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1111111111111111111111111111111
PB98-108814 Informati"onilourb"UllnSII.
CUMULATIVE SCONCRETE EISMIC DAMABRIDGE PIERS GE OF REINFORCED
2 SEP 97
u.s. OEPARTMENational TeChniC~(1~FCOMMERCEn ormation S .ervlce
,I 11111111111" III
NATIONALCENTER FOREARTHQUAKEENGINEERINGRESEARCH
Headquartered at the State University of New York at Buffalo
SSN 1088-3800 III 1111111111111111111111 "1111PB98-108814
Cumulative Seismic Damage ofReinforced Concrete Bridge Piers
by
Sashi K. Kunnath, Ashraf EI-Bahy, Andrew Taylor and William StoneUniversity of Central Florida
Orlando, Florida 32816and
National Institute of Standards and TechnologyGaithersburg, Maryland 20899
Technical Report NCEER-97-0006
September 2, 1997
This research was conducted at the University of Central Florida and the National Institute ofStandards and Technology and was supported by the Federal Highway Administration
under contract number DTFH61-92-C-OOl06.
REPRODUCED BY: t!Illl!u.s. Department of Commerce
National Technical Information ServiceSpringfield, Virginia 22161
NOTICEThis report was prepared by the University of Central Florida and the NationalInstitute of Standards and Technology as a result of research sponsored by theNational Center for Earthquake Engineering Research (NCEER) through a contract from the Federal Highway Administration. Neither NCEER, associates ofNCEER, its sponsors, the University of Central Florida, the National Institute ofStandards and Technology, nor any person acting on their behalf:
a. makes any warranty, express or implied, with respect to the use of any information, apparatus, method, or process disclosed in this report or that suchuse may not infringe upon privately owned rights; or
b. assumes any liabilities of whatsoever kind with respect to the use of, or thedamage resulting from the use of, any information, apparatus, method, orprocess disclosed in this report.
Any opinions, findings, and conclusions or recommendations expressed in thispublication are those of the author(s) and do not necessarily reflect the views ofNCEER or the Federal Highway Administration.
50272-101
REPORT DOCUMENTATION 11. REPORT NO.
PAGE NCEER-97-00064. Title and Subtitle
Cumulative Seismic Damage of Reinforced Concrete Bridge Piers
7. Author(s)
9. Performing Organization Name and Address
University of Central FloridaOrlando, Florida 32816andNational Institute of Standards and TechnologyGaithersburg, Maryland 20899
12. Sponsoring Organization Name and Address
National Center for Earthquake Engineering ResearchState University of New York at BuffaloRed Jacket QuadrangleBuffalo, New York 14261
PB98-1088141/1111/ 1/ 11/1111/1111//111111111 1/ 1//
5. Report Date
September 2, 19976.
10. Project/Task/Work Unit No.
11. Contract(C) or Grant(G) No.
(C) DTFH61-92-C-001 06
(G)
13. Type of Report & Period Covered
Technical report14.
--
15. Supplementary Notes
This research was conducted at the University of Central Florida and the NationalInstitute of Standards and Technology and was supported by the Federal HighwayAdministration under contract number DTFH61-92-C-00106.
16. Abstract (limit: 200 words)
This report describes a comprehensive experimental study to investigate cumulativedamage in reinforced concrete circular bridge piers subjected to a series of earthquakeexcitations. Twelve identical quarter-scale bridge columns were involved. These weredesigned and fabricated in accordance with current AASHTO specifications~ Testing wasin two phases. Phase I testing consisted of benchmark tests to establish the monotonicforce-deformation envelope and the energy capacity under standard cyclic loads; andconstant amplitude tests to determine the low-cycle fatigue characteristics of the bridgecolumn. Phase II testing was composed of a series of analytically predicted displacementamplitudes representing the bridge response to typical earthquakes. Test observationsindicate two potential failure modes: low cycle fatigue of the longitudinal reinforcing bars;and confinement failure due to rupture of the confining spirals. An analytical study ofcumulative damage was also conducted. A simple fatigue-based model was used to predictcumulative damage in flexural bridge piers. Critical damage measures, such as stiffnessdegradation, dissipated hysteretic energy, ductility, and fatigue were evaluated againstobserved behavior. It was found that none of these damage measures consistently predictobserved damage limit states, although fatigue-based models demonstrated better reliabilit~.
It was further observed that the energy-dissipation capacity of members is pathdependent: models of seismic damage that rely only on measures of energy dissipation cannot oredict failure if it is not related to ductilitv. Findinas from this studv will orovide
17. Document Analysis a. Descriptors additional input into the development of performance-based designspecifications.
b. Identifiers/Open-Ended Terms
Earthquake engineering. Experimental tests. Damage indices. Energy dissipation.Ductility, Load paths. Analytical studies. Cumulative damage models. Bridge piers.Reinforced concrete. Highway bridges. Low cycle fatigue. Cyclic loads. Failure modesLongitudinal reinforcement. Confinement reinforcement.c. COSATI Field/Group
18. Availability Statement
Release unlimited19. Security Class (This Report) 21. No. of Pages
Unclassified 1921-------------11---------
(See ANSI-Z39.18)
20. Security Class (This Page)
UnclassifiedSee Instructions on Reverse
22. Price
OPTIONAL FORM 272 (4-77)(Formerly NTIS-35)n ....._ ........... ,..... _
_
NATIONAL~FOREARTHQUAKEENGINEERINGRESEARCH
Cumulative Seismic Damage ofReinforced Concrete Bridge Piers
by
S.K. Kunnath1, A. EI-Bahy2, A. Taylor3 and W. Stone4
PublicationDate: September 2, 1997Submittal Date: October 17, 1996
Technical Report NCEER-97-0006
NCEER Task Number 106-E-5.3
FHWA Contract Number DTFH61-92-C-00106
1 Associate Professor, Department of Civil and Environmental Engineering, University of CentralFlorida, Orlando
2 Graduate ResearchAssistant, DepartmentofCivil andEnvironmentalEngineering, Universityof CentralFlorida, Orlando
3 KPFF Consulting Engineers, Seattle; formerly ResearchStructuralEngineer, National Institute ofStandards and Technology, Gaithersburg
4 Research Structural Engineer, National Institute ofStandards and Technology, Gaithersburg
NATIONAL CENTERFOR EARTHQUAKE ENGINEERING RESEARCHState University ofNew York at BuffaloRed Jacket Quadrangle, Buffalo, NY 14261
PREFACE
The National Center for Earthquake Engineering Research (NCEER) was established in 1986 todevelop and disseminate new knowledge about earthquakes, earthquake-resistant design andseismic hazard mitigation procedures to minimize loss of life and property. The emphasis of theCenter is on eastern and central United States structures, and lifelines throughout the countrythat may be exposed to any level of earthquake hazard.
NCEER's research is conducted under one offour Projects: the Building Project, the NonstructuralComponents Project, and the Lifelines Project, all three of which are principally supported bythe National Science Foundation, and the Highway Project which is primarily sponsored by theFederal Highway Administration.
The research and implementation plan in years six through ten (1991-1996) for the Building,Nonstructural. Components, and Lifelines Projects comprises four interdependent elements, asshown in the figure below. Element I, Basic Research, is carried out to support projects in theApplied Research area. Element II, Applied Research, is the major focus of work for years sixthrough ten for these three projects. Demonstration Projects under Element III have beenplanned to support the Applied Research projects and include individual case studies andregional studies. Element IV, Implementation, will result from activity in the Applied Researchprojects, and from Demonstration Projects.
ELEMENT IVIMPLEMENTATION• ConferenceslWorkshops• EducationfTraining courses• Publications• Public Awareness
ELEMENT IIIDEMONSTRATION PROJECTS
Case Studies• Active and hybrid control• Hospital and data processing
facilities• Short and medium span bridges• Water supply systems in
Memphis and San FranciscoRegional Studies
• New York City• Mississippi Valley• San Francisco Bay Area• City of Memphis and Shelby
County, Tennessee
• The Building Project
• The NonstructuralComponents Project
• The Lifelines Project
• The Highway Project
ELEMENT IIAPPLIED RESEARCH
ELEMENT IBASIC RESEARCH
• Seismic hazards andground motion
• Geotechnicalengineering
• Risk and reliability
• Structures and systems
• Socioeconomic issues
• Intelligent and protectivesystems
111
Research under the Highway Project develops retrofit and evaluation methodologies forexisting bridges and other highway structures (including tunnels, retaining structures, slopes,culverts, and pavements), and develops improved seismic design criteria and procedures forbridges and other highway structures. Specifically, tasks are being conducted to: (1) assess thevulnerability ofhighway systems and structures; (2) develop concepts for retrofitting vulnerablehighway structures and components; (3) develop improved design and analysis methodologiesfor bridges, tunnels, and retaining structures, with particular emphasis on soil-structure interaction mechanisms and their influence on structural response; and (4) review and improve seismicdesign and performance criteria for new highway systems and structures.
Highway Project research focuses on one of two distinct areas: the development of improveddesign criteria and philosophies for new or future highway construction, and the development ofimproved analysis and retrofitting methodologies for existing highway systems and structures.The research discussed in this report is a result of work conducted under the existing highwayconstruction project, and was performed within Task 106-E-5.3, "Performance-Based Specificationsfor the Seismic Design, Retrofit and Repair ofReinforced Concrete Bridge Columns," ofthe project asshown in the flowchart.
The research reported herein is part ofa larger research program that has as its objective thedevelopment of a performance-based approach to the seismic design, retrofit and repair ofreinforced concrete bridge columns. This report provides the results from an experimental andanalytical study ofcumulative damage to circular columns with apredominatelyflexural response.Specifically, research in this task includeda study of(1)progressive damage in bridgepiers throughan examination of critical damage parameters including ductility, low-cycle fatigue, energydissipation capacity, and loss ofconfinement; (2) the influence ofductility on energy dissipationcapacity ofmembers; and (3) the effects ofrandom cyclic loads and loadpaths on the cumulativedamage ofbridge piers. In addition, observed damage was visually correlated with damage limitstates and the relationship between damage parameters and observedfailure modes for existingcumulative damage models was investigated It is expected that this study will contribute to theoverall effortofcalibratingafatigue-basedcumulative damage model, which is a necessaryfirst steptowards developing performance-based design guidelines.
IV
SEISMIC VULNERABILITY OF EXISTING HIGHWAY CONSTRUCTIONFHWA Contract DTFH61·92·C·00106
State-ofthe-artReview
BridgeRetrofit
Guidelines(Interim)
PerformanceCriteria Vulnerability
Assessment:
Seismic Hazard,Ground Motion,Spatial Variation
VulnerabilityAssessment:
Soil &Foundations,Components,
Structures,Systems
RetrofitTechnologies
Soil &Foundations,Components,
Structures,Systems
SpecialStudies
Vol IVol IIVol III
Seismic Vulnerability Assessment of Highway SystemsRetrofitting Manual for Highway BridgesRetrofitting Manual for Highway Tunnels, RetainingStructures, Embankments, CUlverts, and Pavement
DemonstrationProjects
v
ABSTRACT
A comprehensive experimental study was undertaken in this research effort to investigatecumulative damage in reinforced concrete circular bridge piers subjected to a series ofearthquake excitations. Twelve identical quarter-scale bridge columns were designed andfabricated in accordance with current AASHTO specifications. A unique setup to expedite thetesting process was designed and built in the structural test facility at NIST.
The testing was divided into two phases. Phase I testing consisted of benchmark tests toestablish the monotonic force-deformation envelope, the energy capacity under standard cyclicloads, and constant amplitude tests to determine the low-cycle fatigue characteristics of thebridge column. Phase II testing was composed of a series of analytically predicted displacementamplitudes representing the bridge response to typical earthquakes. The results of Phase Itesting provided information on the fatigue behavior of reinforced concrete and Phase II provideddata on the effect of load path on cumulative damage.
Test observations indicate two potential failure modes: low cycle fatigue of the longitudinalreinforcing bars; and confinement failure due to rupture of the confining spirals. The formerfailure mode is associated with relatively large displacement amplitudes in excess of 5% driftwhile the latter is associated with a larger number of smaller amplitude cycles. Analyticalstudies indicate that most earthquakes induce few large amplitude cycles pointing to the need forproper confinement to prevent catastrophic failure.
The results of the testing were also used in an analytical study of cumulative damage. A simplefatigue-based model, derived from existing theories in the literature, was used to predictcumulative damage in flexural bridge piers. Critical damage measures, such as stiffnessdegradation, dissipated hysteretic energy, ductility, and fatigue were evaluated against observedbehavior. It was found that none of these damage measures consistently predict observeddamage limit states though fatigue-based models demonstrated better reliability. It was furtherobserved that the energy-dissipation capacity of members is path-dependent, hence, models ofseismic damage that rely only on measures of energy dissipation cannot predict failure if it is notrelated to ductility. Findings from this study will provide additional input into the developmentofperformance-based design specifications wherein design is linked to damage limit states.
vii
ACKNOWLEDGMENTS
Financial support for this project provided by the National Center for Earthquake EngineeringResearch (NCEER), the Federal Highway Administration (FHWA), and the CaliforniaDepartment of Transportation (CALTRANS) is gratefully acknowledged. The followingindividuals are recognized for being instrumental in supporting and coordinating this project: atNCEER Dr. Ian Buckle, Dr. John Mander and Mr. Ian Friedland; at FHWA Mr James Cooperand Dr. Phillip Yen; and at CALTRANS Mr. James Roberts and Mr. James Gates. In addition,special thanks are due to the technical staff in the Structural Testing Laboratory at the NationalInstitute of Standards and Technology - Steve Johnson, Frank Rankin, Erik Anderson, Max Peltzand James Little - whose assistance was instrumental in completing the experimental phase ofthis study.
ix
TABLE OF CONTENTS
SECTION TITLE PAGE
11.11.21.3
22.12.22.2.12.2.22.2.32.2.3.12.2.3.22.2.42.2.52.2.62.2.6.12.2.6.22.2.6.32.2.6.42.2.72.2.8
3
3.13.1.13.1.23.23.33.3.13.3.2
4
4.14.24.3
INTRODUCTIONResearch IssuesResearch Objectives and Scope of StudyOrganization ofReport
DESIGN OF TESTING PROGRAM, SETUP AND INSTRUMENTATIONReview ofPrevious Experimental WorkDetails of Testing ProgramDesign ofPrototype Circular Bridge PierDesign ofModel SpecimenMaterial PropertiesProperties ofReinforcing SteelConcrete PropertiesConstruction of Columns and Base BlocksTest SetupInstrumentation ofModel ColumnsForce-Displacement MeasurementCurvature MeasurementRotational MeasurementStrain MeasurementsControl and Data Acquisition SystemsUltrasonic Measurements
ANALYTICAL MODELING AND DEVELOPMENT OFLOAD mSTORIESAnalytical Model ofBridge ColumnComponent ModelingHysteretic ModelingPrototype vs. Model CalibrationSelection ofDisplacement HistoriesBenchmark TestingRandom Loading
CUMULATIVE DAMAGE TESTING I:PUSH OVER, BENCHMARK AND FATIGUE LOADINGSpecimen AI: Monotonic LoadingSpecimen A2: Standard Cyclic LoadingQuasi-Fatigue Loading
Xl
1335
77111115161619232932323234363637
3939404346464949
53565961
TABLE OF CONTENTS (continued)
SECTION TITLE PAGE
4.3.14.3.24.3.34.3.4
Specimen A3: Constant Amplitude Cycles at 2% Lateral DriftSpecimen A4: Constant Amplitude Cycles at 4% Lateral DriftSpecimen A5: Constant Amplitude Cycles at 5.5% Lateral DriftSpecimen A6: Constant Amplitude Cycles at 7% Lateral Drift
64677171
5 CUMULATIVE DAMAGE TESTINGII: RANDOM CYCLIC LOADING 79
5.1 Background and Selection ofRandom Histories 795.2 Selected Ground Motions 815.3 Random Loading: Testing and Observations 875.3.1 SpecimenA7 875.3.2 SpecimenA8 915.3.3 SpecimenA9 955.3.4 Specimen A10 995.3.5 Specimen All 1035.3.6 Specimen A12 107
6 CUMULATIVE DAMAGE MODELING:EVALUATION OF EXPERIMENTAL RESULTS 111
6.1 Fatigue-Based Damage Models III6.2 Damage vs. Performance 1136.3 Models Evaluated in this Study 1136.4 Damage Analysis of Tested Specimens 1196.5 Proposed Fatigue-Based Cumulative Damage Model 128
7 RESEARCH FINDINGS AND CONCLUSIONS 1337.1 Research Findings 1337.1.1 Findings Related to Cumulative Damage 1347.1.2 Findings Related to Energy-Dissipation Capacity 1367.1.3 Findings Related to Inelastic Modeling 1387.2 Development ofPerformance-Based Design for Bridge Columns 1407.4 Recommendations for Future Research 142
8 REFERENCES 145
APPENDIX A: Ultrasonic Testing A-I
Xll
LIST OF FIGURES
FIGURE TITLE PAGE
2-12-22-32-42-52-62-72-82-92-102-112-122-132-142-152-162-172-182-192-202-212-222-232-24
3-13-23-33-43-5
4-14-24-34-44-54-64-74-8
Caltrans Design Spectra Used in Prototype DesignStress vs. Strain Curve for #3 Longitudinal SteelStress vs. Strain Behavior ofAnnealed Wire Used for SpiralsStress-Strain Curve for #5 Rebars Used in Footings and End BlocksStress vs. Strain for Concrete Mix 1 at 28 daysStress vs. Strain for Concrete Mix 2 at 28 daysStress vs. Strain for Concrete Mix 3 at 28 daysStress vs. Strain for Concrete Mix 4 at 28 daysForm Construction to Permit Simultaneous Casting of Six SpecimensCage Assembly for 1:4 Scale Model PiersPost Tensioning ofEnd Blocks to FootingCage Assembly for 1:4 Scale Model ColumnReinforcement Arrangement for Specimen with Base BlockConfiguration and Dimensional Details of Specimen with Base BlockDimensional Details ofEnd Block Attached to Right Side of SpecimenDimensional Details ofEnd Block Attached to Left Side of SpecimenDetails ofLoad Frame and Test Set-upView ofTest Set-Up Prior to Attaching Out-of-plane Support SystemOverhead View of Out-of-Plane Support SystemTest Setup with InstrumentationClip Gage Mounted on Column for Curvature MeasurementElectric Clinometers Used for Rotational MeasurementControl and Data Acquisition SystemUltrasonic Readings Across Concrete Column
Inelastic Component Model ofBridge ColumnCalibration ofHysteresis ModelComparison ofPrototype vs. Model ResponseSummary ofDisplacement Histories Used in TestingTypical Loading Scenario for Random Amplitude testing
Computation of Column Moments and Shear Including P-DeltaDamage to Specimen Al at 3.5% DriftSpecimen Al at End ofTestBase Shear vs. Displacement Response ofColumn AlDamaged State of Specimen A2 at Cycle No. 30Final Damaged State of Specimen A2Displacement History Applied to Column A2Shear vs. Displacement Response ofColumn A2
Xlll
141717182121222223242526272728283031313335353738
4145474851
5558585962626363
LIST OF FIGURES (continued)
FIGURE TITLE PAGE
4-94-104-114-124-134-144-154-164-174-184-194-204-214-224-234-24
5-1
5-2
5-3
5-45-55-65-75-85-95-105-115-125-135-145-155-165-175-185-19
Specimen A3 at Cycle 100Specimen A3 at End ofFatigue TestingDisplacement History Applied to Column A3Shear vs Displacement Response ofColumn A3Condition of Specimen A4 at Cycle No. 18Specimen A4 at End of TestingDisplacement History Applied to Column A4Shear vs. Displacement Response of Column A4Specimen A5 at Cycle No.3Condition of Specimen A5 at End of TestingDisplacement History Applied to Column A5Shear vs. Displacement Response ofColumn A5Specimen A6 at Cycle No.3Specimen A6 at End of TestingDisplacement History Applied to Column A6Shear vs. Displacement Response ofColumn A6
Acceleration and Corresponding 5% Damped Spectra for Input MotionsUsed to Generate Displacement History for Specimens A7 & A8Acceleration and Corresponding 5% Damped Spectra for Input MotionsUsed to Generate Displacement History for Specimens A9 & A10Acceleration and Corresponding 5% Damped Spectra for Input MotionsUsed to Generate Displacement History for Specimens All & A12Damage to Specimen A7 at Half Cycle No. 145 During Earthquake #2Final Damaged State of Specimen A7Displacement History Applied to Column A7Force vs. Displacement Response ofColumn A7Specimen A8 at Half-Cycle #267 During Earthquake 4Specimen A8 at Final Damaged StateDisplacement History Applied to Column A8Shear Force vs. Displacement Response of Column A8Damage to Specimen A9 at end ofHalf-Cycle 188Final Damaged State of Specimen A9Displacement History Applied to Column A9Base Shear vs. Displacement Response ofColumn A9State of Specimen AlO at Half-Cycle #121Final Damaged State of Specimen A10Displacement History Applied to Column A10Shear vs. Displacement Response ofColumn A10
XlV
65666667696970707273737475767677
84
85
86898990909393949697979898101101102102
FIGURE TITLE
LIST OF FIGURES (continued)
PAGE
5-20 Specimen All at Half-Cycle # 139 1055-21 Final Damaged State of Specimen All 1055-22 Displacement History Applied to Column All 1065-23 Shear vs. Displacement Response of Column All 1065-24 Specimen A12 at Half-Cycle 206 1095-25 Final Damaged State of Specimen A12 1095-26 Displacement History Applied to Column A12 1105-27 Base Shear ys. Displacement Response ofColumn A12 110
6-1 Parameters Used in Softening Index 1156-2 Parameters Used in Kratzig Damage Model 1166-3 Curvature-Strain Relationship for Plane Sections 1186-4 Comparative Evaluation ofProgressive Damage for Specimen A2 1206-5 Comparative Evaluation ofProgressive Damage for Specimen A3 1216-6 Comparative Evaluation ofProgressive Damage for Specimen A4 1216-7 Comparative Evaluation ofProgressive Damage for Specimen A5 1226-8 Comparative Evaluation ofProgressive Damage for Specimen A6 1236-9 Comparative Evaluation ofProgressive Damage for Specimen A7 1246-10 Comparative Evaluation ofProgressive Damage for Specimen A8 1246-11 Comparative Evaluation ofProgressive Damage for Specimen A9 1256-12 Comparative Evaluation ofProgressive Damage for Specimen AlO 1266-13 Comparative Evaluation ofProgressive Damage for Specimen All 1276-14 Comparative Evaluation ofProgressive Damage for Specimen A12 1276-15 Coffin-Manson Fatigue Model for Plastic Strain 1286-16 Coffin-Manson Fatigue Model for Total Strain 1296-17 Fatigue Life Model for Total Lateral Drift ofWell-Detailed Flexural Columns 1306-18 Performance ofProposed Plastic Strain Fatigue Damage Model
to Specimens A7-A12 1316-19 Performance ofProposed Total Strain Fatigue Damage Model
to Specimens A7-A12 132
7-1 Cumulative Energy to Failure ofBridge Columns SubjeCted toConstant Amplitude Loading 137
7-2 Cumulative Energy to Failure ofBridge Columns Subjected toRandom Loading 137
7-3 Local Loop Behavior Under Random Cyclic Response 1397-4 Proposed Modeling ofLocal Hysteresis Loops 140
xv
LIST OF TABLES
TABLE TITLE PAGE
2-12-22-3
3-1
4-14-24-34-44-54-64-7
5-1a
5-1b
5-25-35-45-55-65-7
6-1
7-1
Details ofPrototype and ModelSummary ofRebar CharacteristicsMix Proportions
Identified Control Parameters
Average Material Characteristics for Phase I TestingSummary ofTest Observations for Specimen AlSummary ofTest Observations for Specimen A2Summary of Test Observations for Specimen A3Summary of Test Observations for Specimen A4Summary ofTest Observations for Specimen A5Summary ofTest Observations for Specimen A6
Ground Motions Selected for Generating Random Displacement Historiesfor Specimens A7-A9Ground Motions Selected for Generating Random Displacement Historiesfor Specimens AlO-A12Summary of Observations During Testing of Specimen A7Summary of Observations During Testing of Specimen A8Summary of Observations During Testing of Specimen A9Summary ofObservations During Testing of Specimen AIOSummary ofObservations During Testing of Specimen AllSummary ofObservations During Testing of Specimen Al2
Damage Categories Proposed in ATC-38
Damage Correlation Limit States with Visual Observations
XVII
151920
44
55576165687275
82
83889296100104108
114
136
SECTION 1
INTRODUCTION
The failure of numerous structures during the 1971 San Fernando earthquake ushered in a new
era of seismic design. It recognized the need to detail critical sections for ductility so that the
imposed seismic forces may be resisted by the ability of these sections to dissipate energy. Past
and current design practices are being put to the test regularly with each severe earthquake. Each
failure points to either a flaw in the basic design approach or a lack of understanding of the
inelastic behavior of structural systems resulting from seismic loads.
The function of a structure during and after an earthquake usually dictates the methodology
employed in the design of the structure. Lifeline structures, such as bridges, are assigned a much
higher "importance" factor in the design process since these structures are "essential facilities"
necessary for emergency operations subsequent to an earthquake. Such structures should resist
minor earthquakes without damage, moderate earthquakes without significant structural damage,
and in the case of a major earthquake, some structural and non-structural damage is allowed,
provided it does not affect the functioning ofthe structure after the earthquake.
Damage to bridge structures in past earthquakes have been significant. The 1971 San Fernando
earthquake significantly damaged as many as forty-one bridges. More recently, the 1989 Lorna
Prieta earthquake caused over $5.5 billion in damage of which almost a third was attributed to
highway failures, the most notable of course being the collapse of a section of the Cypress
viaduct (Housner, 1990). Post-earthquake reconnaissance and follow-on research studies have
indicated that most of the damage in highway bridges is a result of some or all of the following
reasons: (a) insufficient column ductility and/or energy dissipation capacity to sustain the large
imposed lateral displacements; (b) insufficient shear capacity in short columns; and (c) lack of
adequate anchorage length in the longitudinal reinforcing bars of the piers.
1
Pre-1950 highway construction (of which the Cypress viaduct is an example) in seismic zones
which followed either CALTRANS or AASHTO had very low seismic requirements compared
to those for buildings which used the Uniform Building Code (UBC). Despite many changes in
seismic design codes over the years, the basic philosophy behind prescribing design guidelines
have remain unchanged. For example, past and current AASHTO specifications for the seismic
design of bridge columns have taken a generally prescriptive approach. That is, the specifications
place constraints on such factors as material properties, minimum reinforcement or confinement
requirements, and column geometry, without specifically linking these requirements to the
performance of the column when it is subjected to a particular earthquake. A designer who
follows the prescriptive code requirements is ostensibly assured that the structural safety of the
bridge pier will be preserved under maximum likely earthquakes at the bridge site. However, the
designer cannot make a clear or precise decision on the amount of damage suffered by the bridge
column under small or moderate earthquakes. The larger issue of seismic safety under future
earthquakes, as well as the criteria to be used in upgrading, remains unresolved.
Much of the strength and deformation requirements in current highway bridge design procedures
have been derived from experimental testing and limited analytical studies. However, it must be
noted that most of the testing conducted in the past was directed towards the objective of
understanding post-yield behavior under cyclic load reversals to develop detailing strategies to
ensure satisfactory performan~e under seismic action. As such, these tests have provided
pertinent knowledge regarding the effects of various important parameters, such as the influence
of varying axial forces, the presence of high shear, confinement, and multidirectional loading, on
the failure of reinforced concrete components. Issues related to performance or correlation of
observed behavior to damage have not been addressed directly, hence efforts related to
calibrating damage models have not met with any success. Additionally, a number of analytical
models to predict seismic damage have been proposed by many researchers. These models, either
derived from or verified against results of past laboratory testing of RC components and
2
structures, have offered some clues on the factors affecting damage but fall short of the objective
of assessing structural integrity in terms of serviceability and reparability.
A major factor that has hindered the development of a performance-based design methodology is
the fact that no systematic experimental program has yet been undertaken wherein the imposed
loading, the system variables, and the measured or observed response were tailored to
specifically monitor, model and calibrate cumulative seismic damage.
1.1 Research Issues
The motivation for this research study stems from the following questions:
• Is it possible to predict failure in highway bridges due to a potential earthquake event, in the
context of the damage model theories to be found in the literature?
