i
'Wi~
~I.~
NN
44
0.0
.T
ubin
g
61
0
30
5
Imbe
dmen
tIt. r
Tran
sver
seC
ohm
nS
teel
64
16
4
68
6
o
9at
51
I I I I I I I.
(All
Dim
ensi
ons
inm
m)
Fig.
A.3
Det
ail
of
Bas
e-G
irde
rR
einf
orce
nent
Ste
elP
edes
tal
Tes
tst
ruct
ure
(All
Dim
ensi
ons
InM
eter
sl St
eel
Ref
eren
ce
F"~~
Hyd
raul
icS
ervo
ram
~ N.....
..<J
1m
I.09
1I.
2.29
I09
1J.
0.91
.I09
1\
Fig.
A.4
Ove
rall
Con
figu
rati
onof
Tes
tSe
tup
CJ'1
'-l
Ma
ss--
Co
lum
n
Was
hers
Pin
ned
Inte
rio
rC
olum
n
Pe
rfo
rate
dC
hann
el
Exte
rio
rC
olum
n
bOrn
@
ED
CB (a
)V
iew
edT
rans
vers
eTo
Line
of
Mo
tion
(b)
Vie
wed
Alo
ngL
ine
of
Mot
ion
Fig.
A.5
Det
ai1
ofr~ass-to-FrameConnection
158
APPENDIX B
COMPLEMENTARY DATA
B.l Introductory Remarks
The purpose of this appendix is to compare various measured waveforms
so as to provide a check on the functioning of the experimental system. The
waveforms are presented separately from the main 'text because of their
limited importance concerning response of the test structure to earthquake
type excitations.
B.2 Hori zonta1 Response Measurements
Absolute accelerations and relative 9;splacements were measured on
each of two frames which composed the test structure (Fig. 3.1). Waveforms
measured during the first simulated earthquake on each frame at levels
three, six, and nine are compared in Fig. B.l. Magnitudes of accelerations
measured during any earthquake simulation were essentially the same on
each frame at each level except for occasional peaks which could differ
by as much as ten percent. Magnitudes of displacements were found to
differ by a maximum of five percent. Despite these slight differences in
magnitude, waveforms plotted for a given level were nearly identical.
An accelerometer fixed to the tenth-level mass (Fig. 3.1) produced
the same acceleration waveform as observed for the tenth level of the test
frames. Therefore, the masses and frames can be assumed to have moved
i denti ca lly.
159
B.3 Torsional Motions
Two accelerometers were fixed to the tenth level mass (Fig. 3.1) to
measure accelerations transverse to the line of input motion. The two
accelerometers were oriented so that response readings would be of the
same sign if the acceleration was torsional or of opposite signs if the
acceleration was caused by lateral sway of the test structure. Waveforms
obtained during the first simulated earthquake are plotted in Fig. B.2
(minor directional accel.) to a scale equal to that used for accelerations
in the figures for Chapter 4. Waveforms from other simulations were similar.
Most of the motion indicated in Fig. B.2 is torsional. The maximum measured
in any simulation was 0.13 g during the first simulation. A torsional
frequency of about three Hz could be obtained from the waveform.
B.4 Vertical Motions
Two accelerometers measured vertical accelerations at opposite ends
of the test structure (Fig. 3.1). Waveforms obtained during the first
earthquake simulation are plotted in Fig. B.2. Waveforms from other
simulations indicated increasing vertical acceleration with increasing
base motion intensity. The peak vertical acceleration was 0.18 g during
the third earthquake simulation. None of the obtained waveforms indicated
a definite rocking frequency of the test structure. nor were all accelera
tions of a rocking nature. Accelerations of the same sense were often
evident at any given time. It is possible that vertical accelerations
measured on the test structure were induced by like accelerations of the
simulator test platform. However. this cannot be confirmed because vertical
accelerations of the test platform were not measured.
II
II
I,
II
I,
II
II
II
20
.0Nl~1H
LEVE
LOl
SPLA
CEM
EN1
-N~RTH.
UN
I1=
NM
Nl~1H
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B.2
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Tra
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Ver
tica
lA
ccel
erat
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![Development of Electrostatic Precipitator (ESP) for …¼r...r D d r D U Ezyl r ln 2 ln ( ) 0 ∗ = ∗ = πε λ 1E+4 1E+5 1E+6 1E+7 1E+8 1E-4 1E-3 1E-2 1E-1Radius [m] Feldstärke](https://static.fdocuments.net/doc/165x107/5e86afb1a903b22d2c563cb1/development-of-electrostatic-precipitator-esp-for-r-r-d-d-r-d-u-ezyl-r-ln.jpg)