• Is it possible to predict the associated mode of failure?
• Can damage models be used to measure level of performance, or reserve capacity in a
structural member, following a seismic event?
• Can the predicted "level of performance" or "reserve strength" be used to assist engineers in
deciding between rehabilitation, retrofit and demolition ?
• Is energy capacity of a member independent of the applied load history, or is it load path
dependent?
• Can damage estimates be related to simple measurable quantities such as dissipated energy,
ductility and the loss of strength or stiffness ?
1.2 Research Objectives and Scope of Study
Numerous analytical and experimental studies have been conducted in the past to study the
inelastic response of typical bridge piers. The objective in such studies, as pointed out in the
previous sub-section, has been to quantify the influence of certain material or system parameters
3
(level of axial load, amount of transverse reinforcement, etc.) on the cyclic response of columns.
Very few experimental programs have been designed to reproduce observed failure modes in
bridge piers. Another issue that has received very little attention is the effect of load path on the
response and failure of typical components and subassemblages. Almost without exception,
imposed displacement histories in standard cyclic tests are based on a fixed number of reversed
cycles applied at increasing levels of ductility until failure.
While this work is concerned with the behavior ofbridge piers in general, it was decided to focus
initially on the response of circular piers which have the advantage of possessing fairly uniform
properties about any arbitrary cross-section. It was considered important to keep other system
variables to an absolute minimum so that the effects of load path on the structural response could
be isolated.
This research endeavor is concerned primarily with load path and the effect of ductility on energy
dissipation capacity. It is also concerned with identifying criteria for low-cycle fatigue and the
role of confinement, as prescribed in modem codes, in altering flexural failure modes.
Ultimately, the results of this study will contribute to the overall task of damage modeling and
the prediction of flexural failure modes.
The primary objectives of the study may be summarized as follows:
1. Develop an experimental program dedicated to the study of progressive damage in bridge
piers through an examination of critical damage parameters such as ductility, low-cycle
fatigue, energy-dissipation capacity and loss of confmement due to repeated cyclic loads
resulting from earthquake motions.
2. Study the influence of ductility on energy dissipation capacity ofmembers.
3. Study the effects of random cyclic loads and load path on the cumulative damage of bridge
pIers.
4
4. Correlate visually observed damage with damage-limit states.
5. Investigate existing models of cumulative damage against observed behavior, and identify the
relationship between damage parameters and observed failure modes.
6. Suggest an alternate test method, using random displacement cycles or some combination of
equivalent ductility cycles, which reflect realistic displacement histories under imposed
seismic motions.
7. Suggest further studies, based on the findings of this work, to address issues related to
damage prediction and the development of performance-based design criteria for highway
bridges.
1.3 Organization of Report
The remainder of this report is organized into six sections. Section 2 begins with an overview of
past work on experimental investigations on the seismic response of bridge piers. This is
followed by details of the test setup and various aspects of the design and construction of the
model specimens. Section 3 presents the analytical model of the bridge pier, calibration of the
hysteresis model used in the analyses, validation of the dynamic response of the scaled model
specimen, and the process of generating the random displacement histories used in the second
phase of the testing. The results of Phase I testing are summarized in Section 4. The testing is
composed of two phases: in the first phase, two benchmark tests consisting of monotonic
loading and a standard cyclic load is followed by constant amplitude fatigue-type loading. The
second phase of testing, reported in Section 5, is devoted exclusively to random load tests.
Various existing theories of damage are examined in Section 6. A few selected models,
representing distinct approaches to damage indexing are applied to the results of the test
program. Relevant findings from the study and suggestions for additional work are discussed in
the seventh and final section.
5
SECTION 2
DESIGN OF TESTING PROGRAM, SETUP AND INSTRUMENTATION
The objectives set forth in Section 1 of this report were addressed as part of a comprehensive
study on cumulative damage of bridge piers under seismic loads. It was considered appropriate
to begin on a simple scale: hence flexural columns with circular cross-sections were used in the
testing. While the literature is abundant with cyclic tests on columns, both circular and
rectangular, it does not provide the essential information needed to calibrate damage. Dynamic
loads, such as those imposed by an earthquake, are random. The effect of such randomness,
wherein large amplitude cycles are interspersed with innumerable small amplitude cycles, on the
response of structures is unclear.
This project is an attempt to correlate observed damage with well recognized damage parameters.
As such, a new test methodology using random cycles is proposed. Prior to describing the
experimental program, a brief overview of previous experimental work in bridge testing is
presented.
2.1 Review of Previous Experimental Work
The earliest tests on bridge columns under simulated seismic loads were carried out in Japan and
New Zealand. Davey (1975) tested three 1:3 scale model piers with different shear span ratios.
Numerous cyclic tests were conducted by the Building Research Institute (1975, 1978) in Japan
on columns bent in double curvature. The first shaking table study was conducted by Munro et
al. (1976) on a 1:6 scale model pier. Since then, a number of additional experiments have been
carried out in Japan, New Zealand and the United States on the inelastic shear and flexural
behavior ofbridge columns, the most significant ofwhich are summarized below.
Mander et al. (1984, 1988) tested the first large scale square hollow bridge piers under lateral
cyclic loading. They attempted to experimentally establish the ductility capacity of hollow
7
bridge piers that are commonly used in New Zealand. A theoretical stress-strain model for
confined concrete was developed. The model took into consideration the effects of confmement,
shear deformation and strain rate. Confinement was modeled by equating the strain energy
required to first fracture the lateral reinforcement with the strain stored in concrete due to
confinement. It was determined that the main parameter that controlled the ductility capacity of
the columns was the amount of the lateral reinforcement.
Ang et al. (1985, 1989) investigated the shear strength of circular bridge piers subjected to
seismic action. Twenty five one-third scaled model columns with aspect ratios of 1.5, 1.75,2.0
and 2.5 were tested under a sequence of imposed displacements.
Stone et al. (1989, 1990) tested the first set of full scale bridge piers under combined quasi-static
cyclic lateral and axial loading at the National Institute of Standards and Technology (NIST).
The full scale columns had aspect ratios of 6 and 3, to simulate flexural and shear behavior,
respectively. Both columns were designed to meet CALTRANS specifications for seismic
loads. The loading history used on both columns were standard ductility-based displacement
inputs. The study concluded that the predicted ductility capacity based on the New Zealand code
(NZ-3101) was higher than that actually observed during the experiment. It was also observed
in both the flexure and shear specimens that the energy dissipated below a certain threshold
displacement stabilized without substantial decrease in load carrying capacity. The testing
indicated that the design requirements of CALTRANS were sufficient to provide a ductility of 6
for flexural bridge piers.
A parallel series of testing at NIST consisted of six circular model columns with a 1:6 ratio
compared to the full scale columns (Cheok and Stone, 1986, 1990). The variables in the study
were the load history, concrete mix and size of aggregate. It was concluded that the
CALTRANS design specifications for embedment length of longitudinal bars inside the footings
are adequate to prevent pullout failure. Fracture of the spiral reinforcement and buckl,ing of the
longitudinal bars occurred at displacement ductilities beyond ten for flexural columns, and above
8
five for the shear columns. The observed moment capacity during the tests were higher by 10%
25% than those predicted by ACI procedures (ACI-318, 1989). Higher displacement ductilities
were observed on increasing the axial load. But no so-called "threshold displacement" was
observed similar to that of the full scale columns.
Wong et al. (1990, 1993) tested sixteen 400 mm diameter columns with an aspect ratio of2. The
objective of the testing was to determine the strength and the deformation capacity of columns
primarily in shear. The displacement pattern of the first column was uniaxial cyclic loading. Of
the remaining, fourteen columns were tested under different sequence of biaxial cyclic loading.
The sixteenth column was tested under random cyclic loading. The axial load ranged between
0.1 0 - OJ9f:. This work concluded that biaxial loading patterns led to more severe stiffness
degradation than uniaxially imposed loads. The hysteretic response and the ductility capacity
were distinctly improved by increasing the volume of spiral reinforcement. The elastic shear
deformation of squat circular columns was determined to be significant enough that it should be
considered in the initial estimation of the stiffness so that dependable ductility and drift values
are established.
.The adequacy of interlocking spiral reinforcement has been investigated by Tanaka and Park
(1993) who conclude that the specifications of CALTRANS (1990) for this type of confmement
is sufficient to ensure reliable behavior under cyclic loads compared to similar specimens with
rectangular hoops and cross-ties. Recently, Priestley and Benzoni (1996) tested two large-scale
circular columns with low longitudinal reinforcement ratios. One of the columns had 0.5%
longitudinal steel while the second column had 1%, which represents 50% and 100% of the
minimum reinforcement requirement by ACI. Both columns performed well, pointing to the
possibility that the ACI minimum requirements for flexure can be further reduced.
Additionally, there have been a number of tests conducted at the University of San Diego
examining retrofit ofcolumns and bridge bents. Priestley et al. (1993a, 1993b) tested a half-scale
model ofa typical section of a double-deck viaduct under simulated seismic loading. The 90,000
9
kg model was controlled by fourteen hydraulic actuators and represents one of the most complex
civil structures ever tested. The test was used to validate capacity design procedures that were
proposed to retrofit existing double-deck bents in the California freeway system following the
collapse of the Cypress viaduct in the 1989 Lorna Prieta earthquake. Later, Priestley et al.
(1994) conducted large-scale tests of as-built rectangular and circular columns and companion
specimens with steel jacket retrofit. All as-built columns failed in shear at low ductility levels
(less than 3.0), while similar columns with steel jackets achieved ductility ratios in excess of 8.0.
While such tests provided invaluable insight into performance of RC members and some
information on damage mechanisms, they fail to provide the kind of fundamental information
necessary to calibrate seismic damage. Also, most of the above mentioned laboratory testing of
components usually involve large inelastic reversals with unrealistic drift demands. Any attempt
to calibrate a damage model using such tests cannot be applied to real structures wherein the
sequence, magnitude and reversals are arbitrary. Evidence to this is provided by Hwang and
Scribner (1984) who were the first and perhaps only investigators to study the effect of variations
in displacement history. They clearly conclude that methods previously used to calculate energy
dissipation capacity of members (for standard cyclic tests) do not predict consistently the cyclic
capacity of a flexural member subjected to an arbitrary displacement history. This is despite the
fact that the tests conducted by Hwang and Scriber were not truly random, but a small variation
from the customary process in which they alternated cycles of low ductility with cycles of larger
ductility demand.
Based on the current state-of-the-art in experimental dynamics of reinforced concrete, it is
obvious that the literature is lacking in data on RC behavior which examines failure as a low
cycle fatigue phenomena or the consequence of random load paths on the energy dissipation
capacity of specimens. A new test program is, therefore, proposed to address these important
issues. The proposed scheme will include characteristics of RC member response under realistic
seismic action. These will include, but are not limited to: (1) arbitrary displacement history; (2)
10
duration and sequence of applied histories; (3) relative magnitudes of successive histories; and
(4) the effect of ductility on energy dissipation capacity.
2.2 Details of Testing Program
As indicated earlier, the test program was designed to keep material, geometric and section
variables to a minimum. Since different failure modes may result in different critical damage
parameters, only flexural failure modes were considered in this study. The experimental program
was composed of testing twelve quarter-scale circular reinforced concrete columns. Only
dimensional scaling was considered and material properties were kept constant in both the model
and the prototype. In keeping with the main objectives of the study, the primary variables
considered were the amplitude, sequence and type of loading pattern. Two specimens were used
for benchmark testing: the first specimen was loaded monotonically and unidirectionally up to
failure, and the second specimen was subjected to a standard quasi-static cyclic load. Four
specimens were tested for fatigue characteristics under constant amplitude cycling. The final set
of six specimens were subjected to random displacement histories.
In subsequent sections, details of the prototype and model design, scaling considerations, test
setup, material properties, construction and assembly of specimens, instrumentation and data
acquisition are described.
2.2.1 Design of Prototype Circular Bridge Pier
A full scale single-bent bridge pier was designed to specifications of the CALTRANS (1990)
code though the same design can be achieved using AASHTO (1994). The CALTRANS design
procedure assumes a linear elastic, lumped mass and space frame model subjected to a design
spectral acceleration. This design response spectrum uses three factors: A, the peak rock
acceleration determined from records of fault activity and attenuation data; R, the peak spectral
acceleration based on actual recorded earthquake data; and S, the soil amplification factor. The
11
equivalent static force for design also incorporates a ductility/risk reduction factor, Z. The
product of A*R*S yields an elastic response spectra curve for the site which represents the
maximum credible seismic event corresponding to the closest active fault.
The design procedure involves the determination of "T", the natural period of the single bent
column from:
T= 2n .Jm/K (2-1)
where m is the mass of the bridge deck (= W / g) and K is the lateral stiffness of the bridge
pIer.
K=
(2-2)
(2-3)
where Ag is the gross cross-sectional area, E is the Young's Modulus of the concrete, I is the
moment of inertia and L is the height of the bridge.
Assuming a 28-day concrete compressive strength of 27.6 MPa, column diameter D = 1.22 m
and length L = 5.5 m, we get W ~ 3225 kN and T = 0.515 sec. Using A = 0.3 g and 0 - 3 m
alluvium for the soil parameter, the static coefficient for the acceleration response spectrum,
ARS = 0.7. The design lateral force is determined from:
F = ARS* W/Z (2-4)
Taking Z = 6 for a well confined single bent ductile column, the design lateral load F = 376 kN.
Using CALTRANS Pn-Mn interaction diagrams, it is required to use 2% reinforcing steel ratio
12
which is equivalent to 24 # 11. The spirals were designed using a plastic moment (Mp) of 130%
of the balanced moment (MJ as follows.
M p = 1.3 Mb = 1.3*6570 kN-m (2-5)
(2-6)
(2-7)
(2-8)
where bw is taken as the column diameter and d is the distance from the centroid of the
longitudinal reinforcement to the extreme compression fiber. The minimum shear reinforcement
is given by the following expression:
Psmin
A f/= 0.45 (-g - 1) _c_ = 1%
Ac f y
(2-9)
where Ac is the area of the confined core. Using # 5 (16 mm) bars for ties, the required spacing
was approximately 75 mm.
13
8
6
~
~IIIu.. 4CCJ)
EinOJ'5'«
2
:("/Well confined, dculile :
.•... _. ~in.I1I,::-_~n.tcolurnn.s .. ;
: :Piers:iJiiUi,neniwalis -ari~· wirig·walis·(z~ibY·······
V Hinge resliainer cables (z=1.0)
:~Well-reinfbrced concrete shear keys (~=0.8)o
0.0 0.5 1.0 1.5 2.0
Period of Structure, T (Sec)
2.5 3.0
Adjustment for Ductility and Risk Assessment
6.05.04.03.0
Period of Structure (Sec) T2.0150.2 0.4 0.6 0.8 1.0
I Smooth Elastic Surface Spectra 5"10 damped fork=(J.7g levels of Peak Rock Acceleration shown.
I/o.! r\
I/,J f\\6
'/ 01• 1\\l\ 3 m - 24.4 m Alluvium
, I;;";'
A~R·S SPECTRA4
.1 \\0.''I \
f" \\\' ~o II I. [\\[\~/~8
1/ J "~". "----6 V i'"'-.. I"~~1/ r-... t::--4
I'-..~s::::~I-----t:::-==:::--.
0
1.8
0.2
1.
o.
o.
o.
2.6
1.
2.2
2.4
2.0
o.
C!J 1.eI:-=: 1.2
FIGURE 2-1 CALTRANS Design Spectra Used in Prototype Design
14
2.2.2 Design of Model Specimen
The model scale was dictated by several factors: (1) available actuators for application of vertical
and lateral loads; and (2) minimum size for which primary reinforcement could be scaled without
use of special model materials. A quarter scale model was selected as an appropriate size for
which no special modeling treatment was necessary. Only dimensional scaling was used.
Material properties were selected to match those of the prototype. Table 2-1 shows the
dimensions, reinforcement details, applied axial load and lateral load capacity for both the
prototype and the model.
TABLE 2-1 Details of Prototype and Model
ITEM PROTOTYPE MODEL REMARKS
Longitudinal Steel 24 # 11 (36 mm) 21 # 3 (9.5 mm) p=2%
Spirals #5 (16mm) wire = 4 mm dia.
Spiral Pitch 76mm 19mm
Spiral Yield Strength 414MPa 380 - 450 MPa
Column Diameter 1.22m 0.3 m Scale 1:4
Column Length 5.5m 0.32m Scale 1:4
Cover 50mm 12.5 mm Scale 1:4
Embedment length Tension = 1.4 m Tension = 0.35 m
Compo = 0.72 m Compo = 0.18 m
Axial Load 3225 kN 806kN 0.1 f: Ag
Lateral Load Capacity 1550 kN 388kN ~=~/L
Spacing of long. steel 100mm 25mm
15
2.2.3 Material Properties
Similitude relationships reqUIre that the model materials must have the same stress-strain
characteristics as the prototype. This was achieved easily for the main longitudinal
reinforcement. However, the column ties could not be scaled adequately using available steel.
Some heat treatment was required to alter the characteristics of commercially available wire
reinforcement to achieve proper similitude requirements.
2.2.3.1 Properties of Reinforcing Steel
The reinforcing steel used in the bridge pier construction was Grade 60 reinforcing bars. At a
scale of 1:4, the model pier required 9.5 mm (# 3) Grade 60 longitudinal bars conforming to
ASTM A615-90, which was not a problem since this size is commercially available. Figure 2-2
shows typical stress-strain curve of the #3 bars used as main longitudial reinforcement.
However, for the hoop reinforcement, the dimensional scaling resulted in the use of 4 mm
diameter wires. These wires do not have the specified yield strength (414 MPa) of the prototype
nor a yield plateau similar to the # 3 (9.5 mm) bars that were used as spirals for the full scale
bridge pier. The gage wire had to be annealed through extensive heat treatment of the cold
formed wires. After several laboratory oven heat tests of samples, a temperature of
approximately 1050 - 1070 OF was used to heat treat the spiral wires. This heat treatment
produced a wire yield strength of 380 - 450 MPa with similar yield characteristics of Grade 60
bars. Figure 2-3 displays the achieved stress-strain behavior of the annealed wire used as
confining spirals following heat treatment.
The footings and the end blocks were reinforced with # 5 bars conforming to ASTM 615-90.
Figure 2-4 shows the stress strain relationship for the #5 rebar used in the footings and end
blocks.
16
700 r....... . '..:.:.~b::::::~~==-;:;:;:;:;;;;::;-~" ~
~--~600 1-······-:~···········;,;,r6'·,r..; , , , : .
500 ~.
400 f-f :- c : ; ; ...........•.................... -1
300 H·········:···········,··········:··········,·········.; : ; ~
-Bar3a200 -Bar3b ..... , ... _-
-€)- Bar3c
100
0 i i0 2 3 4 5 6 7 8
Strain (%)
FIGURE 2-2 Stress vs. Strain Curve for #3 Longitudinal Steel
--- -- .?~f..r,
-WireW1-WireW2-€)-WireW3 -- ... _-.- ...
i
500
400
m 300Cl.e.UlUl
~ 200U5
100
oo 2 4
Strain (%)
6 8 10
FIGURE 2-3 Stress vs. Strain Behavior of Annealed Wire Used for Spirals
17
:
-~
fj : : j-BarSa-BarSb-.>- BarSc
700 I
600
~~500 7:ma.. 400~enen
300~U5
200
100
108642
O'--'----L---'--'--L.......C.---L--'----'--'---'---'---L-~---'----'----'--'---'
oStrain (%)
FIGURE 2-4 Stress-Strain Curve for # 5 Rebars Used in Footings and End Blocks
The stress-strain curves presented in Figures 2-2 through 2-4 do not include the fracture strain.
The extensometers used to measure the specimen elongation had to be removed prior to fracture
to prevent damage to the instrument. However, the total elongation of the gage length was
measured, the resulting final strain calculated, and these results are tabulated in Table 2-2. The
energy to fracture was computed by assuming that the stress-strain diagram was linear from the
last instrumented strain reading to the fracture strain. Assuming that a typical hoop bar exhibits
characteristics similar to a 9.5 rom (#3) or a 16 rom (#5) bar, strength and ductility parameters
obtained for the annealed steel wire may be considered acceptable in terms of fracture energy and
peak strength with variations not exceeding 15-20%. Additionally, there is no well-distinguished
ultimate strain because of the lack of a yield plateau and strain hardening regime. A comparative
summary of the different rebar test results is displayed in Table 2-2.
18
TABLE 2-2 Summary of Rebar Characteristics
SPECIMEN f y Es fsu Esu Esf EfrGroup No. (MPa) (MPa) (MPa) (%) (%) (MPa)
3a 463 213,500 733 8.5 14.6 9,925Rebar 3b 472 215,900 714 9.7 13.8 9,095
3c 476 227,300 723 7.9 15.7 10,659WI 419 234,600 471 - 17.5 8,044
Wire W2 407 210,900 455 - 19.1 8,501W3 398 216,100 475 - 16.9 7,8405a 422 220,600 650 8.2 16.9 10,270
Rebar 5b 430 226,100 664 7.7 17.3 10,5805c 423 203,200 656 8.3 16.2 9,772
Notations:
2.2.3.2 Concrete Properties
f y = Yield stress; Es = Young's modulus
f su = Ultimate (peak) stressEsu = Strain at peak stressEsf =Fracture strain; Efr = Fracture Energy
In order to ensure monolithic reinforced concrete specimens, the columns were poured with
footings at the same time. All the specimen were cast in an inverted position, as described later.
This required a concrete with an average slump of 8 inches and a maximurn aggregate size of 1/2
inch. The specimens were cast in two batches of six specimens each. The cement used in the
concrete mix was Portland Blast Furnace slag cement, Type IS, meeting ASTM C599-85
specifications and the requirements of ACI 318 and 301. The fme aggregate used was concrete
sand meeting requirements of ASTM C-33-90. The coarse aggregate used was SR #7/ASTM #8
crushed limestone, meeting the requirements of ASTM C-33-90. Air entraining admixtures
complying with ASTM C-260 were also used in the mix. In order to achieve 8 inches of slump, a
high range water reducer which complies with ASTM C-494 was added. The concrete mix
proportions used are presented in Table 2-3.
19
Batch
TABLE 2-3 Mix Proportions
Material Quantity Concrete Strength (MPa)(kg/m3
) AveragePIERSMix 1: Batch 1 & 2 30.9
Cement 280Fine aggregate 1136112" Coarse Aggr. 848Water 184
Mix 2: Batch 3 & 4 40.1Cement 336Fine aggregate 984112" Coarse Aggr. 848Water 201
END BLOCKS 45.6Cement 476Fine aggregate 8981/2" Coarse Aggr. 988Water 149
Mix 1 was used for the first six specimens. The specimens were cast in two batches of three
specimens per batch. Due to project delays, testing did not commence for over 12 months.
Hence, Mix II was designed with a higher strength so that all twelve specimens would have
approximately the same strength during testing. The target strength was based on cylinder tests
of the concrete used in the construction of the first six columns. As shown in Figures 2-5
through 2-8, there is considerable variation in concrete strength even for the same mix.
The end blocks were poured from a different concrete mix and was designed to achieve a
strength of 42 MPa at 28 days. The design mix for the end blocks is also shown in Table 2-3.
Six cylinders were cast from each batch: three to be used to determine the 28-day strength, and
the remaining three to be tested at the same time as the corresponding column test.
20
0.40.30.2
Strain (%)
0.1
-_ .. _--_ _ _--_.-.~.~_ .. - ..#J': ..." .
................. .... .."-0'-.:.:;;.----.;:~
-Mix1-C11/--·· .. ······.. ·,··.... ················'··I-Mix1-C2
~-Mix1-C3
40
35
30
ro 25a..5
20UlUlQ).....
U5 15
10
5
00.0
FIGURE 2-5 Stress vs. Strain for Concrete Mix 1 at 28 days
40
: ~',"~
30 ~ .,.~.
20 r if .•........... .........................................-Mix2-C1-Mix2-C2
10 r···· ~-Mix2-C3
0.40.30.2
Strain (%)
0.1
Ol....-''--'--'---'---'---'---'---"--'---'--'--'--'---'--.L-'--'--'--'---'
0.0
FIGURE 2-6 Stress vs. Strain for Concrete Mix 2 at 28 days
21
30
25
20r0-o..e.
15enenlE
en10
-Mix3-C1-Mix3-C2
5~-Mix3-C3
00.0 0.1 0.2 0.3 0.4
Strain (%)
FIGURE 2-7 Stress vs. Strain for Concrete Mix 3 at 28 days
25
20
ro- 15a..e.enen~ 10en
-Mix4-C1-Mix4-C2
5 ~-Mix4-C3
00.0 0.1 0.2 0.3 0.4
Strain (%)
FIGURE 2-8 Stress vs. Strain for Concrete Mix 4 at 28 days
22
2.2.4 Construction of Columns and Base Blocks
It was decided to construct the pier and foundation for all specimens monolithically, which
meant that the base block and the column would be poured together at the same time. Based on
this decision, the form had to be designed to accommodate both the column and the foundation
block. The forms, which were cut and assembled together on top of a steel frame shoring, were
constructed in a manner so that it could be folded together and be reused later. Additionally,
forms were tied together to permit six specimens to be cast in a single pour. For ease of
construction and pouring, all specimens were cast in an inverted position. The completed
formwork is shown in Figure 2-9.
FIGURE 2-9 Formwork for Six Specimens
23
FIGURE 2-10 Cage Assembly for 1:4 Scale Model Piers
Steel cages for the columns were assembled first. The steel reinforcement for the footings were
then constructed around the column cages. As shown in Figure 2-10, the columns were
assembled on three discs which were notched to allow exact spacing and placement of the
longitudinal bars. The spirals were tied to the longitudinal # 3 bars at a spacing of 0.75 inch.
This spacing was kept constant throughout the column. The side base blocks were designed to
allow post tensioning of the foundation block (Figure 2-11). The foundation block is composed
of three parts: the mid-section is cast as part of the pier, while the side blocks were cast
separately as re-usable blocks which were to be connected to the specimen through post
tensioning.
Four prestressing ducts were installed inside the specimen footings and in corresponding
locations in the end blocks such that 1-5/8" high-strength high alloy threadbars could be passed
through the two end blocks and footing and post-tensioned before testing each specimen. One
such post-tensioning operation for one of the specimens is shown in Figure 2-11. Figure 2-12
shows the reinforcement details for a typical column and its footing.
24
FIGURE 2-11 Post Tensioning of End Blocks to Footing
Dimensional details of the final specimen of the fmal specimen are presented in Figure 2-13 and
2-14. Two views of the reinforcement used in the column and the base block are shown in
Figure 2-13. A number of V-stirrups were used in both directions of the foundation block as
shown in the figure to provide the necessary flexural capacity. Essential dimensional details of
the finished specimen are displayed in Figure 2-14. The height of the column above the base
block is 1525 nun. The center of gravity of the point of application of the load was
approximately 1370 nun from the base. Prestressing forces were applied at four locations spaced
approximately 610 nun in either direction. The foundation block of the specimen, as poured in
place, measures approximately 460 X 875 nun. However, once the side blocks are attached and
post-tensioned, the width of the foundation in the direction of loading is approximately 2.08
meters. The horizontal dashed lines in the figures represent the post-tensioned bars and the
vertical dashed lines represent threaded rods used to anchor the base blocks to the floor.
25
FIGURE 2-12 Cage Assembly for 1:4 Scale Model Column
The post-tensioned end-blocks are shown in Figures 2-15 and 2-16. Three views of a single
block are shown in the figures. Two such blocks were used on either side of the column
specimen. The blocks were anchored to the strong floor by means of threaded rods, displayed by
dashed vertical lines in the both figures. The use of post-tensioned blocks considerably reduced
the amount ofconcrete required to cast each specimen.
26
1--t---21 - 9.5 "'''' bOors
L..+--4 "'''' splrOols@ 19 "'''' c/c
H--~21 - 9.5 "'''' bOorsH=~1
t---16 - 16 "'''' hoopse---2 - 9.5 "'''' hoops
for shl'" co.ge
Splro.ls
@ 19 "''''2 - 9.5 "'''' hoopsfor shl'" co.ge
9 - 16 "'''' U-bOors10 - 16 "'''' U-bOors
---+--t 1----;21 - 9.5",,,, bOors
4 "'''' splrOols@ 19 "'''' c/c
SplrOols@_1_9_"''''_-.I,--+,
Elevo.tlon Side View
FIGURE 2-13 Reinforcement Arrangement for Specimen with Base Block
132 132
875
-f r 305--.--"""'T""-_.i-....;
1525
24001
l!~:_~o+---,..-610
h60
r 305
ELEVATION
diMensions in MM
SIDE VIE\I
~60 305 clio..
FIGURE 2-14 Configuration and Dimensional Details of Specimen with Base Block
27
It It It~5 -11-235
I ~-r-r== [J I II II ~875 605 II 875 II (( 610
j lt~ ====11 L ° II II It
135 !--1220--1 265 j 1-1 L265
1-875-1
ELEVATION SIDE VIEW'
330
diMensions in MM
PLAN
FIGURE 2-15 Dimensional Details of End-Block Attached to Right Side of Specimen
It
-11-80
-, It. 0-=-1875 610 II
~===I
135 ~810~
ELEVATION
diMensions in MM
1°11 It875 (( 610
L oil It
I 610 I
~875~SIDE VIEW'
.---: Ch330I -t ---
875 610
Lt ---~810~
fI.&i
FIGURE 2-16 Dimensional Details of End-Block Attached to Left Side of Specimen
28
2.2.5 Test Setup
The test setup was assembled from available steel sections. The main consideration, after the
prediction of the expected maximum strength of the built specimen, was to minimize the
deformation and stresses in the members and connections of the test frame. The calculated
maximum deformation of the testing frame was 0.001 inches. A lateral brace was provided to
resist a significant portion of the reaction from the horizontal actuator. The second concern was
the floor anchoring pattern. The NIST strong floor is a 1.8 m thick heavily reinforced slab with
anchorage points for connecting test fixtures located in a grid 1.5 m on center. Each anchorage
point consists of two 40 mm bolt holes capable of resisting 900 kN in both the vertical and
horizontal direction. The placement of the two end blocks, the tying of the specimen base block
to the strong floor, and the layout of the test frame along with the loading actuators were carried
out with sufficient precision to allow a ± 6 inches testing displacement in the main lateral degree
of freedom.
The [mal setup with the specimen and the loading mechanisms is shown in Figure 2-17. This
figure does not show the support system designed to prevent out-of-plane movement which is
described in the paragraph below. A photograph of the as-built test-rig with the specimen in
place is shown in Figure 2-18. Details of the specimen instrumentation is discussed in the next
sub-section.
To avoid any out-of-plane displacement during testing, two steel beams with smooth surface
plates were attached to the testing frame on either side of the specimen parallel to the direction of
loading. Four rollers were attached to the column head to permit relatively friction-free
movement on the side plates and confine the specimen against any out of plane displacements.
Figure 2-19 shows a top view of the support system with the top of the column grip in contact
with the side plates.
29
REACTION FRAME
0 0 0 0 0 00 0 o I 0 0 00 0
~ I0 0 0
0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
LVDTs
END BLOCKS
220 kN VERTICALACTUATOR
HEAD CAP
+/- 150 mm STROKEACTUATOR
SPECIMEN
FIGURE 2-17 Details of Load Frame and Test Set-Up
30
FIGURE 2-18 View of Test Set-Up Prior to Attaching Out-of-Plane Support System
FIGURE 2-19 Overhead View of Out-of-Plane Support System
31
2.2.6 Instrumentation of Model Columns
The objectives of the testing typically dictate the required instrumentation. The instrumentation
program for the experimental testing consisted of measurements of linear (lateral), curvature and
rotational response of the specimens. A minimal set of strain gages were also installed to
monitor yielding of the longitudinal reinforcing steel bars in the potential plastic hinge zones.
The placement of the various measuring instruments is displayed in Figure 2-20. Pertinent
details of the instrumentation and measurements are described below.
2.2.6.1 Force-Displacement Measurement
The lateral displacement was applied by a servo controlled 670 kN MTS hydraulic actuator. The
hydraulic power supply is a 4.5 cubic meter per second, variable volume pump rated at a pressure
of 34 MPa. The actuator stroke was ± 150 mm contolled by a D/A & AID assembled and
programmed data aquisition system. The applied lateral displacement and load were measured
from the MTS ram using a calibrated LVDT and load cell, respectively. On the opposite side of
the loading actuator a string potentiometer and two LVDT's were mounted against the specimen
to measure the lateral displacemnt of the specimen at different elevations. The string
potentiometer was placed at the same level of the actuator center line 1370 mm from the top of
the footing. The two LVDTs were placed at 455 mm and 910 mm from the top of the footing.
The vertical load was applied using a 220 k:N servo-controlled MTS ram. The vertical load was
recorded using the calibrated load cell of the vertical actuator. The applied vertical load during
testing was approximately constant at O.I/c'Ag which is the estimated weight of the bridge deck.
2.2.6.2 Curvature Measurement
The curvature was calculated using six clip gages mounted on opposite sides of the specimen in a
plane parallel to the loading direction. The clip gages were designed and manufactured at NIST.
These clip gages were used successfully in previous testing offull scale columns at NIST.
32
FIGURE 2-20 Test Setup with Instrumentation
33
The clip gages consist of two strain gages mounted on light gage C-shaped steel sections which
in turn are hooked between two points on the specimen equal to the gage length, L(Figure 2-21).
The curvature is calculated using the following expression:
(2-11)
where
Ll l is the contraction or expansion measured by clip gage 1.
Llz is the expansion or contraction measured by the opposite clip gage 2.
L is the gage length
x is the distance between the gage mount points
The above equation is generally valid only under the assumed condition that plane sections
remain plane after bending. Curvature measurements beyond yield were also affected by
spalling of the cover concrete.
2.2.6.3 Rotational Measurement
Four electric clinometers were mounted on the specimen in the central plane to measure the angle
of rotation at the base of the column during testing. The clinometers were connected to a special
base, which in turn was connected to threaded rods that were embedded inside the specimens.
The clinometers were attached to the specimen at 150,300,450 and 600 mm, respectively, from
the base of the column (top of the footing). The electric clinometer is composed of a metal
gravity sensor with no moving parts such that when rotated, its sensitive axis provides a linear
variation in capacitance, which is electronically converted into angular data (Figure 2-22).
34
I·
FIGURE 2-21 Clip Gage Mounted on Column for Curvature Measurement
FIGURE 2-22 Electric Clinometers Used for Rotational Measurement
35
2.2.6.4 Strain Measurements
Four strain gages were installed: two each on opposite longitudinal reinforcing bars in the
loading plane. The strain gages were installed at 100 mm and 200 mm from the base of the
column. These locations were based on estimates of the plastic hinge length of the specimen
after yielding, which is typically a distance equal to the depth of the specimen. The strain gages
readings were used primarily to check the yielding load of the specimens.
2.2.7 Control and Data Acquisition Systems
The set up of the control system to coordinate (a) the movement of the hydraulic actuator, (b) the
data acquisition, and (c) the data display, was a significant and tedious task since there was no
existing controller or data acquisition system readily available for use with the experiment. The
control system consisted of a microcomputer with the usual peripherals, an analog-to-digital
(AID) converter, a digital-to-analog (D/A) converter, two servo-controllers (one for the vertical
actuator applying the gravity load on the specimen and the other for the lateral actuator applying
the simulated earthquake displacements) and computer software (see Figure 2-23). Both
controllers had a full scale range of± 10 volts.
The data acquisition system had 2 - 32 channel real time AID cards and 1- 2 channel D/A card.
The control system was programmed to send a voltage signal through the D/A card to impose the
required displacement history on the lateral hydraulic actuator. A special-purpose computer
program was written using system software to achieve various levels of control during testing.
This included the ability to stop the testing at any intermediate loading point and altering the
displacement history, if necessary. A predefined set of AID channels which were to be sampled
during testing were established. Sampling rates were based on available disk storage space since
the system was capable of sampling 50,000 samples per second. The data acquisition program
also had the capability ofreading different output channels at previously specified frequencies.
36
FIGURE 2-23 Control and Data Acquisition System
2.2.8 Ultrasonic Measurement
Nondestructive test methods are gaining popularity these days as a means of assessing structural
integrity. It was, therefore, decided to validate the feasibility of using ultrasonic measurements
in assessing the damaged state of selected specimens after testing. Consequently, ultrasonic
readings were taken across the column in a plane parallel to the loading at different heights. The
readings for the travel time of an ultrasonic wave across the concrete specimen were taken once
before testing and later after the test was completed. Figure 2-23 shows the locations at which
the readings were taken. It was very difficult to take measurements during testing since the noise
and vibrations of the hydraulic pump interfered with ultrasonic measurements. The objective of
37
including this measurement in the experimental program was to seek a correlation between
damage and the wave travel time through concrete.
FIGURE 2-24 Ultrasonic Readings Across Concrete Column
38
SECTION 3
ANALYTICAL MODELING AND DEVELOPMENT
OF LOAD HISTORIES
The development of load histories for the random phase of testing was accomplished through the
use of a nonlinear computer program, IDARe (Kunnath et al., 1992). Prior to using random
loads, however, it was essential to conduct certain benchmark tests to permit rational
interpretation ofthe results. The benchmark testing was composed of monotonic, standard cyclic
and constant-amplitude fatigue loading. Following this, a series of random displacement
histories were analytically simulated for the second phase of testing. Details of the bridge
column model used in analytical simulations, calibration of the hysteresis loops and selection of
the load histories are outlined in this section.
3.1 Analytical Model of Bridge Column
The prediction of the inelastic response of the model column was an important subset of the
overall task of developing the experimental test program. The imposed random displacement
histories were meant to reflect realistic displacements under actual earthquake loads. Hence,
every effort was made to use reliable element and material models to predict displacements under
inelastic load reversals. The conceptual framework in which the nonlinear time-history
evaluations are carried out represent a macromodel approach, summarized in Kunnath and
Reinhom (1995). It consists of characterizing member behavior through assumed flexibility
distributions and monitoring stiffuess at selected critical location through prescribed hysteresis
models. The success of this approach has been documented in Kunnath et al. (1992). The two
main elements of the macromodel are: (1) a flexibility-based member model; and (2) a versatile
hysteresis model that characterized moment-curvature behavior at the plastic hinge zone. Details
of each are briefly described.
39
3.1.1 Component Modeling
Seismic moments induced in the bridge column have a linear variation along the length as shown
in Figure 3-1. When the tensile stress due to these moments exceed the tensile strength of
concrete, cracks form along the length of the member which in turn influences the moment of
inertia of the section. The member curvature parameter is inversely proportional to the moment
of inertia of the section and varies along the member length. The bridge column was modeled as
a single component with distributed flexibility. A linear variation of flexibility is used up to the
yield point of the member, after which a constant plastic region is assumed, as shown in Figure
3-1. Flexibility coefficients for this assumed distribution is calculated from the principles of
virtual work:
where:
L
/y = fmi(x)mix)IEI(x)d(x)o
mi (X) = moment distribution for unit moment at end i
mj (x) =moment distribution for unit moment at end j
EI(x) = flexural rigidity
(3-1)
.The flexural rigidity, EI, at the ends of the member is monitored throughout the analysis. The
moment rotation relationship for such an element can be derived by integrating the MlEI diagram
across the length ofthe member, as follows:
(3-2)
where ~e and 11M are the incremental rotations and moments at the ends A and B of the
member, respectively. The flexibility coefficients of the above matrix are:
40
111 = (3 + 3a - 3a 2+a 3- P - p2 - p3 + 2ap -a2p +ap2) / (12E1a
)
+ (I- 3a + 3a2-a3+ P + p2 + p3 -2ap +a2p _ap2) / (12E1h
)(3-3)
J;2 =-Ill =(I+a +a 2_a 3- p - p2 + p3 +a 2p -ap2)/(I2E1a
)
+ (I-a -a 2+a 3+ P + p2 _ p3 +ap2 -a2p) / (12E1h
)(3-4)
h2 = (I +a +a 2+a 3- 3p + 3p2 - p3 -2ap _a 2p +ap2) / (12E1a )
+ (3-a _a 2_a 3+ 3P - 3p2 + p3 +2ap +a 2p _ap2) / (12E1h
)(3-5)
where a and p are the plastic hinge length ratios (expressed as a function of the member
length) at the ends A and B, respectively. The term (EI) represents the instantaneous flexural
rigidity at the ends of the member. In the case of a single bridge column, the top end always
remains elastic and no plastic hinge length needs to be computed which greatly simplifies the
above expressions (i.e. p= 0).
N--..f~~
I--I
II
II
III1
DEFORMEDSHAPE
MIEI DIAGRAM
MyJlp
1 M=Pln
MOMENTVARIATION
COLUMNSECTION
In
p
FIGURE 3-1 Inelastic Component Model ofBridge Pier
41
Since lateral loads, such as those caused by an earthquake, produce only linear variations in the
moment diagram, the above formulation works effectively and efficiently. If additional
moments, such as those caused by distributed member loads, are significant, then the nonlinear
distribution of moments may not be sufficiently overcome by the lateral loads leading to
potential errors in the assumed flexibility distribution. In such cases, it is necessary to sub-divide
the element into smaller sections so that the assumed linear distribution is valid.
The element stiffuess matrix is derived from the equilibrium of forces at the ends of the member
and can be expressed in the following form:
(3-6)
where [ksJ is sub-local stiffuess matrix determined through inversion of the flexibility matrix
given in Equation (3-2), and:
-lLo
'lLI
(3-7)
in which L is the length of the member. In general, the system of equations to be solved, at any
stage of analysis, is in the form:
[K]{u} = {F} (3-8)
where [.K] is the global stiffuess matrix, u is the vector of unknown nodal displacement and [F]
is the vector of applied equivalent forces on the system. Since the stiffuess matrix is symmetric,
only one half band width is stored by offsetting the main diagonal. The global stiffuess matrix is
obtained by assembling the element matrices and updated only in the event ofa stiffuess change.
42
The rest of the analysis procedure is similar to matrix frame analysis wherein the assembled
structure stiffness matrix is inverted through numerical techniques and solved for each step of the
imposed force or displacement. Dynamic time-history analysis is carried out by explicit direct
integration using Newmark's unconditionally stable "beta" method (Newmark, 1959). The
moments at the base of the column are updated at every step. The corresponding stiffness is
established from a predetermined hysteresis model with user-specified control parameters for
stiffness and strength degradation. The hysteresis model was calibrated using observed results
from Specimens A-I and A-2 as described in the next section.
Equilibrium errors resulting from changes in state (stiffness transition) are treated by means of a
single-step force correction. This consists in computing unbalanced forces at the end of any
given analysis step and applying them as corrective forces in the next step. Such a procedure
was first used in DRAIN-2D (Kanaan and Powell, 1973) since the compuational effort required
for a fully iterative nonlinear analysis is substantial.
3.1.2 Hysteretic Modeling
The primary difference between a macromodel approach as used in the present study and
standard finite element representation is that, in the present scheme, no constitutive equations are
used. Instead, the inelastic behavior is described using force-deformation rules which attempt to
capture overall member behavior. In theory, it is possible to construct force-deformation curves
using constitutive models. However, constitutive laws hold true only for a microscopic point in
the material. For an inhomogeneous material such as reinforced concrete, it will take a very fine
discretization of the cross-section to represent the material behavior in terms of local concrete
steel interaction. Such an approach, however, is tedious and computationally intensive.
The force-deformation model used in the IDARC program is based on three primary control
parameters and an additional secondary parameter to establish the rules under which inelastic
loading reversals take place. Details of the model and the control parameters can be found in
43
Kunnath and Reinhom (1995). A variety of hysteretic loop shapes can be achieved by a proper
combination of a monotonic trilinear force-deformation envelope and the control parameters
which characterize stiffness degradation, strength deterioration and pinching or slip behavior.
While automatic identification of hysteretic parameters is possible (Kunnath et al., 1996), the
control parameters were identified directly from one of the experiments conducted in this study.
A graphical evaluation of the hysteresis loops generated from the cyclic testing of Specimen A2
yielded control parameters as shown in Table 3-1. The simulated loops using these parameters
are shown in Figure 3-2. Except for some minor discrepancy in the shape of the loops just above
and below the zero-force axis, the overall behavior matches the experiment with adequate
accuracy. The identified control parameters listed in Table 3-1 were used in all IDARC analyses
for the generation of the random displacement histories.
TABLE 3-1 Identified Control Parameters
Parameter Meaning Value
a Degree of Stiffness 8.0
degradation
13d Strength degradation 0.025
based on ductility
13e Strength degradation 0.0
based on ductility
y Pinching coefficient 1.0
44
-z~'-'
EXPERIMENT
-60 -40 -20 o 20 40 60 80
DISPLACEMENT (mm)
80604020o-20-60 -40
SIMULATION
100
80
60
40
20
o 1----f'}"'9-~==------'tfF---;~'----I-----I-I'I1
-20
-40
-60
-80
-100
-80
w()~
oLL~«wIen
-z~'-'
DISPLACEMENT (mm)
FIGURE 3-2 Calibration of Hysteresis Model
45
3.2 Prototype vs. Model Calibration
The IDARC runs to generate the random displacement histories were carried out on the model
specimen. If similitude requirements had been satisfied in every aspect, it would have been
equally logical to carry out the analyses on the prototype and scale the resulting displacements by
a factor of 4.0. However, given the probability that some discrepancy in material property
similitude may exist, it was decided to carry out the simulations using the model geometry and
material properties. A verification analysis was conducted, however, to check model response
against corresponding prototype response for a specified ground motion. The prototype bridge
column was subjected to the 1940 El Centro earthquake, assuming fixed based conditions, while
the model column was subjected to the same record using a compressed time scale of 1/.JS,
where S is the scale factor as required by similitude. The same intensity (PGA) earthquake was
used in both runs since the time compression applied to the model structure accounts for the scale
factor. Results are presented in Figure 3-3 in which the model response is clearly seen to be
scaled down by the model scaling factor, viz., 4.0.
3.3 Selection of Displacement Histories
The main focus of this research is the investigation of load path effects and its effect on structural
damage. However, to enable meaningful comparison of random load response with tests
conducted by others using standard cycles with increasing ductility, it was considered essential to
carry out a few benchmark tests. A few critical parameters were deemed important in
establishing such benchmarks. First, it was decided that a lateral load test under monotonically
increasing load until failure was essential, since numerous models of damage use the monotonic
envelope as a base line for comparing strength deterioration, normalizing energy dissipation
and/or peak deformation, etc. Secondly, a standard cyclic test using traditional displacement
amplitudes was also considered vital so that differences in load paths could be characterized.
Finally, it was considered crucial to conduct a few fatigue tests under constant amplitudes to
establish a basis for validating cumulative damage theories. The fatigue tests were conducted at
46
slow strain rates since typical earthquakes do not impose high strain rates on bridge structures.
These tests were needed to provide fundamental data on the fatigue life of typical flexural
columns. The remaining specimens were all tested under random load histories. The complete
set of experiments showing the type of imposed displacement is presented in Figure 3-4.
60Prototype Subjected
E 40 to EI-Centro (0.29).s-c:20(])
E(])0ro 0c..II)
isc. -20i=
-40
0 2 3 4 5 6 7 8 9 10
Time (sec)
15Model Subjected
E 10 to EI-Centro (0.29).s-c:
5(])
E(])0ro 0c..II)
isc. -5i=
-10
0 1 2 3 4 5 6 7 8 9 10
Time (sec)
FIGURE 3-3 Comparison of Prototype vs. Model Response
47
SPECIM. LOAD X-DIR. LOAD Y-DIR. LOAD PLAN VIEWNO. ROUTINE HISTORY HISTORY OF LOAD
MONOTONIC
~~ +Al PUSHOVERTESTSTANDARD
~~ +A2 DISPLAC.PATTERN
A3 2 /).y TO
~~ +FAILURE
A4 3 /).y TO
~~ +FAILURE
AS4 /).y TO --~ +FAILURE
A6 5 /).y TO - ~ +FAILURE
RANDOM
~~ +A7 EARTHQUAKELOADINGRANDOM
~~ +A8 EARTHQUAKELOADINGRANDOM
~~ +A9 EARTHQUAKELOADINGRANDOM
~~ +A1D EARTHQUAKELOADINGRANDOM
~~ +All EARTHQUAKELOADINGRANDOM
~~ +A12 EARTHQUAKELOADING
FIGURE 3-4 Summary of Displacement Histories Used in Testing
48
3.3.1 Benchmark Testing
Benchmark tests are typically carried out to calibrate future testing. In this project, the
benchmark tests were a critical part of the overall objective of identifying damage parameters; It
was necessary to relate dissipated energy, number of inelastic cycles, and peak/average inelastic
cyclic strains, to be observed in the random tests, to corresponding estimates in standard testing.
The first specimen designated Al was tested under a monotonically increasing lateral load until
failure. Failure would be defined, in this case, as a significant drop in load carrying capacity and
incipient P-delta collapse. The significance of the monotonic envelope cannot be underestimated
since it forms the basis for defining a host of control parameters in many existing damage
models.
Specimen A2 would be subjected to a normal cyclic load with three full cycles at increasing
ductility up to failure. Following each set of cycles at a given ductility, a small cycle at
approximately b = O.5~y would be imposed to measure change in system stiffuess.
Specimens A3 - A6 were tested under constant amplitude reversed cyclic displacements.
Specimen A3 was tested under a constant cyclic displacement amplitude of approximately b = ±
2~y. Specimen A4 was cycled under a constant displacement of b = ± 3~y. Similarly,
Specimens A5 and A6 were cycled at amplitudes of b = ± 4~y and b = ± 5~y until failure.
Failure was defmed as either the loss of confinement following hoop fracture or significant loss
ofvertical load carrying capacity following longitudinal bar failure.
3.3.3 Random Loading
Specimens AT through AI2 were designated for random load testing. The choice of the
displacement history to be imposed was crucial. Hence, a great deal of time was spent trying to
develop a rational basis for identifying and specifying random displacement histories. Two
49
issues were considered more important than others since it addressed directly the research
objectives of this study of cumulative damage:
1. The imposed earthquakes had to represent realistic scenarios. And the damage resulting from
the sequence of selected events had to induce adequate damage so that calibration of damage
through each of the limit states, from undamaged (elastic) to collapse would be viable.
2. The effect of load path on the ultimate response, both in terms ofphysical damage limit states
and in terms ofmeasurable damage parameters, had to be identified.
Item 1 addressed above is shown conceptually in Figure 3-5. The question as to how one might
ensure a certain level of damage after each event posed innumerable challenges. This is where
the benchmark tests would contribute significantly. It was decided to utilize the damage data
from the first series of six tests to calibrate a fundamental fatigue-based damage theory. This
would then be utilized to plan the fmal series of six tests based on a predicted damage scenario.
Section 5 of this report will discuss the development of the random histories in greater detail.
The effect of load path would be considered by taking a given random displacement history and
altering the sequence of the displacement cycles. Hence, the number and amplitude of the
displacement cycles would remain unchanged - the only variable being introduced is the
sequence in which the displacements are applied. Again, since the selection of the random
histories is dependent on the outcome of the testing of the first six specimens, further discussion
on the imposed random histories is deferred until Section 5.
50
Event 4
-..-------------------cl- ------------
Event 2 Event 3~ ~. ~ • ~ ..---;---=---~
o
100
E 50E'-'
'EQ)
EQ)(JIII0..Ul
is: :
: :~ ...$ -50 ------------- - ----------------------------------------------III
...J
-100o 20 40 60 80
Cycle Number
100 120
EVENT DESCRIPTION PURPOSE
1 Major event Significant Damage from
potential earthquake
2 Minor event Aftershocks
3 Minor event Intermediate non-critical
events at site
4 Maximum credible Failure of structure
event at site
FIGURE 3-5 Typical Loading Scenario for Random Amplitude Testing
51
52
SECTION 4
CUMULATIVE DAMAGE TESTING
I: PUSHOVER, BENCHMARK AND FATIGUE LOADING
The mechanics of cumulative seismic damage in reinforced concrete has never been fully
understood. It is the premise of this research that one of the primary reasons contributing to this
lack of knowledge is the fact that past experimental testing has not focused on the mechanics of
damage progression. The present research is directed particularly at the phenomenon of
progressive or cumulative damage, hence the only variable introduced in the testing program is
the applied load history. Since seismic loads induce fairly random cycles of reversed
displacements on structural members, it was important to consider random load paths
representative of typical inelastic dynamic response motions. However, in order to evaluate and
calibrate the resulting response under random loads, it was necessary to establish certain
benchmark parameters. The following tests were conducted to ensure a reasonable database of
parameters against which to compare the random load testing:
1) Monotonic loading: The purpose of this test is to develop the backbone or skeleton
force-deformation envelope for the specimen. Some damage models use strength and
deformation quantities derived from a monotonic test to normalize and/or formulate
the damage expressions.
2) Standard cyclic test: This was considered essential since all past laboratory testing has
been based on this approach. This would provide a convenient benchmark against
which to compare random amplitude testing.
3) Quasi-fatigue testing: Another critical aspect that deserved consideration was the
quantification of low-cycle fatigue failure. In an attempt to calibrate a fatigue-based
damage model for flexural members, a series of tests was carried out in which the
specimen was subjected to reversed cyclic loading at constant amplitudes until failure.
53
The benchmark tests and the constant amplitude tests were expected to provide a basis for
estimating damage so that the displacement histories required for the random testing could be
developed. The testing program was consequently divided into two phases: the fust phase
would comprise benchmark and low-cycle fatigue tests, and the next phase would consider
response under random loads. The importance of the first phase of testing will become evident
at the end of this section. It was essential to develop an understanding of the mechanics of low
cycle fatigue so that the displacement histories in the second phase could be planned in a way to
achieve desired damage states.
Details of the first phase of testing are described in this section. Records kept during testing
included information such as crack widths, spalling, exposed reinforcement, etc. that permit
calibration of damage to visual observations in post-earthquake reconnaissance. Failure was
typically defined by either the rupture of confining spirals or fracture of longitudinal reinforcing
bars. Other essential details such as necking of hoops or buckling of longitudinal bars were also
monitored. In addition to the overall force-deformation response, recorded information such as
cracking, yielding and failure load and displacements will be summarized for each specimen.
The recorded force-deformation data was converted to shear vs. displacement response taking
into consideration the additional moments induced due to P-delta effects. Figure 4-1 shows a
schematic diagram of the test set-up and the relevant quantities required to derive the necessary
forces and moments. With reference to Figure 4-1, the shear force (V) in the column is given by:
NxV=P+
H
where: x = (L + H) sine
(4-1)
(4-2)
(4-3)
Table 4-1 summarizes the material properties of the specimens used in Phase I testing. Concrete
was ordered from a local concrete mixing plant with the stipulation that the strength of the mix
54
be 4000 psi. However, as is evident from the results presented in Table 4-1, despite efforts to
keep material properties the same for all tests, the concrete strengths obtained from the two
batches were different.
Table 4-1 Average Material Characteristics for Phase I Testing
SPECIMENS Al - A3
Concrete Strength:Steel Yield Strength:Spiral Yield Strength:
SPECIMENS A4 - A6
Concrete Strength:Steel Yield Strength:Spiral Yield Strength:
L
H
29MPa448 MPa434MPa
35.5 MPa448 MPa434MPa
Lateral Load(P)
G-o M=Nx+PH
FIGURE 4-1 Computation of Column Moments and Shear Including P-Delta
55
4.1 Specimen AI: Monotonic Loading
Specimen Al was tested under a monotonically increasing lateral loading until failure.
Compression tests on control cylinders tested on the day of specimen testing indicated an average
compressive strength of approximately 29 MPa. The loading was applied in displacement
increments of 2.5 rom at the beginning of testing up to yielding of the specimen. As the system
stiffness dropped significantly, the displacement increments were increased to 5 rom.
Very fme hair-line cracks occurred at 2.5 rom lateral displacement. The cracks became
significant as the lateral displacement increased to 5.0 rom. Spalling of the concrete cover was
initially observed at approximately 33 rom lateral displacement. The spalling became significant
when the displacement exceeded 48 rom (3.5% drift). The crack width at this stage was on the
order of 1-2 rom. At this stage of spalling, the spiral reinforcement was clearly exposed. The
maximum lateral load reached 66 kN before additional displacement caused a gradual softening
of the column stiffness. Two longitudinal bars showed signs of buckling. No necking of hoops
took place, which indicated that neither the spirals nor the longitudinal bars were likely to rupture
under monotonic loading. The specimen lateral load capacity started dropping significantly after
a lateral drift of4.0%.
The defmition of failure in a monotonic test is difficult to establish. While it is conceivable that
large lateral displacements (without reversals) can strain the longitudinal bars to fracture, such a
level of displacement was not possible in the present test given the limitation of stroke capacity
of the hydraulic actuator. Additionally, at these large displacements, P-delta effects are
significant and the resulting secondary moments can result in collapse of the structure. Again,
the test setup, consisting of hydraulic actuators mounted directly onto the specimen, will prevent
this from happening. Given these circumstances, it was decided to stop testing after the load
capacity decreased significantly, on the order of20-30%. In the present test, this was achieved at
about 11 % drift.
56
The results of testing on specimen Al produced the backbone force-deformation envelope that
was used in the initial analytical simulations. A trilinear representation, in which cracking and
yielding are distinguished, was considered in the analytical study. The analytical model was
eventually modified at the end ofphase I testing to reflect average response values rather than the
results of specimen Al alone. Table 4-2 provides a summary of test observations. Figure 4-2
and 4-3 show the state of the specimen at the onset of yielding and at the end of the test,
respectively. Figure 4-4 presents the resulting force-displacement response.
TABLE 4-2 Summary of Test Observations for Specimen At
LOADING TYPE: Monotonic pushover to failure.
LOAD AND DISPLACEMENT VALVES OF INTEREST:
Axial Load:Maximum Lateral Load:Cracking Load:Cracking Displacement:Yield Load:Yield displacement:Maximum Lateral Displacement:Failure Mode:
DAMAGE OBSERVATIONS:
Displacement (Drift%)2.5 - 5 mm (0.2-0.4%)19 mm(l.4%)33 mm(2.4%)60 mm(4.4%)150 mm (ll%)
57
200kN66kN17.8 kN5mm64kN19mml52mmPotential P-delta failure
NotesFirst CrackingYieldingSpallingSignificant SpallingFailure
FIGURE 4-2 Damage to Specimen At at 3.5% Drift
FIGURE 4-3 Specimen At at End of Test
58
803
Drift Angle (%)6 9 12
70 . .....
.................:.... _---_ ... _--- .. __ .. ; ... _------.---
-_. :
.•..•~.!'lo....• ; ~.NQrojn~l. ~tr~1J9th .':- ~ with P-Delta'.... .
....... __ .. __ ...~;<--v
60 ~ -: , ...... '
30
40
20
10
z~ 50>Q)
~o~
"-IIIQ)
.s::(J)
o0.00 40.0 80.0 120 160
Displacement, !:>. (mm)
FIGURE 4-4 Base Shear vs. Displacement Response of Column At
4.2 Specimen A2: Standard Cyclic Loading
The established procedure for seismic testing of specimens consists of applying a series of
reversed displacement cycles with increasing amplitude. Typically, either two or three full
cycles are applied at a specified amplitude (either as a function of drift or ductility) with a
smaller cycle in between each increase in amplitude to characterize the system stiffness at the
end of each amplitude. A major focus of this research is to investigate if this is an appropriate
load history to characterize random loads resulting from earthquake response. In order to study
the differences in response using random loads, it was necessary to test one of the specimens
using the established standard cyclic procedure.
59
Specimen A2 was subjected to three cycles at each displacement amplitude as a function of
lateral drift. Displacement amplitudes used in the testing consisted of three cycles each at 1.0%,
1.5%,2.0%,2.5% 3.0%, 4.0%, 5.0% and 6.0% drift until failure. The smaller amplitude between
each increase in amplitude was 0.5% drift.
The specimen strength was estimated at 29 MPa based on cylinder tests. Cracking and yielding
occurred in the very first cycle. Hair-line cracks began to appear at a lateral displacement in the
range of 2.5 - 5.0 mm. Crack widths were measured at 0.2 mm at the end of the second cycle.
Crack widths grew to almost 0.7 mm by the end of cycle 10, to 1.0 mm at cycle 13, and up to 1.5
mm at cycle 19 when the drift was about 3%.
Yielding was estimated at 20 mm lateral displacement when the lateral load reached
approximately 65 kN. Spalling of the concrete cover was observed at cycle 15 at a drift of
approximately 3%. Significant cracking propagated up to 225 mm beyond the base of the
column at this stage. Minor bar buckling and significant spalling was evident by the end of cycle
22.
. At cycle 30, the specimen was considered to have failed when spiral rupture occurred. Testing
was stopped after the cycle was completed. The spiral fracture was clearly noticeable in the
load-displacement plot. The plastic hinge length was estimated as 180 mm though cracking
propagated beyond this region. The peak lateral displacement at failure was recorded at 76.2 mm
which corresponds to a drift of about 5.5%.
Figure 4-5 shows the damaged state of the specimen near the plastic hinge zone close to the
failure load. Figure 4-6 shows a closer view of the specimen at the end of testing in which the
ruptured spiral is visible. Figure 4-7 shows the imposed displacement history on specimen A2
while Figure 4-8 presents the resulting force-displacement response. Table 4-3 is a summary of
observed data on the results of the testing.
60
TABLE 4-3 Summary of Test Observations for Specimen A2
LOADING TYPE: Standard Cyclic Loading
LOADING AND DISPLACEMENT VALUES OF INTEREST:
Axial Load:Maximum Lateral Load:Cracking Load:Cracking Displacement:Yield Load:Yield displacement:Maximum Lateral Displacement:Failure Mode:
200kN75kN18kN5mm65kN19mm76mmRupture of Spiral on the Right Side
DAMAGE OBSERVATIONS:
Cycle No.(Drift)1 (1%)15 (3%)22 (5%)
30 (6%)
4.3 Quasi-Fatigue Loading
NotesFirst Cracking, YieldingSpalling of coverSignificant Spalling, some buckling oflongitudinal barsFailure of Spiral on Right Side
There is very limited information on the low-cycle fatigue behavior of reinforced concrete. The
only work to be found in the literature is a series of low-cycle fatigue tests conducted by Mander
and Cheng (1995) to validate the applicability of using specially detailed fuse bars in the plastic
hinge regions in bridge columns. Any effort to develop a cumulative damage model for concrete
will be incomplete without an understanding of this important phenomena. Therefore, a
significant portion of the present test program (specimens A3, A4, A5 and A6) was directed
towards studying the failure of bridge columns under constant amplitude loading.
61
FIGURE 4-5 Damaged State of Specimen A2 at Cycle No. 30
FIGURE 4-6 Final Damaged State of Specimen A2
62
80
....... 60 _......
EE........ 40CQ)
E 20Q)()
~~ ~ ~ AltlC.
0Ul V . Vi:5c.
j=: -20"CQ)Ul -400c.§
-60
-800 5
I
.. ...
J I~ A J J JY Y y y V V
.... _-- .. . ..
.. .---
j i10 15 20 25 30
Cycle Number
6.0
3.0
~
CQ)
....... - Cl~¢:.'"Cl
-3.0
FIGURE 4-7 Displacement History Applied to Column A2
Drift Angle (%)
-6 -3 0 3 680 r-r--c---<------,~--,~---r--r--r--r~~~_r---,---r---r--r-__,
80.040.0
___ Nominal Strength
............~j~h. F...:~I~a. ...
0.00-40.0
....~
-<'V
-80-80.0
40
-60
-40
60
z~ 20>cD~ 0o
LLI-
m -20..c:(J)
Displacement, ~ (mm)
FIGURE 4-8 Shear vs. Displacement Response of Column A2
63
4.3.1 Specimen A3: Constant Amplitude Cycles at 2% Lateral Drift
Specimen A3 was subjected to constant amplitude cycles at a displacement amplitude
corresponding to 2% lateral drift. Initial cracking occurred in the very ftrst cycle at this drift
limit and minor spalling was observed on the compression side. The specimen was then
reversed in the opposite direction to the same amplitude. Cracking on the opposite side was
observed accompanied by similar spalling. The maximum crack width at this point was 0.5 mID.
On returning to the zero position, the cracks closed and were almost invisible. At cycle 3, the
crack widths increased to 0.8 mID. The column was cycled an additional 19 times with no
additional cracking or spalling. Maximum crack widths on either side were about 0.8 - 1.0 mID.
The test was stopped at the end of the day after 40 cycles of reversed cyclic loading at a constant
displacement amplitude of about 26 mID without any further deterioration to the specimen.
The following day, testing of column A3 continued at cycle 41. The rate of loading was
increased to the full capacity of the actuator. At cycle 95 some loose concrete was picked off.
Loading of specimen A3 continued until cycle 150 without any further damage. Later, it was
analytically estimated that this specimen would have sustained over 300 cycles. Since one of the
objectives of the test program was to study different damage models, it was decided that the
cyclic loading could be discontinued and a monotonic load applied until failure. This would
provide information on reserve capacity that is crucial to many damage modeling theories. The
specimen sustained a ftnal drift amplitude of over 10% after experiencing 150 cycles at 2% drift
which suggests that the damage from the initial 150 cycles was negligible.
Table 4-4 provides a detailed summary of observed results related to testing of specimen A3.
Figure 4-9 shows the state of specimen A3 after 100 cycles of loading. The column condition at
the end of testing is shown in Figure 4-10. Figure 4-11 shows the imposed displacement history
on specimen A3 and Figure 4-12 displays the resulting lateral force vs. displacement response
history.
64
TABLE 4-4 Summary of Test Observations for Specimen A3
LOADING TYPE: Constant Amplitude Cycles at 2% Lateral Drift
LOADING AND DISPLACEMENT:Axial Load:Maximum Lateral Load:Yield Load:Yield displacement:Lateral Load at failure:Failure Mode:
DAMAGE OBSERVATIONS
200kN72kN65kN19mm64kNNo failure due to cyclic load,Final failure under monotonic load at 10.5% drift
Cycle No.110.5100150.5
NotesFirst CrackingMinor SpallingYieldingSignificant SpallingFailure (due to monotonic load)
FIGURE 4-9 Specimen A3 at Cycle 100
65
FIGURE 4-10 Specimen A3 at End of Fatigue Testing
Ql
ClC«
4.5
140120100
: Monotonic PuthUpTQ11.5%Drift ~
8060
........ ~ -. - : - .: - ,.. -. - : - -- ..
4020
L....L.......L....--L..-CL..-.:...-'-..L-.J--l...--'-..L-.J--l...--'-.l...-..J.---'--"--.L...-.1.........L....-'----'--l...--'-..l........l.--"---'---'---'--J -3.0
160o
60
-40
ES_ 40c:CDECD
~ 20c.Ul
Clc.i= 0"0
CDUl
~ -20E
Cycle Number
FIGURE 4-11 Displacement History Applied to Column A3
66
-1280
-9Drift Angle (%)
-6 -3 o 3
40.00.00-40.0-80.0
- ~ - - - - - - - - - - :- - - - - - - - - .:.. - .. - - - - - - - - - - - - .'
-120
. .: :
A ' : :- - -.-- ti- - -: - - - - - - - - - - - - - - - - ,- - - - - - - - - - - - - - - - - ~ - - - - - - - - - - --
. - - .;... Nominal Strength: with P-Delta
-;- -.. --.. - - - - - - - - - -; - - .. - - -- . ~ . - - - - - - - - - - - - - -.. ~ . .. - .
: Pull
...... - - - - - - - - - ~ - .. - - - ~ - --: . - -. -- .. ..'
. __ _-:--------_ :-_ _--;-_._-- : _---- .
__-:-: _~_.... _~ -.: - - __ - 0 - _
. .... .... ~ ,
---------------------------------_:_-_:_~-~-~----
-80-160
60
- 40Z.::t:-> 20
Q)
e 00u.....ro -20Q).!:en
-40
-60
Displacement, A (mm)
FIGURE 4-12 Shear vs. Displacement Response of Column A3
4.3.2 Specimen A4: Constant Amplitude Cycles at 4% Lateral Drift
Specimen A4 was tested under repeated cyclic loading at a constant displacement amplitude of ±
57 mm until failure. This displacement was equal to a drift of approximately 4.0%. The applied
axial load was 222 kN which corresponds to the desired axial stress based on O.lf:Ag • On the
very first cycle, deterioration (spalling) was observed on the compression side of the specimen.
In the second cycle, cracks propagated along the length from the base of the specimen. In the
third cycle, spalling had progressed to approximately 150 mm on both sides of the specimen. At
the end of the fifth cycle, the crack width was approximately 1.5mm which increased to about 2
mm in the next cycle. At cycle 8, the plastic hinge was fully developed was estimated to be
about 150-160 mm.
On continuing to load the specimen, cracks propagation and spalling of concrete on both sides
increased significantly. Buckling of longitudinal bars was observed on both sides of the
67
specimen. This led to necking of the confining spiral reinforcement. It was clear at this point
that the load capacity of the specimen was beginning to decrease and failure of the specimen was
eminent. It was also observed that a certain threshold demand on the column was being
surpassed beyond which stiffness and strength of well-confined columns begin to degrade
rapidly. This may also be considered as an irreparable damage limit state. Following cycle 25
and heading toward the peak displacement at cycle 26 a spiral approximately in the middle of the
plastic hinge zone ruptured on the tension side. Table 4-5 gives a detailed summary of test
observations for column A4. Figure 4-13 shows the condition of specimen A4 after 18 cycles of
loading. Spalling of the cover and exposed reinforcement is visible at this stage. The state of
the column at the end of testing is shown in Figure 4-14. Figure 4-15 shows the imposed
constant-amplitude displacement history applied to specimen A4. The resulting force vs.
displacement response history is displayed in Figure 4-16.
TABLE 4-5 Summary of Test Observations for Specimen A4
LOADING TYPE: Constant Amplitude Cycles at 4% Lateral Drift
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load: 222 kNMaximum Lateral Load: 72 kNCracking Load: 20 kNYield Load: 64 kNYield displacement: 16 mmFailure Mode: Spiral Rupture on the Left Side.
DAMAGE OBSERVARTIONS:
Cycle No.11131825-26
NotesFirst CrackingSpalling of cover concreteYieldingSignificant SpallingNecking of spirals, some bar bucklingHoop Failure
68
FIGURE 4-13 Condition of Specimen A4 at Cycle No. 18
FIGURE 4-14 Specimen A4 at End of Testing
69
.. ' .. ' .. "'-
... _- 3.0
...... '.- -3.0
Q)
Clc:
<C-=·C
.. . . . . " ,- _ .... "- Cl
". -.-.- _. <. -. -.-.
-. -'" .- _. _.._- .
- . - ... -... - - -..
40
o
60
20
-20
-40
EE.......-c:Q)
EQ)Uell
ali)
Cla-i="'CQ)lI)
oa-E
'--'---1.--,----,-_,--,'--'----'----'---'------li---l.--L---'--'----J.i--L--'--'---'----ki' ------'-----'---'--'------' -4.5
5 10 15 20 25
Cycle Num ber
o-60
FIGURE 4-15 Displacement History Applied to Column A4
80.0
-.
40.0
--------.----- - _---.
..................... _- ... _-_ ... _----
- - - Nominal Strength.. _ ~Jm.t:~lt~ _ .
0.00-40.0
...................... -- ..... -.... - ..
-~
+V
'""'-
40
o
20
-20
-40
-60
-80 '--"'--"'---'---'---'---'---'---'--"--------'---'--"'--"'--'----'----"'--"'---'---'-----.1
-80.0
>cDeou.....ellQ).c:CJ)
60
Drift Angle (%)
~ ~ 0 3 680 r-r-r--r--..-,---r--r-r--r---r--,--r-r-r-r-r-r--r---r------,
Displacement, Ll (mm)
FIGURE 4-16 Shear vs. Displacement Response of Column A4
70
4.3.3 Specimen A5: Constant Amplitude Cycles at 5.5% Lateral Drift
Specimen A5 was tested under repeated cyclic loading at a constant amplitude of ± 75 mm
corresponding to a drift of approximately 5.5%. The axial load applied was kept constant at 222
kN throughout the testing. Since the maximum displacement in the very cycle was slightly in
excess of 5.5%, cracking, yielding and spalling of the concrete cover were all observed in the
very first push to the peak displacement. Testing continued at a steady rate with reversed cyclic
loads being applied to the same peak amplitudes in both directions. Crack widths exceeded 2.5
mm by the end of the sixth cycle and spalling had progressed beyond 150 mm. The plastic hinge
length was recorded at an average value of 175 mm. Significant buckling of longitudinal bars
was observed on both sides of the specimen at cycle 9. This led to necking of the confining
reinforcement. The specimen failed through rupture of a longitudinal bar before cycle 10 was
completed.
Table 4-6 presents a summary of test observations for specimen A5. Figure 4-17 shows the
condition of specimen A5 after 3 cycles of loading. The state of the column at the end of testing
is shown in Figure 4-18. Figure 4-19 shows the constant-amplitude displacement history
applied to specimen A5. The resulting lateral force vs. displacement response history is
displayed in Figure 4-20.
4.3.4 Specimen A6: Constant Amplitude Cycles at 7% Lateral Drift
This was the fourth and fmal specimen to be tested under constant amplitude loading. Specimen
A6 was tested under repeated cyclic displacement of ± 95 mm (corresponding to approximately
7% drift) to failure. The compressive strength of the specimen on the day of testing was 36 MPa.
The applied axial load was 222 kN which remained constant throughout the testing.
71
TABLE 4-6 Summary of Test Observations for Specimen A5
LOADING TYPE: Constant Amplitude Cycles at 5.5% Lateral Drift
LOADING AND DISPLACEMENT VALVES OF INTEREST:Axial Load: 222 kNCracking Load and Displacement: 18 kN and 5 romYield Load: 64 kNYield displacement: 20 romMaximum Lateral Load: 93 kNFailure Mode: Bar Rupture on the Left Side.
DAMAGE OBSERVATIONS:
Cycle No.1389
NotesCracking, spalling and yieldingSignificant SpallingSome buckling, necking of spiralsFailure
FIGURE 4-17 Specimen A5 at Cycle No.3
72
FIGURE 4-18 Condition of Specimen AS at End of Testing
-- --- --- .--. --- --- --- ---- --- ---- --. ---- -:- ---- .-. ---- --- --··f-------
-40 1---- - .. ---- - --. - ------ - ----. - .. --- -
-20 1--- --- ---- --- --. -- ---- -- ,----- -- .---. --
6.0
---_._--------
- . ----.- ..- -3.0
;:- -- -- ------ ;§
- ----.--------- 3.0
_._._-- - ----- ._---._---
------- ----- ------- ----- ------- -_. __ . ------- -
o
20
80
60
40
-60 1---.- .------
E.§.-c:Q)
EQ)()
coC.til
Clc.i="CQ)
tiloc.E
84 6
Cycle Number2
'---'---'---'----'----'--'----'----'---'----'----'---L_'----'----'----'---'---'--'----' -6 .0
10o-80
FIGURE 4-19 Displacement History Applied to Column AS
73
6
8060
I '
3
4020o
Drift Angle (%)
o
-20
-3
-40
... -! i ¢.- ..- .. :
le~·:····~······:··········,··········,···········I .~ _ ~ : __ ~ Nominal Str~ngth, - - . with P-Delta:
~;,;.;.;.;.-.;-.__--,-~'_~ i ..~. ~.6__ .-- ; , .
-6100
75
50Z~
> 25
cD~ 00u."-en -25Q)~
C/)
-50
-75
-100-80 -60
Displacement, Ii. (mm)
FIGURE 4-20 Shear vs. Displacement Response of Column A5
Again, the relatively high amplitude produced cracking, yielding, and spalling of concrete in the
very ftrst cycle. Cracks propagated rapidly and the spalling extended beyond 175 nun on both
sides of the specimen. Within two cycles, severe buckling of most of longitudinal bars occurred
on both side of the specimen. The visible bulging of the spirals caused by necking of the
conftning reinforcement was a sure sign of distress. A signiftcant drop in strength capacity and
system stiffness was noted. The plastic hinge length was recorded to be 250 nun. At cycle 3, a
spiral ruptured on the tension side of specimen.
Table 4-7 presents a summary of recorded test observations for specimen A6. Figure 4-21 shows
the condition of specimen A6 just prior to failure. A closer view ofthe state of the column at the
end of testing is shown in Figure 4-22. Figure 4-23 shows the displacement history applied to
specimen A6. The resulting lateral force vs. displacement response is displayed in Figure 4-24.
74
LOADING TYPE:
TABLE 4-7 Summary of Test Observations for Specimen A6
Constant Amplitude Cycles at 7% Lateral Drift
LOADING AND DISPLACEMENT:Axial Load:Maximum Lateral Load:Cracking Load:Cracking Displacement:Yield Load:Yield displacement:Failure Mode:
DAMAGE OBSERVATIONS:
222kN76kN20kN5mm66kN18mmSpiral Rupture on the Left Side.
Cycle No.112
3
NotesSpalling commenced at quarter cycleYielding (well before end of cycle)Significant Spalling, necking of spirals,buckling of longitudinal barsFailure
FIGURE 4-21 Specimen A6 at Cycle No.3
75
FIGURE 4-22 Specimen A6 at End of Testing
, ', ', '
-50 _ -.: : ' : : - -3.75
.....-.;::Cl
7.5
3.75
~ ~ 'A ~~ ~
Ilf\'\! ...........•.............
L..L.J.----,----,----,---Vi .J........L...l------l.
V-l-i---,----,----,-V_'_____Ji,--------,----,---,-V--,----,-I' .J........L...l------l.~ __'______'___'__'__'_____J _7.5
23456
Cycle Number
o -- -- .- --- , _ - /" .
50
100
-100o
EE--c::CDECDu.!!!0(/l
o0-j::"0CD(/l
o0-
.§
FIGURE 4-23 Displacement History Applied to Column A6
76
6
10075
3
50
d (mm)
Drift Angle (%)
o
-25 0 25
Displacement,
-3
-50
-'- : ~---------- ----------LPI.J?o.:, " '~'
: Pull : , : ::~-:
-75
-6
o
50
75
-50 ~~----, _ ,---- ----·--~-~-L-N~~i~~I-st~e~gth--
, - ~ _: : with p-Delta:~".,....__.....;.. ~-- -------0----- --- -- -:-- --- ----- -,-- ----- --- ----- --- ----75
100
-100-100
>
zC 25
afeo
LL
ffi -25Q).c:U)
FIGURE 4-24 Shear vs. Displacement Response of Column A6
77
78
SECTIONS
CUMULATIVE DAMAGE TESTING
II: RANDOM CYCLIC LOADING
The benchmark tests and low-cycle fatigue loading completed in the first phase of testing
provided the necessary information to validate the analytical model and develop the random
displacement histories required for the second phase of testing. This section will cover aspects
dealing with the choice of ground motion, the generation and selection of displacement histories,
and results and observations during testing.
5.1 Background and Selection of Random Histories
The main objective of the test program was to verify the behavior of bridge piers responding in
flexure to a random displacement input such as those typically experienced under earthquake
loading. The testing was divided into two phases: the first phase was meant primarily to
develop certain benchmark parameters against which to compare the- random response. The
second phase was directed at examining the effects of load path on cumulative damage and
energy-dissipation capacity. It was essential, from a practical and damage calibration point of
view, to choose an appropriate set of displacement histories so that the number of imposed cycles
was reasonable (not so excessive as to require testing to.continue beyond one day) and that the
damage incurred would lead to potential failure at the end of each test.
A suite of over fifty earthquakes, mostly recorded activity in the west coast of the United States,
was selected for a preliminary study. The analytical model of the bridge pier, calibrated using
the force-deformation response from Specimen A2, was utilized in a extensive simulation study
to obtain the final sequence of displacements. Prior to carrying out the simulation study, a
desired sequence of events was chosen. For example, the first specimen was to be subjected to
the following sequence of loads:
79
1. A major earthquake causing significant but repairable damage
2. A minor earthquake representing a possible aftershock
3. Another minor event signifying additional earthquakes pnor to another major
earthquake
4. A final severe event sufficiently large enough to cause failure of the column
In order to achieve such a desired sequence ofevents and the corresponding damage states, it was
necessary to calibrate some measure of damage. A fatigue-based approach was used in which the
number of cycles to failure, based on results of the experimental testing in the first phase, fonned
the basis of defining a certain degree of damage. The elastic cycles were generally ignored in
the damage quantification. To illustrate how the procedure was applied in developing the final
displacement amplitudes, consider the following situation. An earthquake induces about 30
response cycles of which only four exceed the yield displacement as follows: 2 cycles at 3%
drift, 1 cycles at 4% drift and 1 cycle at 5%drift. Based on the results of Phase I testing, the
model columns sustained 26 cycles at 3% drift, 9 cycles at 4% drift and 4 cycles at 5% drift.
Hence the cumulative damage under the imposed earthquakes was estimated, using Miner's
linear damage accumulation rule, as follows:
( 2/26 + 1/9 1 /4) = 0.44
which is likely to inflict significant damage on the specimen but is perhaps repairable. A second
similar event would certainly damage the specimen beyond repair.
In order to achieve a desired damage scenario, it was necessary to try innumerable combinations.
An additional problem in the numerical simulations was the fact that the records were
concatenated so as to retain the damaged state and stiffuess characteristics at the end of each
event. Hence, an earthquake that may have been damaging in the initial state of the structure
may not have any significant effect when applied a second time. After many trials, however,
including the need to scale some records, it was possible to develop three separate damage
scenarios, the details ofwhich are summarized in the next section.
80
5.2 Selected Ground Motions
A total of 10 earthquakes were used in the fmal simulations for the three separate damage
scenarios considered in this study. Each of the three sets of displacements were utilized twice:
during the second usage the sequence of the applied displacements were altered so as to force the
system to follow a different load path. Hence, there were truly only three sets of displacement
histories used, and each was repeated a second time but applied in a different sequence. Table
5-1 presents a complete summary ofthe earthquake records that were applied.
The accelerograms and the corresponding spectra used as input motion for simulating the
displacement histories for specimens A7 - A12 are shown in Figures 5-1 through 5-3. Note that
the accelerations shown include all the earthquakes selected for a given damage scenario. The
analysis was not repeated for the next specimen to develop a new time history by rearranging the
input motions, rather the displacements from the first simulation were rearranged to simply alter
displacement paths on the assumption that some random combination of ground motions could
produce such a displacement path. It is important to remember that one of the primary purposes
of the testing is to investigate effects of load paths. Hence it was essential to use the same "total"
displacement history without introducing additional cycles or altering amplitudes.
Analysis of the model column subjected to the earthquakes shown in Figures 5-1 through 5-3
was carried out using IDARC. Model properties were identified from results of Phase I testing
and have been presented in Section 3 of this report. Results of Phase II testing using the
analytically simulated displacements are presented in the next section.
81
TABLE 5-1a Ground Motions Selected for Generating Random Displacement Histories
for Specimens A7 - A9.
Specimen Event Description Purpose Record Scale* PGA,g
A7 1 Damaging First major Lorna Prieta 1989 12.0 1.20earthquake event Presidio
2 Minor Aftershock Imperial Valley 1979 1.8 0.34earthquake Superstition Mt.
3 Minor 2nd San Fernando 1971 1.2 0.10earthquake aftershock 2011 Zonal Ave.
4 Severe Failure of San Fernando 1971 3.6 0.54earthquake bridge 455 S Figueroa St
A8 1 Minor Minor Imperial Valley 1979 1.8 0.34earthquake damage Superstition Mt.
2 Minor Additional San Fernando 1971 1.2 0.10earthquake damage 2011 Zonal Ave.
3 Damaging First major Lorna Prieta 1989 12.0 1.20earthquake event Presidio
4 Severe Failure of San Fernando 1971 3.6 0.54earthquake bridge 455 S Figueroa St
A9 1 Major First major San Fernando 1971 3.25 1.43earthquake event Orion Blvd.
2 Minor Aftershock San Fernando 1971 1.2 0.10earthquake damage 2011 Zonal Ave.
3 Moderate Additional EI Centro 1940 1.0 0.35earthquake damage
4 Minor Aftershock San Fernando 1971 1.0 0.15earthquake 455 S Figueroa St
5 Severe Failure San Fernando 1971 3.25 1.43earthquake of structure Orion Blvd
* Multiplying factor on acceleration amplitude
82
TABLE 5-1b (continued) Ground Motions Selected for Generating Random
Displacement Histories for Specimens AIO - A12
Specimen Event Description Purpose Record Scale* PGA,g
AlO 1 Minor Minor San Fernando 1971 1.2 0.10
earthquake damage 2011 Zonal Ave.
2 Moderate Additional El Centro 1940 1.0 0.35
earthquake damage
3 Minor Aftershock San Fernando 1971 1.0 0.15
earthquake 455 S Figueroa St
4 Major First major San Fernando 1971 3.25 1.43
earthquake event Orion Blvd.
5 Severe Failure San Fernando 1971 3.25 1.43
earthquake of structure Orion Blvd
All 1 Major First damaging Northridge 1994 1.0 0.42
event earthquake VA Hospital
2 Minor Aftershock Northridge 1994 1.0 0.26
earthquake Griffith observatory
3 Minor Additional Taft 1952 1.0 0.36
earthquake damage
4 Severe Failure of Mexico City 1985 1.0 0.17
earthquake column SCT
A12 1 Minor Minor Northridge 1994 1.0 0.26
earthquake damage Griffith observatory
2 Minor Additional Taft 1952 1.0 0.36
earthquake damage
3 Major First damaging Northridge 1994 1.0 0.42
event earthquake VA Hospital
4 Severe Failure of Mexico City 1985 1.0 0.17
earthquake column SCT
* Multiplying factor on acceleration amplitude
83
0.5-C'l'-'"
C0-ro.... 0Q)
Q)00
c::t:
-0.5 ._ ..i.. _ .. ; _ ) __ .1 .. __ . _
-1o
3.5
10 20 30
Time (sec)
40 50 60
-C'l-co~Q)
Q)o~e:!'0Q)0
en
3.0
2.5
2.0
1.5
1.0
0.5
------_ _--: : __ .
..............: : -- -.- ---.- -
. - .. - -- - - - .. - ~ - -. - - - - - - - - .. . - - . - -- -- - - - -. ~ -:- - - .. - . - . -~ -
--_ .. _ -! _ _ , __ .
0.00.0 0.5 1.0 1.5
Period (sec)
2.0 2.5 3.0
FIGURE 5-1 Acceleration History and Corresponding 5% Damped Spectra for InputMotions Used to Generate Displacement History for Specimens A7 and AS
84
1.0
0.5---Cl......c:.2-11l 0.0....a>a>(J(J
«-0.5
-1.0
: :- --, _--- .. - -_ - .
o 20 40 60
Time (sec)
80 100 120
3.0 _.-.-.- : - --.- :.--.-.- ----~.- -.--- ~._-- --- ---
1.0 : ! : : ; .
-..9c:o~Q)
Q3(Jo«~-oQ)Co
C/)
4.0
2.0
.... - . - _.. - - - . - - - -- -:- - - - - ~ - - - - - -; -. -~ . - - - -. -. - - - ..
0.00.0 0.5 1.0 1.5
Period (sec)
2.0 2.5 3.0
FIGURE 5-2 Acceleration History and Corresponding Spectra for Input Motions Used toGenerate Displacement History for Specimens A9 and AIO
85
1.0
0.5
-C>.......c:0-ttl 0.0....CDCD00«
-0.5 . _.. -- _. -~- --- _ - ~ --- - - _. - -~. - - - - ~ - _ - - - - ~ - - - - - - - - - _.. -- --
-1.0o 20 40 60 80 100
Time (sec)
3.02.52.0
~ .. ---. -.. --.. -:- - - - - . - - - --...
1.5
Period (sec)
1.00.5
- - . - -: -. -- - - -- --. - -. ~ . - - - . - - . - ~ - -- . - - . - . _. .. -- --- - .
. - -_. -- . - _ _. _ -~ _. - - - _ -:. _.. _ --. - .:. - - -. - - -. - - - - _. - - - - - - .
3.5
3.0
........C> 2.5-c0
:;::~ 2.0Q)
Q)00« 1.5~-0Q) 1.0c..
CJ)
0.5
0.00.0
FIGURE 5-3 Acceleration History and Corresponding Spectra for Input Motions Used toGenerate Displacement History for Specimens All and A12
86
5.3 Random Loading: Testing and Observations
As indicated previously, the random displacement histories were composed of three independent
sets of time histories generated through analysis of the model specimen using IDARC. Details
of the testing and relevant damage observations are described in subsequent sections.
5.3.1 Specimen A7
Specimen A7 was subjected to random displacement cycles generated from four different
earthquakes. The actual acceleration records and associated PGA's used and the intended
damage scenario were shown in Table 5-1. The first record produced significant displacements
which was considered sufficient to induce moderate damage to the specimen. The next two
earthquakes were meant to represent aftershocks and/or other minor events which do not result in
any further significant damage. The fmal ground motion was so selected to produce severe
damage and probable failure of the system.
First cracking occurred after 22 cycles (or 45 half-cycles) of loading at a lateral drift ofabout 1%.
On the reverse cycle, at a drift exceeding 1.5%, cracking started in the opposite face of the
column accompanied by considerable spalling which extended up to 100 mm from the base of
the pier. At the end of the 26th cycle, spalling of the cover had taken place on both sides of the
column and cracks had propagated even further along the length. Before cycle 32 was
completed, the specimen had undergone one complete cycle at a drift amplitude of approximately
5%. At this point, some buckling of the longitudinal bars was observed on one side of the
specimen. The next forty cycles were uneventful since it was composed of elastic cycles with
drifts under 0.5%. At the half cycle corresponding to #145, which was part of the second
earthquake, the spalling had stabilized and the slightly buckled longitudinal bars were clearly
visible. The loading had progressed into the third minor earthquake and 94 cycles of
displacement had already been applied and no significant damage progression was observed.
The third earthquake did induce up to one and a half cycles of 2.5% drift by the end of the 110 th
87
cycle. Buckling was observed in 4 bars on each side by this point. No further extension of the
plastic hinge length took place, and crack widths were measured between 2.5 - 4 mm. Finally, at
half cycle #269, and a drift of almost 6%, failure of the specimen was recorded following the
rupture of the spiral in the plastic hinge zone. This occurred during the peak displacement
demand of the fourth earthquake. In all, the specimen had undergone about 8 inelastic cycles of
displacement at an average drift of about 3.6%. Table 5-2 provides a detailed summary of the
test observations.
Figures 5-4 and 5-5 present visually observed damage towards the end of testing. The applied
displacement history and the resulting force-deformation hysteresis is shown in Figures 5-6 and
5-7, respectively.
TABLE 5-2 Summary of Observations During Testing of Specimen A7
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading
32.8 MPa
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load: 222 kNYield Load: 60 kNYield Displacement: 16 mmMaximum Lateral Load: 78 kNMaximum Lateral Displacement: 82.5 mmFailure Mode: Spiral Ruptured on the Left Side
DAMAGE OBSERVATIONS:
Half Cycle No.4549-5264220269-270
NotesFirst CrackingSpallingSignificant SpallingVisible buckling of longitudinal barsSpiral Failure
88
FIGURE 5-4 Damage to Specimen A7 at Half Cycle No. 145 During Earthquake #2
FIGURE 5-5 Final Damaged State of Specimen A7
89
E.s-c:Q)
EQ)()ttl0f/)
o~Q)-ttl
...J
"0Q)f/)
o0-
E
80
60
40
20
o
-20
-40
-60
. - -- .. - . - . -. -: - . -. - -. - . - - - ~ - - - - - - - - - - . - - - :- - - -- - - - - - - - - - - ~ - - -. - - - - - - - - -:- .. -
- - - - - - - . - -~ _ -. - --- ~ -. - : -. -.. ~ . -. -- - --- . ~ - -- - - -
6.0
3.0
~OJc:«....-.;:o
-3.0
250100 150 200Half Cycle Number
50
L.-L..-L......-L-'---l.l-L......-L-L.-L..-L.........J........J'---l...---i-...L-..J--l----i-..J........J---'----i-..J........J--'---'-..L-.J--l----' -6.0
300-80
o
FIGURE 5-6 Displacement History Applied to Column A7
7.5
100
3.75
50.00.00
Drift Angle (%)
o-3.75
-50.0
: Nominal Strength
--.. ... __ .~ _ __~j~h_ p'::p.~~~~. _._ _----o._-'L.i~
-7.580
60
40Z~- 20> ~
a>-<;--
V~ 00u. Pull....ttl -20Q).!:en
-40 --60
-80-100
Displacement. Ll (mm)
FIGURE 5-7 Force vs. Displacement Response of Column A7
90
5.3.2 Specimen A8
The displacement history imposed on Specimen A8 was essentially the same as that used in
specimen A7, but the sequence of events were changed (see Table 5-1). The two minor events
were applied first followed by the two major earthquakes. In order to investigate effects of load
path, it was necessary to use the same number of cycles and amplitudes with the exception that
they be applied in a different sequence.
First cracking occurred at half-cycle #33 of earthquake 1 on the left side of the specimen. By the
end of cycle 23 or half-cycle #46 of the earthquake 1, spalling on the same side of the specimen
was noticed. Cracking and spalling continued and became fairly significant around the end of
cycle #57 at which time the specimen experienced one full inelastic cycle at a drift of nearly 3%.
The third earthquake commenced at about cycle #90. Significant spalling on both sides of the
column was observed by the end of half-cycle #209. The spirals and longitudinal rebars were
exposed along the plastic hinge zone. Some buckling of the longitudinal bars was noticed
towards the end of cycle 110 following a few inelastic cycles at drifts exceeding 2.5%. At half
cycle # 267, during the peak displacement demand of earthquake #4, necking of one of the spiral
bands was observed. In the next cycle, at approximately the same cycle at which failure occurred
in specimen A7, rupture of the spiral reinforcement took place.
The specimen continued to be loaded to observe loss of strength capacity. A second spiral, next
to the previously ruptured spiral, failed in the following half cycle. The plastic hinge length at
this stage was about 150 mm. The specimen continued to be loaded until the end of earthquake
#4, but no further rebar or spiral fracture occurred. It must be remembered that the total
displacement history was identical to specimen A7, hence the failure of specimen A8 at about the
same stage of loading indicated that the load path did not influence the cumulative damage of
this specimen. Table 5-3 summarizes all observations during testing of this specimen.
91
Figure 5-8 displays the accumulated damage to the specimen towards the end of the loading
when significant spalling, necking of spiral reinforcement and some visible buckling of the
longitudinal bars had already taken place. Figure 5-9 shows the failure of the two spirals. The
sequence of the imposed displacements is shown in Figure 5-10 while the resulting force
deformation response is shown in Figure 5-11.
TABLE 5-3 Summary of Observations During Testing of Specimen A8
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading
32.8 MPa
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load:Cracking Load:Cracking Displacement:Yield Load:Yield Displacement:Maximum Lateral Load:Maximum Lateral Displacement:Failure Mode:
222kN20kN3mm64kN15.5 mm72kN81.5 mmTwo Spirals Ruptured on the Left Side.
DAMAGE OBSERVATIONS:
Half Cycle No.
3346-47114220267270
Notes
First CrackingSpallingSignificant SpallingBuckling of longitudinal barNecking of spiral reinforcementTwo Spirals Failed on the Left Side
'92
FIGURE 5-8 Specimen A8 at Half-Cycle # 267 During Earthquake 4
FIGURE 5-9 Specimen A8 at Final Damaged State
93
EE........
80 6.0
-c:CD
ECDoCtl
a.(f)
oCtl"-CD-Ctl
....J
"'CCD(f)
oa.E
60
40
20
o
-20
-40
-60
.............. - - -1- _ - .. 1 .
~ - - - - - - - - . - . -:. - - - .. - ..: - - - . - - - . ---. -. -; . -- - - - - - - . - ~ - --. - . -- - - - - - ~ . - .. - - - - - .
3.0
-3.0
250100 150 200
Half Cycle Num ber50
L.J..--'--'-_C._J'---'---'--'-_C._JL.J..--'-~_C._J__'_-'-~J_..l....Lc._'__'_J_..l____'___'__'_J.-.l-6.0
300o-80
FIGURE 5-10 Displacement History Applied to Column A8
7.53.75
Drift: Angle (%)
o-3.75
-Pull
o
20
40
, ?-60 ..-... d-· ; - ; ,-..--- .
-7.580
-40
-20
-60
....roCD
s:::.CJ)
>cDeoLL
-z~-
-80-100 -50.0 0.00 50.0 100
Displacement, d (mm)
FIGURE 5-11 Shear Force vs. Displacement Response of Column A8
94
5.3.3 Specimen A9
Column A9 was tested under simulated random displacements resulting from a series of five
different earthquakes (see Table 5-1). A fifth earthquake was used in this specimen to introduce
additional small amplitude cycles between two large events.
Hair-line cracks were first observed at half-cycle # 22 of earthquake #1 at a lateral displacement
of 8 mm (about 0.5% lateral drift) on the left side of the specimen. The first significant crack
was observed on the right side of the specimen at half cycle # 29 (about 14 full cycles) when the
lateral drift reached 2% in one cycle. First spalling occurred at half-cycle # 49 of the first
earthquake on the left side of the specimen accompanied by major crack propagation. Spalling
took place on the opposite side of the specimen in the very next cycle at a drift exceeding 3%.
After nearly five inelastic cycles at an average drift of 3.0% , the crack widths had reached about
2.0mm.
The next two earthquakes did not produce any significant damage since all of the imposed drifts
remained less than 1.5%. Earthquake #4 was ofmoderate intensity and was composed of about 2
inelastic cycles at a drift of about 2.5%. By the end of this event, at half-cycle #190, minor
buckling was noticed in the longitudinal bars. However, it appeared that the specimen was still
repairable. The buckling of longitudinal bars increased and became more prominent during cycle
#120 (or half-cycle #240) of the fifth and fmal earthquake. At half-cycle #260, at an imposed
drift exceeding 5.5%, failure of one of the spirals occurred on the left side of the specimen.
Figure 5-12 displays the state of damage at the end of cycle # 94, following which the initial
buckling of the longitudinal bars was observed. Figure 5-13 shows the failure of the hoop
reinforcement at the center of the plastic hinge. The plastic hinge length stabilized at
approximately 200 mm towards the end of testing.
95
The entire displacement history generated by IDARC and applied to specimen A9 is displayed in
Figure 5-14. The base shear vs. lateral displacement hysteresis of the bridge column is plotted in
Figure 5-15. A summary ofobservations during testing is reported in Table 5-4.
TABLE 5-4 Summary of Observations During Testing of Specimen A9
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading
32.5 MPa
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load:Cracking Load:Cracking Displacement:Yield Load:Yield Displacement:Maximum Lateral Load:Maximum Lateral Displacement:Failure Mode:
DAMAGE OBSERVATIONS:
222kN20.5 kN5mm65kN16.5 mm75kN91.6mmTwo Spirals Ruptured on the Left Side.
Half-Cycle No.
2249122190260
Notes
First CrackingSpallingSignificant SpallingInitial buckling of longitudinal barSpiral Failed on the Left Side of Column A9
96
FIGURE 5-12 Damage to Specimen A9 at end of Half-Cycle 188
FIGURE 5-13 Final Damaged State of Specimen A9
97
ES
1007.5
-c::Q)
EQ)uroaIII
Cl
~Q)-ro--I
"0Q)IIIoa-§
50
o
-50 . _ --" ~ - - - - - - -) - _. _ - . - - - ;- . -. _ .
3.75
-:=....Cl
-3.75
250100 150 200
Half Cycle Number50
L---<.---,-~"--..l.-,---,--,---,----l.-...l-..J---,---,-..L-.o-----,-----,-.J.......J.-----,---,--,---,--,-~,---,-~- 7.5
300o-100
FIGURE 5-14 Displacement History Applied to Column A9
7.5
100
3.75
50.00.00
: Nominal Strength
____ .~ _.~!~~_P__:P.~!~~ -..
Drift Angle (%)
o
-50.0
-60
-80-100
-7.5 -3.7580
60
- 40Z~
> 20~
cD -e;:--u V.... 00u.....ro -20Q).l:Cf)
-40
Displacement. ~ (mm)
FIGURE 5-15 Base Shear vs. Displacement Response of Column A9
98
5.3.4 Specimen AIO
Specimen AI0 was subjected to essentially the same displacement history as Specimen A9,
however, the sequence of applied displacements was different. The objective of altering only the
sequence of loading was to monitor the effect of load path on the capacity of the specimen. A
similar test conducted on Specimen A8 did not reveal any significant influence of load path,
however, in this test a larger number of low-amplitude cycles were introduced between cycles of
larger amplitudes.
The axial load on this specimen had to be reduced because the concrete strength obtained from
cylinder testing was lower than the previous three specimens which were cast from a different
batch. All tests were conducted at an axial stress of 0.1/:.
The first sign of damage in the form of hair-line cracks was observed at cycle #6 on the right side
of the specimen. Cracking of the left side was noticed in the very next cycle in the reverse
direction of loading. Crack widths at this stage of loading was about 1 mID. and were distributed
from the base up to a distance of 450 mID. At half-cycle #30, some signs of spalling were
observed on the left side. Earthquake #1 did not cause any further damage. The second
earthquake, like the first, induced only one significant cycle of displacement which resulted in a
lateral drift of about 2%. At half-cycle # 121, which was part of the third earthquake, spalling
was observed on the right side of the specimen. This was a moderate earthquake with only a few
cycles beyond 2% drift. At the end of this earthquake, at approximately half-cycle # 194, the
column did not sustain any irreparable damage.
Significant buckling of the central longitudinal bar was recorded at half-cycle # 258. This was
part of the peak displacement amplitude of earthquake #5. Accompanying this was some
necking of the spirals - a normal tendency following the initiation of longitudinal bar buckling.
The very next cycle resulted in failure of one of the spirals. The plastic hinge length was
estimated between 190 - 200 mID.
99
Figure 5-16 displays the state of damage at the end of half-cycle # 122 at which point significant
spalling of the cover concrete in the plastic zone was observed. Figure 5-17 shows the failure of
the hoop reinforcement at the center of the plastic hinge.
The entire displacement history applied to specimen AI0 is displayed in Figure 5-18. The
hysteresis loops showing base shear vs. lateral displacement response of the bridge column is
plotted in Figure 5-19. A summary of test observations and general damage behavior during
testing of specimen AI0 is presented in Table 5-5.
TABLE 5-5 Summary of Observations During Testing of Specimen AIO
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading.
27MPa
LOADING AND DISPLACEMENT VALUES OF INTEREST:
Axial Load:Cracking Load:Cracking Displacement:Yield Load:Yield Displacement:Maximum Lateral Load:Maximum Lateral Displacement:Failure Mode:
200 k:N18 k:N5.5mm58 k:N17mm74k:N91.2mmSpiral Ruptured on the Left Side
DAMAGE OBSERVATIONS:
Half-Cycle No.1230194260
NotesFirst CrackingSpallingSignificant SpallingSpiral Failed on the Left Side of Column
100
FIGURE 5-16 State of Specimen AI0 at Half-Cycle # 121
FIGURE 5-17 Final Damaged State of Specimen AI0
101
.....-E§.
1007.5
-3.75- - - - .. ---.. ., .. - ... - - -- - - - . ~ ..... - . - - - - - .. " .. -. -. - . - .
~
::R0~
..!!10 Cl
c:«--i§
-50
~Q)
iii...J
"CQ)l/loQ.
.E
-c:E 50 . 3.75
Q)omQ.
.~Cl
250100 150 200
Half Cycle Number50
L-J..~-L-l--'----'-L......L~.L...J.---'--'---''--'---'-L......L-L-.L...J.---'--'--l-.L.~-L-l---'--.1- 7.5
300.-100
o
FIGURE 5-18 Displacement History Applied to Column AIO
50.0
Drift Angle (%)
o-7.580
60
.....- 40Z~-> 20cD~ 00u.-.ן
m -20Q).cen
-40
-60
-80-100
-3.75
-50.0 0.00
3.75
___ Nominal Strengthwith p-Delta
7.5
100
Displacement, A (mm)
FIGURE 5-19 Shear vs. Displacement Response of Column AIO
102
5.3.5 Specimen All
A relatively recent set of unscaled earthquakes were used to simulate the displacement history
for specimens All and A12. The only exception to the set was the 1952 Kern County (Taft)
record. Two recorded accelerograms from the 1994 Northridge earthquake and the SCT record
from the 1985 Mexico City earthquake composed the remainder of the input motions. The
combined accelerogram record and the corresponding spectra of the unique multiple motion was
shown previously in Figure 5-3.
First cracking was observed on the right side of the specimen at half-cycle 27 of the first
earthquake. Minor spalling was also observed. First cracking on the opposite side occurred in
the very next half-cycle. The drift at this point was over 2.5%. By half-cycle #38, concrete
spalling had extended to indicate extension of the plastic hinge zone and cracks had propagated
75 - 100 mm above the hinge zone. The maximum crack width was about 2 mm which increased
to almost 4 mm following the 21st complete cycle.
The next two earthquakes which represented potential aftershocks did not cause any further
damage to the column. The final earthquake imposed several large displacement cycles in excess
of 3.5% combined with a single cycle with a maximum drift of almost 7%. Buckling of the
longitudinal bars was observed at half cycle # 252 on both sides of the specimen which forced
spiral to start necking in the center of the plastic hinge zone. Two spirals failed in consecutive
half cycles (#270 and 271).
The plastic hinge length was about 200 mm in length at the instant of failure. The specimen was
further loaded for the remainder of the earthquake induced displacement until fracture of a
longitudinal bar was recorded at half-cycle # 275.
103
Figure 5-20 displays the state of damage at the end of half-cycle # 139 at which point significant
spalling of the concrete cover in the plastic zone had occurred and the spiral reinforcement was
exposed. Figure 5-21 shows the final damaged state of the specimen.
The entire displacement history applied to specimen All is shown in Figure 5-22. The recorded
shear force vs. lateral displacement behavior of the bridge column is plotted in Figure 5-23. A
summary of the observations during testing and general damage of specimen All is presented in
Table 5-6.
TABLE 5-6 Summary of Observations During Testing of Specimen All
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading.
27MPa
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load:Cracking Load:Cracking Displacement:Yield Load:Yield displacement:Maximum Lateral Load:Maximum Lateral Displacement:Failure Mode:
DAMAGE OBSERVATIONS:
200kN18kN6mm65kN18mm69kN103mmSpiral Rupture
Cycle No.
2738252
270-271275
Notes
First CrackingSpallingSignificant Spalling, Some bar buckling,and necking of spiralsTwo Spiral Failed on the Right SideFracture of longitudinal bar
104
FIGURE 5-20 Specimen All at Half-Cycle # 139
FIGURE 5-21 Final Damaged State of Specimen All
105
120 9.0
EE- 80 ---------- -- ------------- --------------.- --- -- -- -- -- - -- -- -- -- -- -- - - -- -- -- -- -- 6.0
o
40.......~~C)c::«~o
-3.0
-6.0
3.0
__ • • _ ••• _ L _ _ _ _ _ _ _ _ _ _ • _ ~ •••• • _ •••• ~ • _ •••••••••••• :_ _ _ _
.. - - ~ .. - .. - ~ - - -; - . - .. - - - - - - .. ~ - - - -. - - - - - - ; - .
cQ)
EQ)om0..(J)
15~Q)-~ -40"0Q)(J)
& -80E
250100 150 200
Half Cycle Number50
'---L-'-L-.L-'--L-.L--'-.L-L-'-.L-L-'-.L-L-'-.L-L-'-.L-L-'-.L-L----!--'---'-~ -9.0
300-120
o
FIGURE 5-22 Displacement History Applied to Column All
120
9.06.0
80.040.00.00
i. _ ...;. Nominal Strength: : : with P-Delta :-....-<;;-------:--------:--------:-----_._;-----_.;------
-40.0
80
60
- 40Z~
> 20 ~
Q) ~:
e :V0 0
LL Pull....m -20Q)
..r::::C/)
-40
-60
-80-80.0
Displacement, A (mm)
FIGURE 5-23 Shear vs. Displacement Response of Column All
106
5.3.6 Specimen Al2
Specimen All failed mid-way through earthquake 4. However, the largest amplitudes were
imposed by earthquake #1. For specimen A12, the displacement cycles corresponding to
earthquake #4 up to failure of the column were first applied, followed by the two minor
earthquakes, followed by the original earthquake #1, and then followed by the remainder of
earthquake #4. Hence the largest amplitudes were reserved for the final cycles. Since all the
previous specimens failed in confinement, it was of interest to see if longitudinal bar fracture
could be induced through an alternate sequence ofcycling.
First crack occurred on the right side of the specimen at half-cycle #72 accompanied by minor
spalling. The specimen had experienced a couple of cycles at 2% lateral drift at this stage.
Cracking on the opposite face of the column did not occur until half-cycle #83 when the drift in
one cycle exceeded 3.5%. By the end of the first minor earthquake, the crack widths were no
larger than 2 mm.
The second earthquake, which did not contain any large amplitude cycles, did no further damage
to the column. At the onset of the large amplitudes due to earthquake 3, corresponding to half
cycles 205 and 206, significant spalling was observed on both sides of the specimen. At this
time, the column had undergone one large inelastic excursion with a lateral drift of almost 6%.
The average crack width was 2-3 mm. Buckling of the longitudinal bars was first noticed at half
cycle # 254 leading to a kink (or necking) in the spirals.
First signs of failure were recorded during the fourth earthquake at half-cycle # 255 when one of
the spirals on the right side ruptured. The maximum lateral drift at this cycle exceeded 7%
lateral drift. It was decided to continue loading column Al2 with the rest of the displacement
history. At half-cycle # 276, one of the longitudinal bars fractured on the east (left) side of the
specimen.
107
Figure 5-24 shows the condition of the specimen at half-cycle # 236, at which point significant
spalling and damage was evident in the column. The final damaged state of the specimen is
shown in Figure 5-25. The displacement history imposed on the specimen is shown in Figure 5
26. The corresponding force vs. lateral displacement response of the column is presented in
Figure 5-27. Table 5-7 summarizes observations during testing.
TABLE 5-7 Summary of Observations During Testing of Specimen A12
LOADING TYPE:
Concrete Strength:
Simulated Seismic (Random) Loading.
27MPa
LOADING AND DISPLACEMENT VALVES OF INTEREST:
Axial Load: 200 kNCracking Load: 18.5 kNCracking Displacement: 6 mmYield Load: 64 kNYield displacement: 13 mmMaximum. Lateral Load: 72 kNMaximum. Lateral Displacement: 103 mmFailure Mode: Spiral Rupture
DAMAGE OBSERVATIONS:
Half-Cycle No.2283205-206
255
NotesFirst CrackingSpallingSignificant Spalling; Buckling of long. Barsand initiation of spiral neckingSpiral Failed on the Right Side ofColurnn
108
FIGURE 5-24 Specimen A12 at Half-Cycle 206
FIGURE 5-25 Final Damaged State of Specimen A12
109
-EE-
120
80 .-- - 6.0-c::Q)
EQ) 40o~a.
.!Qo 0
~Q)-~ -40'0Q)enoCo -80E
3.0.......~Ql
..... 0 ~«~....o
............. : ~ : --: . -3.0: ~: : : :
.......: ~ ~ ; -6.0
250100 150 200
Half Cycle Number
50
L...L-'--'--'--'--L-L-L-'--'--'---'--L-L-l...--'--.L-l.-L.....L-l--'--'--L-l...-'--'--'---L-J - 9.0
300-120
o
FIGURE 5-26 Displacement History Applied to Column Al2
Drift Angle (%)
0 3.0 6.0 9.080
:
60 .. -*. ~" ........:... " ---:....... .?~.
- 40Z~-> 20 ~
a> ~-,-:
V~ 00u. Pull....eu -20Q).c:(f)
-40
-60
-80-80.0 -40.0 0.00 40.0 80.0 120
Displacement, !!:. (mm)
FIGURE 5-27 Base Shear vs. Lateral Displacement Response of Column Al2
110
SECTION 6
CUMULATIVE DAMAGE MODELING:
EVALUATION OF EXPERIMENTAL RESULTS
The bridge column specimens tested in the experimental program, and presented in Sections 4
and 5 of this report, will be examined in this section from the perspective of damage modeling.
Since a number of damage models have been proposed by other researchers in the past, it was
considered beneficial to compare the relative performance of selected models by applying them
to the observed response and damage of specimens tested in this research.
The next sub-section will provide a brief overview of typical fatigue-based damage models
proposed for use in seismic structural analysis. The models selected for systematic evaluation
will then be discussed. Finally, the performance of each of the selected models against data
generated from the present experimental testing will be presented.
6.1 Fatigue-Based Damage Models
A review of the literature reveals that there are essentially five approaches to damage modeling:
estimates based on measures of deformation and/or ductility; models based on the degradation of
a selected structural parameter (typically stiffness); models developed from considerations of
energy-dissipation demand and capacity; hybrid formulations combining some aspects of the
aforementioned parameters; and more complex theories based on concepts derived from fatigue
models. Comprehensive reviews of damage modeling techniques can be found in Powell and
Allahabadi (1988) and Williams and Sexsmith (1994).
Since seismic loads induce several inelastic cycles at relatively large ductilities, the concept of
using low-cycle fatigue theories to model damage is logical. Though high-cycle fatigue of
metals and concrete have been evaluated in the past, few have attempted to extend these concepts
to evaluating seismically induced fatigue damage. The formulation of Chung et al. (1987)
combines Miner's rule (Miner, 1945) with a failure criteria:
111
[
+ - ]n. n·D= "" w: _'_+ W :- _,_L.. I + I-
i nj,i nj,i
(6-1)
In the above expression, where both positive and negative cycles are treated separately, Wi is a
weighting factor, ni is the number of cycles at a given amplitude, and nj,i is the number of
cycles to failure at the same amplitude. The similarity of this approach to the well-known
Miner's hypothesis is evident.
Jeong and Iwan (1988) use a more straight-forward extension of Miner's rule by combining it
with another well-known law postulated by Coffin-Manson:
D =L nif.lii C
(6-2)
where c = nj f.l and nj is the number of cycles to failure at a specified ductility f.l.
Other approaches to modeling fatigue failure have also been developed. The most practical of
these is a mechanics-based derivation by Mander and Cheng (1995). They express local section
curvature at the plastic hinge region directly in terms of strain in the rebar:
~ D = 0.113 N-O.5
p 1-2d/D j(6-3)
The above expression is derived from the plastic strain vs. fatigue life relationship obtained from
actual testing of steel reinforcing bars (Mander et al., 1994) and the relationship between
curvature and strain in a reinforced concrete circular cross-section assuming a linear strain
profile. In Equation (6-3), ~ p is the plastic curvature, D is the overall column diameter, dis
the depth from the outermost concrete fiber to the center of reinforcement, and Nf is the number
112
ofcycles to the appearance of the first fatigue crack in steel. A variation of this representation is
utilized in this study.
It must be remembered though that using fatigue theories presupposes a flexural fatigue failure
mode. Other potential failure modes resulting from the combined effects of axial force, shear
and confinement are not incorporated in these models.
6.2 Damage vs. Performance
The ability to predict damage in a structural member does not necessarily reflect the success of a
damage model. It is the ability to calibrate a model such that it can be used by a practicing
engineer to assess structural integrity following a seismic event that ultimately determines the
effectiveness ofdamage modeling.
Structural engineers in zones of high seismic risk have been faced with the constant challenge of
having to associate serviceability limit states with observed visual damage to structures
following an earthquake. The Applied Technology Council (ATC) report (ATC, 1985) on
Earthquake Damage Evaluation provided engineers with damage categories for estimating loss
assessment. A more recent ATC effort following the Northridge earthquake introduces the
notion of damage states that engineers can use more readily in assessing structural damage from
essentially visual observations. The proposed classification is shown in Table 6-1. This
classification provides an important guideline that can be used in damage calibration studies.
The present study will attempt to correlate observed damage during testing to computed damage
values using different models using the above guidelines.
6.3 Models Evaluated in this Study
Four independent models characterizing different damage measures were selected for detailed
evaluation in this study. The purpose of this evaluation is to identify the merits and drawbacks of
different models so that future work on damage model development may utilize these fmdings.
113
TABLE 6-1 Damage Categories Proposed in ATC-38
Damage State
None
Insignificant
Moderate
Heavy
Descriptor
N
I
M
H
Description
No visible damage, either cosmetic or structural.
Damage requires no more than cosmetic repair.
No structural repairs necessary.
Repairable structural damage has occurred. The
existing elements can be repaired essentially in
place, without substantial demolition or
replacement of elements.
Damage is so extensive that repair of elements is
either not feasible or requires major demolition or
replacement.
The first model selected for evaluation is a modified form of the system softening index. The
change in structural stiffuess is associated with system degradation which translates into a
lengthening of the fundamental period. An additional advantage of this model is the fact that it
can be monitored in actual structures without much difficulty. In the present study, the following
normalized expression is used to quantify damage:
(6-4)
With reference to Figure 6-1, km is the stiffuess of the structure at the maximum induced
displacement, kf is the pre-established stiffuess at failure of the system (typically under
monotonic loads), and ko is the initial stiffuess prior to loading.
114
Force •/
/~km/
/, --/ / /' /'-f:Y M.onotonic
/'~ kf fail~re/' point
Deformation
FIGURE 6-1 Parameters Used in Softening Index
The second model investigated is the Kratzig model (Kratzig and Meskouris, 1987), since it
incorporates only energy terms in its formulation. The terminology used to define this model is
illustrated in Figure 6-2. A primary half cycle (PRC) is the energy contained in the half cycle at
the maximum deformation point. Additional cycles with displacement amplitudes less than the
peak deformation are accumulated as follower half cycles (PRC). Positive and negative
deformations are treated separately. Accumulated dro,nage for the positive portions of the
response is defmed as:
(6-5)
where Epi is the energy in a PRC, Ei is the energy in an FRC and E1 is the energy absorbed in a
monotonic test to failure (area enclosed by OABCF in Figure 6-2). A similar expression is
computed for negative deformations, and the two quantities are normalized as follows:
(6-6)
115
The inclusion of the follower cycles in the numerator and denominator suggest that their
contribution to damage is small, or less significant than deformations that extend the response
envelope.
Force
FHC
PHC~/_--~
F- C> Monotonic
I failureI pointI
II
I
I
Deformation
FIGURE 6-2 Parameters Used in Kratzig Damage Model
The next model considered in this study is the Park-Ang model (park and Ang, 1985). This
model represents a hybrid model, and was included in the evaluation partly because of its ease in
implementation and partly because it is one of the most widely used damage models today. The
model is used in its original form as follows:
(6-7)
The constant 13 was identified directly from the standard cyclic test conducted on Specimen A-2.
The fourth and fmal model considered for evaluation was derived from principles of low-cycle
fatigue. As pointed out earlier, the identification of the failure mode is critical prior to using a
116
fatigue model. Since the bridge columns tested in this study were essentially flexural columns
with well detailed plastic hinge zones, only two important failure modes had to be considered:
confinement failure or longitudinal rebar fracture from low-cycle fatigue. Modeling confinement
failure is somewhat more complex. Hence only the fatigue behavior of the longitudinal steel was
monitored, as described below.
The derivation shown below is a variation of the procedure developed by Mander and Cheng
(1995). The fatigue behavior of the longitudinal steel under reversed cyclic loading is
formulated in terms of the Coffin (1954) - Manson (1953) equation:
(6-8)
where: EP = plastic strain amplitude
E; = a material constant to be determined from fatigue testing
2 Nf = Number of complete cycles to failure
An experimental fit to this expression was obtained by Mander et al. (1994):
Ep
=0.08 (2Nf
)-0.5
A similar expression using total strain instead ofplastic strain was also developed:
(6-9)
(6-10)
A relationship between strain and curvature is possible, assuming the plane-section theory, as
displayed in Figure 6-3.
(6-11)
117
0 -1---
I0 0 I
I
- I
0 0 d d I ¢ =¢l ¢P
II
0 0 I
0 --l-
I I&p &y
FIGURE 6-3 Curvature-Strain Relationship for Plane Sections
If the plastic hinge length is defined as Ip, an expression for the plastic strain in terms of plastic
curvature (or rotation) can be established (priestley and Paulay, 1992) assuming that the plastic
rotation takes place about the center of the plastic hinge:
(6-12)
which upon substitution into Equation (6-11) can be used directly in Equation (6-9) to define the
number of cycles to failure for a given plastic strain or a given plastic deformation. Cumulative
damage is then defined as:
(6-13)
The following additional notations were used in the above expressions:
Ip = plastic hinge length
d = distance between centers of longitudinal bars
118
ep = plastic rotation
<I> p =plastic curvature (difference between total and yield curvature)
L = specimen (member) length
In the present study, the fatigue-based damage index was derived in terms of plastic strain. Since
random displacement cycles were used in the second phase of testing, the model was re-written
in terms of half cycles since the positive and negative peaks in a given cycle were not of the
same amplitude.
6.4 Damage Analysis of Tested Specimens
The control parameters required in the application of the different damage models selected for
evaluation were initially identified from the monotonic test specimen and then adjusted to match
the average response of specimens A2 through A6. The variation from the mean values for any
of the specimens did not exceed 10%.
The following fixed parameters were used throughout the evaluation:
Yield force:Yield displacement:Ultimate displacement:Initial Stiffuess of column:
65kN18mm155mm10.5 kN/mm
The computed damage to specimen A2 using the different models described in Section 6.2 is
shown in Figure 6-4. Of all the models, the Softening Index and the Kratzig model show severe
damage fairly early in the response. The fatigue model shows little or no damage through the
first ten cycles where displacement ductilities are below two. The Park-Ang model shows a
gradual progression of damage throughout the load history with increasing accumulation of
damage at each increase in displacement level. The fatigue model suggests rapid deterioration of
the specimen towards the end of the loading while the damage appears to be in the repairable
range after 24 cycles. The actual observed damage state was probably between the predictions of
the fatigue model and the Park-Ang model. In summary, for this specimen, the Park-Ang model
provided a very good measure ofdamage at different limit states.
119
32282412 16 20
Cycle Number
84
--e-- Softening Index--....- Park-Ang Model
...., - Kratzig Model- - x - . Fatigue Model
: I
........~.. , : ; , ............•............." : ·.. ·.. ··x·:·/-··········
,, I " '.................·-;-J,I·······································:········.....•... ;,' : .
: ,/ :,
/ - ~
: / ,........... j , - ..-.: : ~ , : .
o
1.0
0.8
0.0
x 0.6Q)"0c:Q)C>enE 0.4en0
0.2
FIGURE 6-4 Comparative Evaluation of Progressive Damage for Specimen A2
Specimen A3 was subjected to 150 cycles at a lateral drift of about 2%. As described earlier in
Section 4, these 150 cycles produced only reparable damage to the column. The application of
the damage models to this specimen is displayed in Figure 6-5. All non-fatigue based models,
including the Park-Ang model fail to predict accurately the damaged state of the component at
the end of the testing. The Kratzig model and the Softening index, as before, show significant
damage accumulations early in the response which is inconsistent with observed behavior. The
fatigue model performed the best with predicted damage states correlating to observed damage.
The next specimen, A4, was subjected to a much larger drift amplitude. Failure of the specimen
was recorded in less than 30 cycles. The Park-Ang model seems to perform better when the
displacement amplitudes are significantly larger than the yield displacement. The Kratzig model
and the damage represented by the Softening Index do not span a reasonable range of limit states
due to the fact that severe damage is predicted very early in the response.
120
. ....... ~ .. -- ;. --. -- -- -- , -.:' ~~.~ .~ .
. x-··
r - I _ J -7('" -
- Softening Index--Park-Ang Model
-oJ - Kratzig Model- - x - . Fatigue Model
;.--,jiI_.I~--01 .
"I"
~
.!. .-- -- .. ' .--.-- -- .... -- -- -- ....... -- ... -- .--I
II
.1. . __ .,,,
0.8
1.0
0.2
x~ 0.6£:Q)0>IIIE 0.4IIICl
0.0o 30 60 90
Cycle Number
120 150
FIGURE 6-5 Comparative Evaluation of Progressive Damage for Specimen A3
- Softening Index--Park-Ang Model-- - Kratzig Model
- - x - . Fatigue Model
~---
/ :
---
-_ :-._-. __ _----- ..: __ _--_ : -- _--- ."
__ • - - - _~ ••••• ;/" :._. __ .:_. o. __ ." A .~~ :__ ._. ••• '0_' __ .~ ••• __ ."._. _
--:-.--:
/
X
"X: /
/ : : :. - .. - - - -.... :;..: - -.- - - . - ... _.. - - - - - - ~ -... - - - -- -... - - - --, ... -.. - -. -
0/... .l ... __ .__ .;..... __ .__ .. __ ... ;.. __ ... .__ .,.....
I .,,.1... ..,,,
0.2
0.8
1.0
x~ 0.6£:Q)0>III
E 0.4IIICl
0.0o 4 8 12
Cycle Number
16 20 24
FIGURE 6-6 Comparative Evaluation ofProgressive Damage for Specimen A4
121
The fatigue model over predicts damage with failure reported at the end of the 17th cycle. Figure
6-6 displays the computed damage history for each model.
Figure 6-7 presents the cumulative damage for specimen A-5. The Park-Ang damage model
reaches an index of 0.5 with the fIrst cycle representing primarily the deformation damage at a
drift of 5.5%. Since the fatigue model is based on cycles to failure using Miner's rule, and is
evaluated at the end of each cycle, the damage progression is essentially linear.
The last specimen subjected to constant amplitude loading failed at the end of the 4th cycle. The
imposed drift was slightly larger than 7.0%. The severe damage predicted by the non-fatigue
models in the very fIrst cycle indicate their inability to deal with low-cycle fatigue damage. The
fatigue model, on the other hand, has been fairly consistent in their prediction levels. Failure in
this specimen was indeed by longitudinal bar fracture. Results of the evaluation are shown in
Figure 6-8.
1.0 -/
. /
0.8
~ 0.6"0.£Q)0>ctl
E 0.4ctlCl
0.2
" / :...•...•~.............•....•. : .•..................•........< : ., /,
I....., .
I
: /
X/ . .
•••••• 0. 'w'" --- _ --- _.- ""r0' .:. • __ •• ••••••••••••••• -- -_: • ._ •••••••••••••••• ----
/ :
X/ - Softening Index
............ ~.: - Park-Ang Model- - Kratzig Model
- - x - - Fatigue ModelX
/
0.0
o 3
Cycle Number
6 9
FIGURE 6-7 Comparative Evaluation of Progressive Damage for Specimen AS
122
- '.. -- _-- - -- _~--- .. _--- ,. --_ .. _-_ ~:, .
- -- -: -- - ---- - -- - --- -- - --- --- ;. -~~ - - - -- - -- -- - - - - -- -- - -- -- ----- - -- - -- - - -- -- --
1.0
0.8
~ 0.6"U.EQ)0)C'llE 0.4C'llo
0.2______________________x~ _
, .
--- -----
~ Softening Index--+- Park-Ang MJdel
.-l - Kratzig MJcIel- - x - -Fatigue MJcIel
0.0
o 1 2
Cycle Number
3 4
FIGURE 6-8 Comparative Evaluation ofProgressive Damage for Specimen A6
Specimens A7 through Al2 were subjected to random cyclic reversals. Figure 6-9 shows the
progression of damage for Specimen A-7 which was subjected to a major earthquake followed
by two smaller events (aftershocks or minor tremors) and finally another severe event which
resulted in failure by rupture of the confining spirals. All of the damage models show a
significant increase in damage at each of the imposed large amplitude reversals. The Softening
Index, the energy-based Kratzig model and the Park model indicate severe damage following the
single peak cycle at 6% drift during the 1st earthquake. The fatigue model shows little evidence
of such damage. While it may be stated that visual observations support the non-fatigue models,
only the Park model picks up additional damage in the fourth and [mal earthquake.
Specimen A-8 was subjected to essentially the same total history but the sequence of events was
changed. Here two severe events followed two minor ones. The results of the damage model
application to the recorded response is presented in Figure 6-10. Interestingly, this specimen
failed at approximately the same cycle of displacement indicating no effect ofload path.
123
! ~ ..i. ... ~ -.",.~---
I
r---::=-==-==-=:-=-=-"':lP"'l~-_"""=:.-=!~";;;;;;''';';;;''';;;;'';;;;;'''''---l:,.
1.0
. :.••... ;>( --.-
~ Softening Index--Park-Ang Model
- - Kratzig Model- - x - . Fatigue Model
...............•....................................•.....................~:1 ..r-jv
. ' -- --.: ~ -- ;:.::c:
0.8
~ 0.6 f-------.-- ... -- ."'C..=Q)C)
roE 0.4 '---.-- ~ -- --.-------- .~ f
-------.-,0.2 -- .... ··--··--1:· .,__. ~_i_ - __.-*-- .__ o.;.ox ------ ... --.;-- .. ---- ..... --.-
,.~
:'".,.- i i i0.0
a 50 100 150 200 250 300
Cycle Number
FIGURE 6-9 Comparative Evaluation of Progressive Damage for Specimen A7
_ l- ".or - -:~
- Softening Index-- Park-Ang Model-- - Kratzig Model
,-'_-x_-_'F_a_ti_gu_e_M_o_d_e_I_.. · __..__.,,,,,~.-,~ ..~.~,~,,., ~
". ,
0.8
1.0
x~ 0.6E
1- : __ --. -- -- __ .:__ ., ~ __ :__ . --~ --. -- ".-. c..-":;;
':. "....Q) rC) f ' >!.co :.. : : : : I
~ 0.4 f- :.~.,,~ : -- :---- ~ : ,: -
Cl ...r:0.2 +-~--.!'"',J...................................•....................;'::-::- .
Jr , r _ , , ~ ~ r
0.0 r,. .. - -'" -:- -' i
o 50 100 150 200
Cycle Number
250 300
FIGURE 6-10 Comparative Evaluation of Progressive Damage for Specimen A8
124
All the damage models, which do not take into account the effect of load path, show the same
final damage state, as expected. But an interesting observation must be noted: the degree of
damage from the minor earthquakes is fairly significant for the non-fatigue models which is
inconsistent with observed behavior. There seems to be a tendency for such models to
accumulate damage at unreasonable rates during low amplitude cycling - this was also observed
in the constant amplitude tests where all of the non-fatigue models predicted failure after 150
cycles at 2 % drift.
Specimens A9 and AI0 were subjected to a different set of load reversals resulting from a
different sequence of events. A9 experienced strong ground shaking representing a severe event
followed by two minor earthquakes, a moderate earthquake, and another major event. In the case
of Specimen AlO, the final event was retained as before but the first four earthquakes were
interchanged to produce an entirely different path leading up to the fmal earthquake. The
predicted damage using the different damage models are shown in Figures 6-11 and 6-12.
~: ~~-~--~~-~--~:- -~ ~ - - . : : : :
I
: I
. '. ,
- - - - ~ .. - ..... - - - ~ .... ! .. - -. "
: :'-_ ••••• _---:.--_ ••••••• -:- •••1••••••
--eo- Softening Index~ Park-Ang M::>del
...., - Kratzig M::>del- - x - . Fatigue M::>del
:xt:"" ).0.0 .o-Xo >.-..-. ~..-.~..-. ~.~-..-..-;~..-..-~.~..<:<~. ~.~- ~:. ~.~ ~./.~ i.. ..
, ":
..........: -J--.~ : - ~ ; .,I
. I.. '..---- ·· ·r ·:-- .. -- ·.. ·--·--····: -- ..II
0.2
0.8
1.0
~ 0.6"0.£(J)C>roE 0.4roC
0.0o 60 120 180
Cycle Number
240
FIGURE 6-11 Comparative Evaluation of Progressive Damage for Specimen A9
125
, J - - ,- - - - J
; - _. ~ . -_. ------ . ~. -- - - - -' - - - ~ - - - - . - - - - - - ~. - - - - - . _ .. - ~ .. _.. -~ . - - . ~ .. - - - - - - - - - ~ - - -- - - - - _.
I
II,
:x
240
................... "tJ
120 180
Cycle Number
60
-~~--_. _. "I__~_. -- - __ -- ~_. - __ .. _._ - _: .... .. _:_. -_..... _. _:- ..... _....~.. _... _.. - - _:_ -- - II. •
~ Softening I'vbdel~ Park-Ang I'vbdel~ - Kratzig I'vbdel
- - x - - Fatigue I'vbdel: : oJ:~ ~~__~~ r :
----- --- -f---· -- .---- .:.. --- -- --- -.:- -. -.. ---·f- ----- --- --~-- --- ----- -~- -- .. _.,--_--r.-.: r: J
o
1.0
0.2
0.0
0.8
~ 0.6"0.E(J)C>coE 0.4coo
FIGURE 6-12 Comparative Evaluation of Progressive Damage for Specimen AI0
As in the case of the previous two specimens, the damage models respond primarily to large
displacements. And, as was the case with the constant amplitude cycles, the Kratzig model and
the Softening Index predict significant damage very early in the response. Since both specimens
failed in confmement, the present fatigue damage model, which essentially monitors fatigue in
the longitudinal rebars, did not predict failure.
The final two specimens were subjected to four earthquakes. Two minor events were placed
between two significant events. The objective in this series of testing was to induce fatigue
failure of the longitudinal bars, hence the events were so selected to produce significantly larger
displacement amplitudes. The predicted accumulation of damage is presented in Figures 6-13
and 6-14 for specimens A-II and A-12, respectively. Failure in the two specimens did not take
place at exactly the same cycle, instead the second specimen which sustained relatively smaller
amplitudes early in the history survived a few additional inelastic cycles before failure.
126
,--- _-_ ,-- -- .,
I -
,I
_.... ..,.r--~---~, ,
: :, ,
: :- - - - - - . . .. - - - ~ - - .. - - - -~ - - - -, .. - - '. - - - ~ -: ,,,
I... J : ; ' .
I.I :
r : ,....... f: T~·~:~··_·:.:·.:~·~~··_··.:~·~·~·:.:·_·:.:--J·~-: -:.-,.-. - -.-: - .-..-..~.-: -:.-:.-.' .-:.-. -::-..-.7<: ......
0.8
1.0
~ 0.6"0.E<llClcoE 0.4
~
O2 l; .........'....... .. .
,:, :
-e- Softening M:>del~ Park-Ang M:>del~ - Kratzig M:>del
- - x - . Fatigue M:>del
0.0
o 40 80 120 160
Cycle Number
200 240 280
FIGURE 6-13 Comparative Evaluation of Progressive Damage for Specimen All
1.0 I ! ! ~---_ ....
,¥
i
rJ,~~f~~"~~~~~jL
r :- •• , - -. _. L •• •• - - - - •• -··i· --- ---~ --_ - --:- -. -_. -'" --. -. ~ _. ---.. ,------j_ "J/ ~- ~ ••• --,
I,"-',---'" --_.--- .... --
I, - Softening Index
• I ~ Park-Ang M::ldel _' I
)~>JJn _~_x_:-_._~_~_:u_i~_~_d:_II_.. ~·:.. ;· .
.~ ',', :', iX- - - - - - "I - - -x - - - ~ - - - - - -x:'
0.0
0.8
0.2
~ 0.6"t:l.5Q)0)1'OE 0.41'Oo
o 40 80 120 160
Cycle Number
200 240 280
FIGURE 6-14 Comparative Evaluation of Progressive Damage for Specimen A12
127
6.5 Proposed Fatigue-Based Cumulative Damage Model
In general, it was observed that the fatigue-based damage model under-predicted the final
damage state of all column specimens. Since the model used in the study is capable of
evaluating damage due to low-cycle fatigue of the main longitudinal reinforcing bars only, and
all tested specimens experienced confmement failure prior to low-cycle fatigue failure, this
observation is not unexpected.
A modified cumulative fatigue model is now proposed based on experimental fitting of the
Coffin-Manson fatigue expression using results from the constant-amplitude testing of columns
A3, A4, A5 and A6.· The plastic and total strains in the longitudinal rebars were calculated
from expressions previously listed in Equations (6-11 and 6-12). Results of the curve-fitting
exercise are shown in Figures 6-15 and 6-16. On evaluating the model coefficients of both
plastic and total strains vs. the number of cycles to failure, the following expressions are
obtained:
0.1 I
-ן
m..0(\)
c::cc.~....(J)
o:;:;lJ)
~a..
0 ... .. .. ... ~..... ... .. ... .."... ...... .....0.01 - --- -- --- -- ------ -- ---- -- -- .. --- -- --- -- -- ------ ---~-..-..-~-- -- -- -- -- -- -- -- -- ----- -----
.. ...... ..... ...~
.?TExtrapolated Point
0.0011.00
i
10.00 100.00
Number of Cycles to Failure
1000.00
FIGURE 6-15 Coffin-Manson Fatigue Model for Plastic Strain
128
-0.360&t = 0.060 (~2f)
0.1
...ro.0Q)
0:::c:c: 0.01'(ij...-C/)
ro-0f-
0....... :...~ .... .. ....
"00>..
...................
_ : ~.": ;,;:.:: -..... .... .... ~: .------y
Extrapolat~d Point
0.0011.00
i
10.00
i
100.00 1000.00
Number of Cycles to Failure
FIGURE 6-16 Coffin-Manson Fatigue Model for Total Strain
f: p = 0.065(N2f
r°.436 (6-14)
(6-15)
Note that the number of cycles to failure for specimen A3 was not based on experimental
observation since the specimen did not fail after 150 cycles and was eventually subjected to a
monotonic load to induce failure. This point on the graph corresponding to this specimen was
computed analytically from the above equations. The difference in the constants of the above
equations to those obtained by Mander et al. (1994) is the fact that these expressions were
derived for the concrete column as a composite section and indirectly accounts for the
accumulated damage due to shear, axial stress and loss of confinement.
129
Equations (6-14) and (6-15) can be considered as fatigue life expressions for seismically detailed
AASHTO (or CALTRANS) flexural columns and may be used to predict damage and reserve
capacity. Similar expressions can be derived using lateral drift as a variable. To convert the
above equations to a relationship involving lateral drift, Equations (6-11) and (6-12) are used.
Values of the plastic hinge length and yield deformation were taken directly from experimental
records or observations. The resulting expression for fatigue life of flexural columns as a
function oftotal lateral drift is:
Drift (%) = 10. 6 ( N2f) -0.285 (6-16)
The curve-fit for Equation (6-16) is shown in Figure 6-17. A simple procedure to estimate
earthquake damage for a known ground motion is summarized in Section 7.
-tfl.-¢::0;::
oco...2co
....J
o ... ... ... ...-0.285
Drift =10.60 (~2f)
... ... ... ......~ ...
... ... ... ... ... ... ............ ... ... ... ... ... ... ... ...~
~Extrapolated Point
11.00 10.00 100.00
Nurn ber of Cycles to Failure
1000.00
FIGURE 6-17 Fatigue Life Model for Total Lateral Drift of
Well-Detailed Flexural Columns
130
Finally, Equations (6-14) and (6-15) were used to estimate damage to Specimens A-7 through A
12. Essentially, the damage model formulation is identical to the derivation presented in
Equations (6-9) through (6-13) with the fatigue life equations of Equations (6-9) and (6-10)
replaced by Equations (6-14) and (6-15). The results of the evaluation are presented in Figures
6-18 and 6-19. A significant improvement in damage prediction is evident. Final damage
estimates have increased and appear much closer to observed performance. However, only
specimens All and A12 reach a final index of 1.0. The other four specimens show a damage
index ofapproximately 0.8, which is typically representative of irreparable damage.
30025020015010050
..-I;
- Specimen A7 ~
- Specimen A8 ~- - Specimen A9 --_: --------------; ------_. ------~ ---... -_. ----
--x-·SpecimenA10 :~-,
- -~-.SpecimenA11: : :1: ..- - - Specimen A12: : :r";--- -------- --:- _.....----.. _-:.. _- ---.- .'_.. _~- ----_.- _. -_. -;-_ ..-----.- ---1-;--
, ' : . ,.:, ~ ~ ~ I:: : ·... ·;······-+-······r.... ..........: :
---- -- ----:- -~ -_.. -----_.- --: --- --_. ------; ---.-- -- ------~ -_. --_._ ... -j---
"""""- - ....•.. .',.
" :" ."": i
oo
0.8
0.2
0.4
0.6
xwozwC>«::2:«o
Half Cycle Number
FIGURE 6-18 Performance of Proposed Plastic Strain Fatigue Damage ModelApplied to Specimens A7-A12
131
30025020015010050
'.I.~ Specimen A7 i:~ Specimen A8 : "-r~
... - Specimen A9 , ' , ~r. .- -x _. Specimen A10 :J ••··~··SpecimenA11, ~::..... - Specimen A 12 : : ,::
,. , : : ~ •. ~..'; ''; ··"·';40· .~"., •. " ~ ~:' ..~....•.. ~..... I
:-: r••.................... ---•••••· -•. _... - ...•.. -: - - - - -- - - _. - - -,-'.-· :· :· :••·, .-.~.
1
oo
0.2
0.4
0.8
0.6
xwClZ
WC)«:2«Cl
Half Cycle Number
FIGURE 6-19 Performance ofProposed Total Strain Fatigue Damage ModelApplied to Specimens A7-A12
132
SECTION 7
RESEARCH FINDINGS AND CONCLUSIONS
This study was directed primarily towards the experimental and analytical investigation of
cumulative damage. A major departure from past practice of laboratory testing that was pursued
in this research effort was the development and use of random displacement histories rather than
"standard" displacement cycles with increasing amplitudes. Related topics such as the effects of
load path on damage and energy dissipation capacity, low-cycle fatigue failure of longitudinal
reinforcing bars, and the influence of random cyclic loading on failure modes, were also studied.
Given the complexity of the cumulative damage process and the innumerable parameters
affecting the response, every effort was made to keep system variables to a minimum.
Consequently, the imposed displacement history was the only variable introduced in the
experimental testing.
This research investigation was limited to the study of circular columns with a predominantly
flexural response. Circular sections have the advantage of possessing fairly uniform properties
in any direction and are commonly used in bridge construction, particularly in seismic zones.
The observations. findings and conclusions. therefore. are limited to seismically detailed flexural
circular columns only. Additionally, the influence of soil-structure interaction and foundation
flexibility were not considered. Failure, as defined in this study, is restricted to damage to the
bridge pier only. Other potential damage sources such as foundation failure and deck-abutment
connection failures are beyond the scope of this investigation.
7.1 Research Findings
Essential fmdings of this research study, given the limitations set forth in the previous paragraph,
are summarized in this section. The inferences are subdivided into different categories, based on
the nature of the finding. Most of the primary findings are damage related. Findings that shed
further light on the concept of energy dissipation capacity are discussed separately. Likewise,
contributions to inelastic modeling are summarized as a separate category.
133
7.1.1 Findings Related to Cumulative Damage
1. There exists a "threshold" ductility level for well-confined flexural circular columns
designed by current CALTRANS (or AASHTO) specifications beyond which severe
degradation of stiffness and strength takes place. For the bridge columns tested in this
study, this threshold ductility level occurs between 3~y and 4~y, which corresponds to a
lateral drift between 4% and 5%. Specimen A3 which was cycled 150 times at a ductility
of about 2% drift showed no significant signs of damage or deterioration. Specimen A5
which was cycled at a lateral drift of 5.5% failed in less than 10 cycles. It may, therefore,
be stated that earthquakes which impose ductility demands less than 2.0 can survive a
series of similar events without undergoing any significant structural damage. When the
ductility demand approaches 4.0, the likelihood of moderate to severe damage is high and
depends on the number of such inelastic cycles experienced by the structure.
2. Damage models evaluated in this study indicate that most non-fatigue based theories are
incapable of consistently reproducing observed damage. Models based on the degradation
of a single structural parameter, such as the softening index evaluated in this study, are
sensitive in the early stage of damage progression and show little variation beyond this
point to failure, making them difficult to calibrate. Energy-based models, such as the
Kratzig model, which do not account for the level of ductility at which energy is dissipated,
consistently over-predict damage. The Park-Ang model is essentially a ductility-based
model since the energy term is not adequately represented: energy damage is sometimes
overestimated at small inelastic amplitudes and underestimated at large inelastic cycles.
The Park-Ang model predicted failure of specimen A3 after 150 cycles which was contrary
to observation. On the other hand, damage models based on fatigue-life expressions, using
a Coffin-Manson rule in combination with Miner's hypothesis, account only for low-cycle
fatigue of steel. It appears that a model which combines low-cycle fatigue failure in
combination with confinement deterioration will yield excellent results. A simple fatigue
life relationship was proposed, derived from the original work of Mander and Cheng
(1995), based on the experimental data generated from constant-amplitude testing of
specimens A3-A6, and was shown to produce improved damage prediction characteristics.
134
3. Under a sequence of predominantly low amplitude cycles, it is more probable that the
confining spiral will fail prior to low-cycle fatigue failure of the longitudinal reinforcing
bars. Conversely, if the bridge column is subjected to predominantly high amplitude
inelastic cycles, it is more likely that the longitudinal bars will rupture before confinement
failure occurs. In the present study of flexural columns, it was found that the threshold
"low-amplitude" cycle is approximately 2% - 4% drift, while high-amplitude cycles are
those in excess of4% drift.
4. The use of random cycles provides a better means of understanding the phenomenon of
cumulative damage. It is also a more reliable way of testing performance of structures
subjected to low-cycle fatigue damage. Typical earthquakes impose few inelastic cycles
and the energy demand is significantly different from the demand imposed by standard
cyclic testing.
5. A large database of displacement histories were produced for the bridge column specimen
using dozens of recorded ground motions at different soil profiles. A significant finding of
this research study, based on these numerous analytical simulations, is the fact that typical
earthquakes produce few large amplitude cycles, hence failure is generally governed by
confinement rather than low-cycle fatigue of the longitudinal bars. However, damage from
low-cycle fatigue of the longitudinal bars does contribute to overall damage though
estimates of failure must include other failure modes. Damage models that attempt to
predict flexural failure need to target failure modes resulting from confinement in greater
detail.
6. In an attempt to correlate visually observed damage during testing with damage limit states,
all recorded test data were evaluated carefully to develop a correlation chart. This chart
provides a convenient aid in post-earthquake reconnaissance evaluation of structural safety.
This summary is presented in Table 7-1.
135
TABLE 7-1 Correlation of Damage Limit States with Visual Observations
Damage Damage State Description Visual Observation Based
Indicator on current Testing
N None No visible damage, either No visible cracks
cosmetic or structural
I Insignificant Damage reqUires no more Hair-line cracks
than cosmetic repair. No Minor spalling
structural repairs necessary No exposed
Reinforcement
M Moderate Repairable structural damage Excessive spalling
has occurred. The existing Exposed reinforcement
elements can be repaired No buckling of
essentially in place, without longitudinal bars
substantial demolition or No necking of spirals
replacement ofelements
H Heavy Damage is so extensive that Buckling/fracture of
repair of elements is either longitudinal bars
not feasible or requires major Necking/rupture of spirals
demolition or replacement.
7.1.2 Findings Related to Energy-Dissipation Capacity
The constant amplitude and random cyclic testing clearly indicate that the energy capacity
of a member at failure is strongly path (history) dependent. Proof of this observation is
clearly evident in Figures 7-1 and 7-2 which show plots of cumulative energy dissipated for
all specimens tested in both phases of the study. Figure 7-1 is a summary of specimens
tested under standard and constant-amplitude cycles in Phase I while Figure 7-2 shows the
history of dissipated energy for specimens tested under random loads in Phase II. If
specimen A2, tested under standard cyclic displacement amplitudes, is referred to as the
benchmark energy capacity, it is evident that the energy capacity of the columns vary
considerably depending on the displacement amplitude and path.
136
166 kNm
/
100806040
~~tandard cyclicjtest
20
~ Specimen A2- Specimen A3.., - Specimen A4
I --~ __ Specimen A5.' .' . +. . Specimen A6
.................: / : .
:'J. ,
: I:I I
<t':f.:" .. ,.~i I.. , I
+I J:~ I
O~~.:L.-...!....-...L-....J-...J.-...J.-.....l--'--'--'---L---L...---L...---'---L.--'---L.--L.----I
o
150
-EI
Z~->.ClL-Q) 100cW"CQ)-coa.C/)C/)
i550
.~-co::J
E::J()
Cycle Number
FIGURE 7-1 Cumulative Energy to Failure of Bridge Columns
Subjected to Constant Amplitude Loading
300250200150
· ,6. --11I(>-";-_.-..' .
100
Energy capacity from: ,..-c.--.------.-----.---.-standard cyclic test . ;
· ' u
. ..· . :tl!::.-- :.-- : ---- ··r:·!-----····
: : : I'i : •... ~ .... .••,.
.............:~. ~.~.~.~.~.~.~.~ ~.~ .•.•.•-:t".;.~. - ; ~':;.~ ~/ .. . .
. '_: ... ~ .. ~_ ..
--eo- Specimen A 7--Specimen A8.., - Speimen A9
--~--Specimen A10..... - Specimen A 11.. .-L!!- Specimen A12
40
-. :
20
,,
00 50
60
80
100-EZ~>.e>Q)cW"CQ)-«la.C/)C/)
is~
:;:;.!!!::JE::J()
Cycle Number
FIGURE 7-2 Cumulative Energy to Failure of Bridge ColumnsSubjected to Random Loading
137
Standard cyclic testing may provide information on the behavior of members and the potential
effects of certain material and geometric parameters on seismic response, but must not and can
not be used as a measure of energy-capacity of members.
7.1.3 Findings Related to Inelastic Modeling
Another contribution from the results of this study is the identification of inelastic behavior at
small amplitudes. This information is useful in the development of hysteresis models used in
nonlinear programs for dynamic response analysis. To date, most hysteresis models make fairly
arbitrary assumptions on the hysteretic loop behavior for small amplitude cycles which are
enveloped by larger amplitude cycles. The experimental findings in this study provide direct
input into this modeling process.
Figure 7-3 shows segments of the experimental response for two of the specimens in which a few
relevant cycles are separated from the rest of the force-deformation loops. A well-known aspect
of loop behavior is clearly evident: that unloading paths generally attempt to return to the
location of displacement and/or force at the end of the previous half cycle. The path taken to
return to this previous amplitude location may vary depending on the current location of
unloading. The purpose of displaying intermediate force-displacement hysteresis in Figure 7-3 is
to facilitate the development of a model that can be used for earthquake analysis of concrete
structures. Figure 7-4 is a proposed model of expected loop behavior under random amplitudes
wherein the path of small-amplitude cycles are given proper consideration.
If unloading occurs within a displacement amplitude less than the yield displacement, unloading
paths seem to directly target the previous maximum point (shown by paths 'd' and 'e' in Figure 7
4) as opposed to unloading paths beyond the yield displacement which show the ability to
dissipate more energy (paths 'el' and 'c2' in Figure 7-4). (c) If reloading occurs along an
unloading path before the zero force axis is crossed, it is reasonable to reload along the same line
without energy dissipation (paths aa' and bb').
138
80 8060 6040 40-Z 20 20.:.::
"-' 0Ql 0e -20 -200u...
-40 -40
-60 -60
-80 -80-100 -50 0 50 100 -60 -40 -20 0 20 40
10050oDisplacement (mm)
-50
60 80
40 60
20 40- 20Z 0~Ql 0u -20.... -200u... -40 -40
-60 -60
-80 -80
-60 -40 -20 0 20 40 -100
Displacement (mm)
.................................................. Yield deformation
FIGURE 7-3 Local Loop Behavior Under Random Cyclic Response
139
- - - Yield deformation
FIGURE 7-4 Proposed Modeling of Local Hysteresis Loops
7.2 Development of Performance-Based Design for Bridge Columns
One of the pnmary objectives of this research was to formulate a performance based
methodology for seismic design of bridge piers. This design procedure should be capable of
allowing the structural engineer to evaluate the adequacy of a reinforced concrete bridge pier
against expected seismic action. Based on the fmdings of this study, and the fatigue life
expression for flexural columns presented in Section 6.4, the following simple procedure is
proposed:
a) Establish a series of ground motions from seismological prediction and/or historical
records that best fit the bridge site. This would constitute the site-specific loading
criteria.
140
b) Conduct an inelastic time history analysis of the bridge pier for each of the series of the
selected records.
c) Determine the seismic demand from results of the preceding analysis in terms of number
ofhalf cycles at each drift amplitude.
d) Equation (6-16) can be utilized to define the degree of damage resulting from each half
cycle at a given drift amplitude. Solving Equation (6-16) in terms of number of cycles to
failure yields:
(D ifiJ
3.51
N = 2.0 * -.-!.!...!.fi 10.6
(7-1)
The quantity 2.0 accounts for the fact that only a half-cycle is being considered. Calculate
the induced damage to the column using the following expression:
" ndiD.l.= LJ N
fi
(7-2)
where ndi is the number of half cycles at a particular drift "di" obtained from the
analysis indicated in step (a), and Nfl is the number of half cycles to failure at the same
drift "di" obtained from Equation (7-1).
e) If the demand, based on the computed damage index, is close to or exceeds 1.0, then the
bridge will either not survive the expected earthquake activity at the site under
consideration or suffer irreparable damage. In fact, for practical considerations, values of
the above damage index in excess of 0.75 would indicate a high probability of severe
damage.
The above steps can also be used to estimate reserve capacity of a bridge column following a
seismic event if recorded data at the site is available to estimate the drift response during the
event.
141
7.4 Recommendations for Future Research
This research effort must be viewed as a preliminary attempt that contributes to the overall effort
in calibrating a fatigue-based cumulative damage model which is a necessary first step towards
developing a performance-based design guideline. The study provided a number of useful
insights into the mechanics of damage progression and brought to the forefront a number of
issues that still remain unresolved. The following recommendations for future work are based on
the findings of this project:
1. The response of bridge columns with a much smaller aspect ratio must be investigated
using essentially the same approach adopted in this study. This will highlight modes of
shear failure as well as the applicability of fatigue-life expressions for elements responding
primarily in shear.
2. A simple experimental study on the fatigue behavior of deformed reinforcing bars
subjected to random cyclic loads needs to be investigated. Since the behavior of flexural
elements is controlled largely by the response of the steel reinforcement, this study will
provide the basis for developing future test programs that examine cumulative fatigue in
RC members. In particular, the inter-dependence of small and large amplitude inelastic
cycles must be studied to determine load path effects.
3. Circular columns were used in this study to limit the number of system variables. It is
recommended to extend this study to rectangular columns to investigate effects of shape
and cross-section aspect ratio. The study of rectangular columns should obviously cover
both flexure and shear.
4. A fmal aspect of behavior that may deserve some attention is the influence of bidirectional
moments on the deterioration and damage of bridge columns. Since bridge piers are
constrained to respond in the lateral direction of the bridge span due to the relatively large
deck that forces motion in the in-plane direction, it is unlikely that biaxial bending is a
serious concern in bridge design. The use of circular columns also avoids this issue.
5. This testing methodology may also be extended to single bay bridge bents in which the
interaction of the deck beams becomes significant. Single and double deck bents are
common in highway construction. Testing such models at a realistic scale is time-
142
consuming and difficult. Analytical studies of such structures using validated damage
models can provide useful information.
6. Tests of retrofitted specimens may also be investigated using the test methodology
presented in this report. The reliability and adequacy of proposed retrofit and rehabilitation
techniques can be readily evaluated by examining the response of the original and repaired
specimen under the same sequence of random load reversals.
7. Existing damage models need to be enhanced and improved to account adequately for
damage resulting from different failure modes. In the present testing, it was obvious that
failure was a combination of low-cycle fatigue damage and the deterioration of confining
action of the spirals. The fatigue-life expressions proposed by Mander and Cheng (1995)
were extended to composite concrete columns based on limited experimental testing.
However, the proposed model needs to be enhanced further to better characterize damage
resulting from other failure modes.
A performance-based design procedure wherein damage limit states can be identified is urgently
needed by the profession. The proposed procedure in Section 7.3 must be viewed as an initial
step in this direction.
143
SECTION 8
REFERENCES
1. AASHTO (1989), "Standard Specifications for Highway Bridges", (14th Edition), TheAmerican Association of State Highway and Transportation Officials (AASHTO),Washington, D.C.
2. ACI Design Handbook, (1985), Columns, Volume 2, Publication SP 17A, AmericanConcrete Institute, Detroit, Michigan.
3. Ang, RG., Priestley, M.J.N., and Paulay, T., (1985), "Seismic Shear Strength of CircularBridge Columns", Research Report 85-5, Department of Civil Engineering, University ofCanterbury, Christchurch, New Zealand, 408 pp.
4. Ang, B.G., Priestley, M.J.N., and Paulay, T., (1989), "Seismic Shear Strength of CircularBridge Columns", ACI Structural Journal, Vol.86, No.1, pp.45-59.
5. Building Research Institute (1975, 1978), "A Seismic Analysis of Building StructuralMembers: a List of Experimental results on Deformation Ability of Reinforced ConcreteColumn Under Large Deflection", No.3, B.R.I., Ministry of Construction, Japan, 182 pages.
6. CALTRANS (1992), "Bridge Design Specifications," State of California, Department ofTransportation, Office of Structure Design, Sacramento, California.
7. Cheok, G.S., and Stone, W.C., (1986), "Behavior of 1/6 Scale Model Bridge ColumnsSubjected to Cyclic Inelastic Loading", Report No. NBSIR 86-3494, U.S. Department ofCommerce, , National Institute of Standards and Technology, Gaithersburg, MD, 270 pp.
8. Cheok, G.S., and Stone, W.C., (1990), "Behavior of 1/6 Scale Model Bridge ColumnsSubjected to Cyclic Inelastic Loading", ACI Structural Journal, Vol. 87, No.6, pp.630-638.
9. Chung, YS., Meyer, C. and Shinozuka, M., (1987), "Seismic Damage Assessment of RCStructures", NCEER Report 87-0022, State University ofNew York at Buffalo, New York.
10. Coffm, L. F. Jr., (1954), "A Study of the Effects of Cyclic Thermal Stresses on a DuctileMetal", Transactions of the American Society of Mechanical Engineers, New York, N. Y,76,931-950.
11. Davey, RE., (1975), "Reinforced Concrete Bridge Piers Under Seismic Loading", Master ofEngineering Report, Civil Engineering Department, University of Canterbury, Christchurch,New Zealand, February.
12. Hwang, T.H. and Scribner, C.F., (1984), "RC Member Cyclic Response During VariousLoadings", Journal of Structural Engineering, ASCE, 110 (3), pp.466-489.
144
13. Kanaan, A and Powell, G.H., (1973). "General Purpose Computer Program for InelasticDynamic response of Plane Structures", EERC Report No.73-6, University of California,Berkeley.
14. Kratzig, W.B. and Meskouris, M., (1987), "Nonlinear Seismic Analysis of ReinforcedConcrete Frames", Earthquake Prognostics (Vogel and Brandes, editors), Verlag Friedr,Vieweg and Sooo, Braunschweig, pp.453-462.
.;
15. Kunnath, S.K., and Reinhom, A.M., (1995), "Efficient Modeling Scheme for TransientAnalysis of Inelastic RC Structures", Microcomputer in Civil Engineering, Vo1.10, No.1,pp.97-11O.
16. Kunnath, S.K., Mander, J.B. and Lee, F., (1997), "Parameter Identification for Degrading andPinched Hysteretic Structural Concrete Systems", Engineering Structures, Vo1.19, No.3,pp.224-232.
17. Kunnath, S.K., Reinhom, AM and Lobo, RF., (1992), "IDARC: Inelastic Damage AnalysisofRC Structures- Version 3.0", Report NCEER-92-0022, State University of New York atBuffalo, New York.
18. Mander, l B., Panthaki, F. D., and Kasalanati, A., (1994), " Low Cycle Fatigue Behavior ofReinforcing Steel", Journal ofMaterials in Civil Engineering, ASCE, Vol. 6, No.4.
19. Mander, lB. and Cheng, C.-T., (1995), "Renewable Hinge Detailing for Bridge Columns",Pacific Conference on Earthquake Engineering, Melbourne, Australia, November 20-22.
20. Mander, J.B. and Cheng, C.-T., (1995), "Replaceable Hinge Detailing for Bridge Columns",National Seismic Conference on Bridges and Highways, San Diego, CA, December 10-13.
21. Mander, J.B., Priestley, M.lN., and Park, R, (1984), "Seismic Design of Bridge Piers",Research Report 84-2, University of Canterbury, Christchurch, New Zealand.
22. Mander, J.B., Priestley, M.lN., and Park, R, (1988), "Observed Stress Strain Behavior forConfined Concrete", Journal of Structural Engineering, ASCE, 114 (8), pp. 1827-1849.
23. Mander, J.B., Priestley, M.J.N., and Park, R, (1988), "Theoretical Stress Strain Model forConfined Concrete", Journal of Structural Engineering, ASCE, 114 (8), pp. 1804-1826.
24. Manson, S. S., (1953), "Behavior of Materials under Conditions of Thermal Stress", HeatTransfer Symposium, University of Michigan Engineering Research Institute, Ann Arbor,Michigan, pp.9-75.
25. Miner, M.A, (1945), "Cumulative Damage in Fatigue", Journal of Applied Mechanics,Vo1.12, pp. A-159.
145
26. Munro, I.R.M., Park, R., and Priestley, M.J.N., (1976), "Seismic Behavior of ReinforcedConcrete Bridge Piers", Report 76-9, Department of Civil engineering, University ofCanterbury, Christchurch, New Zealand.
27. Newmark, N.M., (1959), "A Method of Computation for Structural Dynamics", ASCEJournal ofEngineering Mechanics, Vol.85, pp.67-94.
28. Park, Y.J. and Ang, A.H-S., (1985), "Mechanistic Seismic Damage Model for ReinforcedConcrete", Journal of Structural Engineering, ASCE, 111, pp.722-739.
29. Powell, G. and Allahabadi, R., (1988), "Seismic Damage Prediction by DeterministicMethods: Concepts and Procedures", Earthquake Engineering and Structural Dynamics,Vol. 16.
30. Priestley, M.J.N and Benzoni, G., (1996), "Seismic Performance of Circular Columns withLow Longitudinal Reinforcement Ratios", ACI Structural Journal, Vol. 93, No.4, pp.474485.
31. Priestley, M.J.N. and Paulay, T., (1992), "Seismic Design of Reinforced Concrete andMasonry Buildings", John Wiley and Sons, New York.
32. Priestley, M.J.N., Seible, F. and Anderson, D.L., (1993), "Proof test of a Retrofit Concept forthe San Francisco Double-Deck Viaducts: Part 1 - Design Concept, Details and Model", ACIStructural Journal, Vol. 90, No.5, pp. 467-479.
33. Priestley, M.J.N., Seible, F. and Anderson, D.L., (1993), "Proof test of a Retrofit Concept forthe San Francisco Double-Deck Viaducts: Part 2 - Test Details and Results", ACI StructuralJournal,
34. Vol. 90, No.6, pp. 616-631.
35. Priestley, M.J.N., Seible, F., Xiao, Y. and Verma, R., (1994), "Steel Jacket Retrofitting ofReinforced Concrete Bridge Columns for Enhanced Shear Strength - Part 1: TheoreticalConsiderations and Test Design", ACI Structural Journal, Vol. 91, No.4, pp. 394-405.
36. Priestley, M.J.N., Seible, F., Xiao, Y. and Verma, R., (1994), "Steel Jacket Retrofitting ofReinforced Concrete Bridge Columns for Enhanced Shear Strength - Part 2: Test Results andComparison with Theory", ACI Structural Journal, Vol. 91, No.5, pp. 537-551.
37. Stone, W.C. and Cheok, G.S., (1989), "Inelastic Behavior of Full-Scale Bridge ColumnsSubjected to Cyclic Loading", NIST Building Science Series Report No. 166, U.S.Department of Commerce, National Institute of Standards and Technology, Gaithersburg,MD,252pp.
38. Stone, W.C., Cooper, J. D. and Carino, N. J., (1990), "Performance of Bridge and HighwayStructures", NlST SP No. 778, National Institute of Standards and Technology,Gaithersburg, MD, 201 pp.
146
39. Tanaka, H. and Park, R., (1993), "Seismic Deisgn and Behavior of Reinforced ConcreteColumns with Interlocking Spirals", ACI Structural Journal, Vol. 90, No.2, pp.192-203.
40. Williams, M.S., & Sexsmith, R.G. (1994), "Review of Methods Assessing Seismic Damagein Concrete Structures", Technical Report 94-02, Earthquake Engineering Research Facility,University ofBritish Columbia, Canada.
41. Wong, YL., Paulay, T., and Priestley, M.J.N., (1990), "Squat Circular Bridge Piers UnderMulti-Directional seismic Attack", Department of Civil Engineering, University ofCanterbury, Report 90-4, 264 pp.
42. Wong, Y.L., Paulay, T., and Priestley, MJ.N., (1993), "Response of Circular Columns toMulti-Directional Seismic Attack", ACI Structural Journal, Vol. 90, No.2, pp.180-191.
147
APPENDIX A
Ultrasonic Testing
Non-destructive test methods are gaining popularity these days as a potential means of
monitoring damage in structures. If it is possible to calibrate such methods with damage limit
states, they could contribute to the overall effort ofperformance-based design.
Hence, in addition to the force-deformation hysteresis and strain gage data recorded during
testing of the bridge columns reported in Sections 4 and 5, minimal non-destructive tests of the
specimens were also carried out. The non-destructiye methodology employed here consisted of
ultrasonic measurements across the height of the specimen before and after testing.
Measurements could not be taken during testing since the extraneous vibrations and noise of the
hydraulic system to which the test specimen was anchored interfered with the ultrasonic
readings. As such, it was not possible to calibrate the data with observed damage during testing.
Rather, the testing was conducted primarily as a feasibility study.
Results of the ultrasonic measurements are presented in Figures A-I through A-9. It is clear that
damage is reflected through an increase in travel time of the sound waves. Also encouraging is
the fact that the change in travel time increases non-linearly with the degree of damage (see
variation across height of specimen). These preliminary studies indicate that such methodologies
hold promise in damage measurement and could be calibrated for use in performance-based
evaluation and post-earthquake damage reconnaissance of bridge piers.
A-I
.. - . -.-.. -. .. --~ -. - - - . -- ~ - -.-- - - .. ~ ---- - ~ . - - -. --- - -.
, '
Undamaged SpecimenBefore Test
_____: Damaged Specime~
After Test '
16014012010080
............ \: ; : : .
,:
... \ : : l ., '": '", '" '" '
........... ···f········~~:':~~ ~~~~~·····················;········ .
""'i ..: -...., ..
.............. ; : : '~'':''~'~''' .;..~ ..::~.
1200
-E1000E-Q)
UlCD
800lD
E0~
c: 6000..~Q)
iIi 400c:E::::l(5 2000
a60
Transmission Time (microseconds)
FIGURE A-I Ultrasonic Readings Across Height of Specimen A4
...... 0ndamage~ Specimen:i :Before Test :
.......: : : : ;"·"'.-·······i·············I: --:------- ;Damaged Specimen :I : :After Test:. : ':....... ·i·· ~ 'j"'" ;-." - : :---- -- ..
I :.:
...\-:- -- + --! -- : -- L ...:(.......
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FIGURE A-2 Ultrasonic Readings Across Height of Specimen AS
A-2
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FIGURE A-3 Ultrasonic Readings Across Height of Specimen A6
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FIGURE A-4 Ultrasonic Readings Across Height of Specimen A7
A-3
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FIGURE A-6 Ultrasonic Readings Across Height of Specimen A9
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FIGURE A-7 Ultrasonic Readings Across Height of Specimen AIO
A-4
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.... :·······,···············7··············,··············, ; .I __: :Damaged Specimen :
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FIGURE A-8 Ultrasonic Readings Across Height of Specimen All
, ,
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FIGURE A-9 Ultrasonic Readings Across Height of Specimen A12
A-5
NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCHLIST OF TECHNICAL REPORTS
The National Center for Earthquake Engineering Research (NCEER) publishes technical reports on a variety of subjects relatedto earthquake engineering written by authors funded through NCEER. These reports are available from both NCEERPublications and the National Technical Information Service (NTIS). Requests for reports should be directed to NCEERPublications, National Center for Earthquake Engineering Research, State University of New York at Buffalo, Red JacketQuadrangle, Buffalo, New York 14261. Reports can also be requested through NTIS, 5285 Port Royal Road, Springfield,Virginia 22161. NTIS accession numbers are shown in parenthesis, if available.
NCEER-87-0001 "First-Year Program in Research, Education and Technology Transfer," 3/5/87, (PB88-134275, A04, MFAOI).
NCEER-87-0002 "Experimental Evaluation of Instantaneous Optimal Algorithms for Structural Control," by R.C. Lin, T.T.Soong and AM. Reinhorn, 4/20/87, (PB88-134341, A04, MF-A01).
NCEER-87-0003 "Experimentation Using the Earthquake Simulation Facilities at University at Buffalo," by AM. Reinhornand R.L. Ketter, to be published.
NCEER-87-0004 "The System Characteristics and Performance of a Shaking Table," by lS. Hwang, KC. Chang and G.C.Lee, 6/1187, (PB88-134259, A03, MF-A01). This report is available only through NTIS (see address givenabove).
NCEER-87-0005 "A Finite Element Formulation for Nonlinear Viscoplastic Material Using a Q Model," by O. Gyebi and G.Dasgupta, 1112/87, (PB88-213764, A08, MF-AOl).
NCEER-87-0006 "Symbolic Manipulation Program (SMP) - Algebraic Codes for Two and Three Dimensional Finite ElementFormulations," by X. Lee and G. Dasgupta, 1119/87, (PB88-218522, A05, MF-A01).
NCEER-87-0007 "Instantaneous Optimal Control Laws for Tall Buildings Under Seismic Excitations," by IN. Yang, AAkbarpour and P. Ghaemmaghami, 6/10/87, (PB88-134333, A06, MF-AOI). This report is only availablethrough NTIS (see address given above).
NCEER-87-0008 "!DARC: Inelastic Damage Analysis of Reinforced Concrete Frame - Shear-Wall Structures," by Y.l Park,AM. Reinhorn and S.K Kunnath, 7/20/87, (PB88-134325, A09, MF-AOI). This report is only availablethrough NTIS (see address given above).
NCEER-87-0009 "Liquefaction Potential for New York State: A Preliminary Report on Sites in Manhattan and Buffalo," byM. Budhu, V. Vijayakumar, R.F. Giese and L. Baumgras, 8/31187, (PB88-163704, A03, MF-AOI). Thisreport is available only through NTIS (see address given above).
NCEER-87-001O "Vertical and Torsional Vibration of Foundations in Inhomogeneous Media," by AS. Veletsos and KW.Dotson, 6/1187, (PB88·134291, A03, MF-AOI). This report is only available through NTIS (see addressgiven above).
NCEER-87-0011 "Seismic Probabilistic Risk Assessment and Seismic Margins Studies for Nuclear Power Plants," by HowardH.M. Hwang, 6/15/87, (PB88-134267, A03, MF-AOI). This report is only available through NTIS (seeaddress given above).
NCEER-87-0012 "Parametric Studies of Frequency Response of Secondary Systems Under Ground-Acceleration Excitations,"by Y. Yong and Y.K. Lin, 6/10/87, (PB88-134309, A03, MF-AOI). This report is only available throughNTIS (see address given above).
NCEER-87-0013 "Frequency Response of Secondary Systems Under Seismic Excitation," by lA HoLung, 1 Cai and Y.KLin, 7/31187, (PB88-134317, A05, MF-A01). This report is only available through NTIS (see address givenabove).
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NCEER-87-0014 "Modelling Earthquake Ground Motions in Seismically Active Regions Using Parametric Time SeriesMethods," by G.W. Ellis and AS. Cakmak, 8/25/87, (PB88-134283, A08, MF-A01). This report is onlyavailable through NTIS (see address given above).
NCEER-87-0015 "Detection and Assessment of Seismic Structural Damage," by E. DiPasquale and AS. Cakmak, 8/25/87,(PB88-163712, A05, MF-A01). This report is only available through NTIS (see address given above).
NCEER-87-0016 "Pipeline Experiment at Parkfield, California," by J. Isenberg and E. Richardson, 9/15/87, (PB88-163720,A03, MF-A01). This report is available only through NTIS (see address given above).
NCEER-87-0017 "Digital Simulation of Seismic Ground Motion," by M. Shinozuka, G. Deodatis and T. Harada, 8/31187,(PB88-155197, A04, MF-A01). This report is available only through NTIS (see address given above).
NCEER-87-0018 "Practical Considerations for Structural Control: System Uncertainty, System Time Delay and Truncation ofSmall Control Forces," IN. Yang and A Akbarpour, 8/10/87, (PB88-163738, A08, MF-A01). This report isonly available through NTIS (see address given above).
NCEER-87-0019 "Modal Analysis of Nonclassically Damped Structural Systems Using Canonical Transfonnation," by IN.Yang, S. Sarkani and F.X. Long, 9/27/87, (PB88-187851, A04, MF-AOI).
NCEER-87-0020 "A Nonstationary Solution in Random Vibration Theory," by IR. Red-Horse and P.D. Spanos, 1113/87,(PB88-163746, A03, MF-A01).
NCEER-87-0021 "Horizontal Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by AS. Veletsos and KW.Dotson, 10/15/87, (PB88-150859, A04, MF-A01).
NCEER-87-0022 "Seismic Damage Assessment of Reinforced Concrete Members," by Y.S. Chung, C. Meyer and M.Shinozuka, 10/9/87, (PB88-150867, A05, MF-A01). This report is available only through NTIS (see addressgiven above).
NCEER-87-0023 "Active Structural Control in Civil Engineering," by T.T. Soong, 11111187, (PB88-187778, A03, MF-A01).
NCEER-87-0024 "Vertical and Torsional Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by KW. Dotsonand AS. Veletsos, 12/87, (PB88-187786, A03, MF-AOI).
NCEER-87-0025 "Proceedings from the Symposium on Seismic Hazards, Ground Motions, Soil-Liquefaction and EngineeringPractice in Eastern North America," October 20-22, 1987, edited by KH. Jacob, 12/87, (pB88-188115, A23,MF-A01).
NCEER-87-0026 "Report on the Whittier-Narrows, California, Earthquake of October 1, 1987," by 1. Pantelic and AReinhorn, 11187, (PB88-187752, A03, MF-A01). This report is available only through NTIS (see addressgiven above).
NCEER-87-0027 "Design of a Modular Program for Transient Nonlinear Analysis of Large 3-D Building Structures," by S.Srivastav and J.F. Abel, 12/30/87, (PB88-187950, A05, MF-AOI). This report is only available throughNTIS (see address given above).
NCEER-87-0028 "Second-Year Program in Research, Education and Technology Transfer," 3/8/88, (PB88-219480, A04, MFA01).
NCEER-88-0001 "Workshop on Seismic Computer Analysis and Design of Buildings With Interactive Graphics," by W.McGuire, J.F. Abel and C.H. Conley, 1118/88, (PB88-187760, A03, MF-AOl). This report is only availablethrough NTIS (see address given above).
NCEER-88-0002 "Optimal Control ofNonlinear Flexible Structures," by 1.N. Yang, F.x. Long and D. Wong, 1122/88, (pB88213772, A06, MF-A01).
B-2
NCEER-88-0003 "Substructuring Techniques in the Time Domain for Primary-Secondary Structural Systems," by G.D.Manolis and G. Juhn, 2/10/88, (PB88-2l3780, A04, MF-A01).
NCEER-88-0004 "Iterative Seismic Analysis of Primary-Secondary Systems," by A Singhal, L.D. Lutes and P.O. Spanos,2/23/88, (PB88-213798, A04, MF-A01).
NCEER-88-0005 "Stochastic Finite Element Expansion for Random Media," by P.D. Spanos and R. Ghanem, 3/14/88, (PB88213806, A03, MF-AOl).
NCEER-88-0006 "Combining Structural Optimization and Structural Control," by F.Y. Cheng and c.P. Pantelides, 1/10/88,(PB88-213814, A05, MF-A01).
NCEER-88-0007 "Seismic Performance Assessment of Code-Designed Structures," by H.H-M. Hwang, J-W. Jaw and H-J.Shau, 3/20/88, (PB88-219423, A04, MF-A01). This report is only available through NTIS (see address givenabove).
NCEER-88-0008 "Reliability Analysis of Code-Designed Structures Under Natural Hazards," by H.H-M. Hwang, H. Ushibaand M. Shinozuka, 2/29/88, (PB88-22947l, A07, MF-AOl). This report is only available through NTIS (seeaddress given above).
NCEER-88-0009 "Seismic Fragility Analysis of Shear Wall Structures," by J-W Jaw and H.H-M. Hwang, 4/30/88, (PB89102867, A04, MF-AOl).
NCEER-88-0010 "Base Isolation of a Multi-Story Building Under a Harmonic Ground Motion - A Comparison ofPerformances of Various Systems," by F-G Fan, G. Ahmadi and LG. Tadjbakhsh, 5/18/88, (PB89-122238,A06, MF-A01). This report is only available through NTIS (see address given above).
NCEER-88-0011 "Seismic Floor Response Spectra for a Combined System by Green's Functions," by F.M. Lavelle, L.ABergman and P.O. Spanos, 5/1/88, (PB89-102875, A03, MF-A01).
NCEER-88-0012 "A New Solution Technique for Randomly Excited Hysteretic Structures," by G.Q. Cai and Y.K. Lin,5/16/88, (PB89-l02883, A03, MF-A01).
NCEER-88-0013 "A Study of Radiation Damping and Soil-Structure Interaction Effects in the Centrifuge," by K. Weissman,supervised by J.H. Prevost, 5/24/88, (PB89-144703, A06, MF-A01).
NCEER-88-0014 "Parameter Identification and Implementation of a Kinematic Plasticity Model for Frictional Soils," by J.H.Prevost and D.V. Griffiths, to be published.
NCEER-88-0015 "Two- and Three- Dimensional Dynamic Finite Element Analyses of the Long Valley Dam," by D.V.Griffiths and J.H. Prevost, 6/17/88, (PB89-144711, A04, MF-A01).
NCEER-88-0016 "Damage Assessment of Reinforced Concrete Structures in Eastern United States," by AM. Reinhorn, M.J.Seidel, S.K. Kunnath and YJ. Park, 6/15/88, (PB89-l22220, A04, MF-A01). This report is only availablethrough NTIS (see address given above).
NCEER-88-0017 "Dynamic Compliance of Vertically Loaded Strip Foundations in Multilayered Viscoelastic Soils," by S.Ahmad and AS.M. Israil, 6/17/88, (PB89-102891, A04, MF-A01).
NCEER-88-0018 "An Experimental Study of Seismic Structural Response With Added Viscoelastic Dampers," by R.C. Lin, Z.Liang, T.T. Soong and R.H. Zhang, 6/30/88, (PB89-122212, A05, MF-A01). This report is available onlythrough NTIS (see address given above).
NCEER-88-0019 "Experimental Investigation of Primary - Secondary System Interaction," by G.D. Manolis, G. Juhn andAM. Reinhorn, 5/27/88, (PB89-122204, A04, MF-A01).
B-3
NCEER-88-0020 "A Response Spectrum Approach For Analysis of Nonclassically Damped Structures," by J.N. Yang, S.Sarkani and F.x. Long, 4/22/88, (PB89-102909, A04, MF-A01).
NCEER-88-0021 "Seismic Interaction of Structures and Soils: Stochastic Approach," by AS. Veletsos and AM. Prasad,7/2I/88, (PB89-122196, A04, MF-A01). This report is only available through NTIS (see address givenabove).
NCEER-88-0022 "Identification of the Serviceability Limit State and Detection of Seismic Structural Damage," by E.DiPasquale and AS. Cakmak, 6/15/88, (PB89-122188, A05, MF-A01). This report is available only throughNTIS (see address given above).
NCEER-88-0023 "Multi-Hazard Risk Analysis: Case of a Simple Offshore Structure," by B.K. Bhartia and E.H. Vanmarcke,7/2I/88, (PB89-145213, A05, MF-A01).
NCEER-88-0024 "Automated Seismic Design of Reinforced Concrete Buildings," by Y.S. Chung, C. Meyer and M.Shinozuka, 7/5/88, (PB89-122170, A06, MF-A01). This report is available only through NTIS (see addressgiven above).
NCEER-88-0025 "Experimental Study of Active Control of MDOF Structures Under Seismic Excitations," by L.L. Chung,R.C. Lin, T.T. Soong and A.M. Reinhom, 7/10/88, (PB89-122600, A04, MF-A01).
NCEER-88-0026 "Earthquake Simulation Tests of a Low-Rise Metal Structure," by 1.S. Hwang, K.C. Chang, G.c. Lee andR.L. Ketter, 8/I/88, (PB89-102917, A04, MF-A01).
NCEER-88-0027 "Systems Study of Urban Response and Reconstruction Due to Catastrophic Earthquakes," by F. Kozin andH.K. Zhou, 9/22/88, (PB90-162348, A04, MF-A01).
NCEER-88-0028 "Seismic Fragility Analysis of Plane Frame Structures," by H.H-M. Hwang and Y.K. Low, 7/3I/88, (PB89131445, A06, fID'-A01).
NCEER-88-0029 "Response Analysis of Stochastic Structures," by A. Kardara, C. Bucher and M. Shinozuka, 9/22/88, (PB89174429, A04, MF-A01).
NCEER-88-0030 "Nonnormal Accelerations Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D. Lutes,9/19/88, (PB89-131437, A04, MF-A01).
NCEER-88-0031 "Design Approaches for Soil-Structure Interaction," by A.S. Veletsos, A.M. Prasad and Y. Tang, 12/30/88,(PB89-174437, A03, MF-A01). This report is available only through NTIS (see address given above).
NCEER-88-0032 "A Re-evaluation of Design Spectra for Seismic Damage Control," by C.J. Turkstra and AG. Tallin,1I/7/88, (PB89-145221, A05, MF-AOI).
NCEER-88-0033 "The Behavior and Design of Noncontact Lap Splices Subjected to Repeated Inelastic Tensile Loading," byV.E. Sagan, P. Gergely and R.N. White, 12/8/88, (PB89-163737, A08, MF-AOI).
NCEER-88-0034 "Seismic Response of Pile Foundations," by S.M. Mamoon, P.K. Banerjee and S. Ahmad, 1I/I/88, (PB89145239, A04, MF-A01).
NCEER-88-0035 "Modeling ofRIC Building Structures With Flexible Floor Diaphragms (IDARC2)," by AM. Reinhom, S.K.Kunnath and N. Panahshahi, 917/88, (PB89-207153, A07, MF-A01).
NCEER-88-0036 "Solution of the Dam-Reservoir Interaction Problem Using a Combination of FEM, BEM with ParticularIntegrals, Modal Analysis, and Substructuring," by C-S. Tsai, G.C. Lee and R.L. Ketter, 12/3I/88, (PB89207146, A04, MF-A01).
NCEER-88-0037 "Optimal Placement of Actuators for Structural Control," by F.Y. Cheng and C.P. Pantelides, 8/15/88,(PB89-162846, A05, MF-A01).
B-4
NCEER-88-0038 "Teflon Bearings in Aseismic Base Isolation: Experimental Studies and Mathematical Modeling," by AMokha, M.C. Constantinou and AM. Reinhom, 12/5/88, (PB89-2I8457, AIO, MF-AOI). This report isavailable only through NTIS (see address given above).
NCEER-88-0039 "Seismic Behavior of Flat Slab High-Rise Buildings in the New York City Area," by P. Weidlinger and M.Ettouney, 10/15/88, (PB90-145681, A04, MF-AOl).
NCEER-88-0040 "Evaluation of the Earthquake Resistance of Existing Buildings in New York City," by P. Weidlinger and M.Ettouney, IO/15/88, to be published.
NCEER-88-004I "Small-Scale Modeling Techniques for Reinforced Concrete Structures Subjected to Seismic Loads," by W.Kim, A El-Attar and R.N. White, 11/22/88, (PB89-I89625, A05, MF-AOl).
NCEER-88-0042 "Modeling Strong Ground Motion from Multiple Event Earthquakes," by G.W. Ellis and AS. Cakmak,IO/I5/88, (PB89-174445, A03, MF-A01).
NCEER-88-0043 "Nonstationary Models of Seismic Ground Acceleration," by M. Grigoriu, S.E. Ruiz and E. Rosenblueth,7/15/88, (PB89-189617, A04, MF-AOI).
NCEER-88-0044 "SARCF User's Guide: Seismic Analysis of Reinforced Concrete Frames," by Y.S. Chung, C. Meyer and M.Shinozuka, 1119/88, (PB89-174452, A08, MF-AOI).
NCEER-88-0045 "First Expert Panel Meeting on Disaster Research and Planning," edited by 1. Pantelic and 1. Stoyle, 9/15/88,(PB89-174460, A05, MF-AOI). This report is only available through NTIS (see address given above).
NCEER-88-0046 "Preliminary Studies of the Effect of Degrading Infill Walls on the Nonlinear Seismic Response of SteelFrames," by C.Z. Chrysostomou, P. Gergely and 1.F. Abel, 12/19/88, (PB89-208383, A05, MF-AOl).
NCEER-88-0047 "Reinforced Concrete Frame Component Testing Facility - Design, Construction, Instrumentation andOperation," by S.P. Pessiki, C. Conley, T. Bond, P. Gergely and R.N. White, 12/16/88, (PB89-174478, A04,MF-A01).
NCEER-89-0001 "Effects of Protective Cushion and Soil Compliancy on the Response of Equipment Within a SeismicallyExcited Building," by 1.A HoLung, 2/16/89, (PB89-207179, A04, MF-A01).
NCEER-89-0002 "Statistical Evaluation of Response Modification Factors for Reinforced Concrete Structures," by H.H-M.Hwang and J-W. Jaw, 2/17/89, (PB89-207187, A05, MF-AOI).
NCEER-89-0003 "Hysteretic Columns Under Random Excitation," by G-Q. Cai and Y.K. Lin, 1/9/89, (pB89-196513, A03,MF-AOI).
NCEER-89-0004 "Experimental Study of'Elephant Foot Bulge' Instability ofThin-Walled Metal Tanks," by Z-H. Jia and R.L.Ketter, 2/22/89, (PB89-207195, A03, MF-AOI).
NCEER-89-0005 "Experiment on Performance of Buried Pipelines Across San Andreas Fault," by J. Isenberg, E. Richardsonand T.D. O'Rourke, 3/10/89, (PB89-218440, A04, MF-A01). This report is available only through NTIS (seeaddress given above).
NCEER-89-0006 "A Knowledge-Based Approach to Structural Design of Earthquake-Resistant Buildings," by M. Subramani,P. Gergely, C.R. Conley, J.F. Abel and AH. Zaghw, 1/15/89, (PB89-218465, A06, MF-A01).
NCEER-89-0007 "Liquefaction Hazards and Their Effects on Buried Pipelines," by T.D. O'Rourke and P.A Lane, 2/1/89,(PB89-218481, A09, MF-AOI).
B-5
NCEER-89-0008 "Fundamentals of System Identification in Structural Dynamics," by H. Imai, CoB. Yun, O. Maruyama andM. Shinozuka, lI26/89, (PB89-2072 I I, A04, MF-A01).
NCEER-89-0009 "Effects of the 1985 Michoacan Earthquake on Water Systems and Other Buried Lifelines in Mexico," byAG. Ayala and M.l O'Rourke, 3/8/89, (PB89-207229, A06, MF-AOI).
NCEER-89-ROIO "NCEER Bibliography of Earthquake Education Materials," by KE.K. Ross, Second Revision, 9/lI89,(PB90-125352, A05, MF-AOl). This report is replaced by NCEER-92-0018.
NCEER-89-0011 "Inelastic Three-Dimensional Response Analysis of Reinforced Concrete Building Structures (IDARC-3D),Part I - Modeling," by S.K. Kunnath and AM. Reinhom, 4/17/89, (PB90-114612, A07, MF-A01).
NCEER-89-0012 "Recommended Modifications to ATC-14," by C.D. Poland and lO. Malley, 4/12/89, (PB90-108648, A15,MF-AOI).
NCEER-89-0013 "Repair and Strengthening of Beam-to-Column Connections Subjected to Earthquake Loading," by M.Corazao and Al Durrani, 2/28/89, (PB90-109885, A06, MF-A01).
NCEER-89-0014 "Program EXKAL2 for Identification of Structural Dynamic Systems," by O. Maruyama, CoB. Yun, M.Hoshiya and M. Shinozuka, 5/19/89, (PB90-109877, A09, MF-A01).
NCEER-89-0015 "Response of Frames With Bolted Semi-Rigid Connections, Part I - Experimental Study and AnalyticalPredictions," by PJ. DiCorso, AM. Reinhom, J.R. Dickerson, J.B. Radziminski and W.L. Harper, 6/lI89, tobe published.
NCEER-89-0016 "ARMA Monte Carlo Simulation in Probabilistic Structural Analysis," by P.D. Spanos and M.P. Mignolet,7/10/89, (PB90-109893, A03, MF-AOl).
NCEER-89-P017 "Preliminary Proceedings from the Conference on Disaster Preparedness - The Place of EarthquakeEducation in Our Schools," Edited by KE.K Ross, 6/23/89, (PB90-108606, A03, MF-A01).
NCEER-89-0017 "Proceedings from the Conference on Disaster Preparedness - The Place of Earthquake Education in OurSchools," Edited by KE.K. Ross, 12/3l189, (PB90-207895, AOI2, MF-A02). This report is available onlythrough NTIS (see address given above).
NCEER-89-0018 "Multidimensional Models of Hysteretic Material Behavior for Vibration Analysis of Shape Memory EnergyAbsorbing Devices, by EJ. Graesser and FA CozzarelIi, 6/7/89, (PB90-164146, A04, MF-AOI).
NCEER-89-0019 "Nonlinear Dynamic Analysis of Three-Dimensional Base Isolated Structures (3D-BASIS)," by S.Nagarajaiah, AM. Reinhom and M.C. Constantinou, 8/3/89, (PB90-161936, A06, MF-A01). This reporthas been replaced by NCEER-93-0011.
NCEER-89-0020 "Structural Control Considering Time-Rate of Control Forces and Control Rate Constraints," by F.Y. Chengand C.P. Pantelides, 8/3/89, (PB90-120445, A04, MF-AOI).
NCEER-89-0021 "Subsurface Conditions of Memphis and Shelby County," by KW. Ng, T-S. Chang and H-H.M. Hwang,7/26/89, (PB90-120437, A03, MF-A01).
NCEER-89-0022 "Seismic Wave Propagation Effects on Straight Jointed Buried Pipelines," by K Elhmadi and MJ.O'Rourke, 8/24/89, (PB90-162322, A10, MF-A02).
NCEER-89-0023 "Workshop on Serviceability Analysis of Water Delivery Systems," edited by M. Grigoriu, 3/6/89, (PB90127424, A03, MF-A01).
NCEER-89-0024 "Shaking Table Study of a lI5 Scale Steel Frame Composed of Tapered Members," by K.C. Chang, J.S.Hwang and G.C. Lee, 9/18/89, (PB90-160169, A04, MF-A01).
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NCEER-89-0025 "DYNA1D: A Computer Program for Nonlinear Seismic Site Response Analysis - TechnicalDocumentation," by Jean H. Prevost, 9/14/89, (PB90-161944, A07, MF-A01). This report is available onlythrough NTIS (see address given above).
NCEER-89-0026 "1:4 Scale Model Studies of Active Tendon Systems and Active Mass Dampers for Aseismic Protection," byA.M. Reinhorn, T.T. Soong, R.C. Lin, Y.P. Yang, Y. Fukao, H. Abe and M. Nakai, 9/15/89, (PB90-173246,AlO, MF-A02).
NCEER-89-0027 "Scattering of Waves by Inclusions in a Nonhomogeneous Elastic Half Space Solved by Boundary ElementMethods," by P.K. Hadley, A Askar and A.S. Cakmak, 6/15/89, (PB90-145699, A07, MF-A01).
NCEER-89-0028 "Statistical Evaluation of Deflection Amplification Factors for Reinforced Concrete Structures," by H.H.M.Hwang, J-W. Jaw and AL. Ch'ng, 8/31/89, (PB90-164633, A05, MF-AOI).
NCEER-89-0029 "Bedrock Accelerations in Memphis Area Due to Large New Madrid Earthquakes," by H.H.M. Hwang,, C.H.S. Chen and G. Yu, 11/7/89, (PB90-162330, A04, MF-AOI).
NCEER-89-0030 "Seismic Behavior and Response Sensitivity of Secondary Structural Systems," by Y.Q. Chen and T.T.Soong, 10/23/89, (PB90-164658, A08, MF-A01).
NCEER-89-0031 "Random Vibration and Reliability Analysis of Primary-Secondary Structural Systems," by Y. Ibrahim, M.Grigoriu and T.T. Soong, 11/10/89, (PB90-161951, A04, MF-A01).
NCEER-89-0032 "Proceedings from the Second U.S. - Japan Workshop on Liquefaction, Large Ground Deformation andTheir Effects on Lifelines, September 26-29, 1989," Edited by T.D. O'Rourke and M. Hamada, 12/1/89,(PB90-209388, A22, MF-A03).
NCEER-89-0033 "Deterministic Model for Seismic Damage Evaluation of Reinforced Concrete Structures," by lM. Bracci,A.M. Reinhorn, J.B. Mander and S.K. Kunnath, 9/27/89, (PB91-108803, A06, MF-A01).
NCEER-89-0034 "On the Relation Between Local and Global Damage Indices," by E. DiPasquale and AS. Cakmak, 8/15/89,(PB90-173865, A05, MF-A01).
NCEER-89-0035 "Cyclic Undrained Behavior of Nonplastic and Low Plasticity Silts," by AJ. Walker and H.E. Stewart,7/26/89, (PB90-183518, AIO, MF-A01).
NCEER-89-0036 "Liquefaction Potential of Surficial Deposits in the City of Buffalo, New York," by M. Budhu, R. Giese andL. Baumgrass, 1/17/89, (PB90-208455, A04, MF-A01).
NCEER-89-0037 "A Deterministic Assessment of Effects of Ground Motion Incoherence," by AS. Veletsos and Y. Tang,7/15/89, (PB90-164294, A03, MF-AOl).
NCEER-89-0038 "Workshop on Ground Motion Parameters for Seismic Hazard Mapping," July 17-18, 1989, edited by R.V.Whitman, 12/1/89, (PB90-173923, A04, MF-A01).
NCEER-89-0039 "Seismic Effects on Elevated Transit Lines of the New York City Transit Authority," by C.J. Costantino,C.A. Miller and E. Heymsfield, 12/26/89, (PB90-207887, A06, MF-A01).
NCEER-89-0040 "Centrifugal Modeling of Dynamic Soil-Structure Interaction," by K. Weissman, Supervised by J.H. Prevost,5/10/89, (PB90-207879, A07, MF-A01).
NCEER-89-0041 "Linearized Identification of Buildings With Cores for Seismic Vulnerability Assessment," by I-K. Ho andA.E. Aktan, 11/1/89, (PB90-251943, A07, MF-AOI).
NCEER-90-0001 "Geotechnical and Lifeline Aspects of the October 17, 1989 Lorna Prieta Earthquake in San Francisco," byT.D. O'Rourke, H.E. Stewart, F.T. Blackburn and T.S. Dickerman, 1/90, (PB90-208596, A05, MF-AOI).
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NCEER-90-0002 "Nonnormal Secondary Response Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D. Lutes,2/28/90, (PB90-25 1976, A07, MF-AOI).
NCEER-90-0003 "Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/16/90, (PB91-251984, A05, MFA05). This report has been replaced by NCEER-92-0018.
NCEER-90-0004 "Catalog of Strong Motion Stations in Eastern North America," by R.W. Busby, 4/3/90, (PB90-251984,A05, MF-AOI).
NCEER-90-0005 "NCEER Strong-Motion Data Base: A User Manual for the GeoBase Release (Version 1.0 for the Sun3)," byP. Friberg and K. Jacob, 3/31/90 (PB90-258062, A04, MF-AOI).
NCEER-90-0006 "Seismic Hazard Along a Crude Oil Pipeline in the Event of an 1811-1812 Type New Madrid Earthquake,"by H.H.M. Hwang and C-H.S. Chen, 4/16/90, (PB90-258054, A04, MF-AOI).
NCEER-90-0007 "Site-Specific Response Spectra for Memphis Sheahan Pumping Station," by H.H.M. Hwang and C.S. Lee,5/15/90, (PB91-10881 I, A05, MF-AOI).
NCEER-90-0008 "Pilot Study on Seismic Vulnerability of Crude Oil Transmission Systems," by T. Ariman, R. Dobry, M.Grigoriu, F. Kozin, M. O'Rourke, T. O'Rourke and M. Shinozuka, 5/25/90, (PB91-108837, A06, MF-AOI).
NCEER-90-0009 "A Program to Generate Site Dependent Time Histories: EQGEN," by G.W. Ellis, M. Srinivasan and AS.Cakmak, 1130/90, (PB91-108829, A04, MF-AOI).
NCEER-90-001O "Active Isolation for Seismic Protection of Operating Rooms," by M.E. Talbott, Supervised by M.Shinozuka, 6/8/9, (PB91-1 10205, A05, MF-AOI).
NCEER-90-00Il "Program LINEARID for Identification of Linear Structural Dynamic Systems," by CoB. Yun and M.Shinozuka, 6/25/90, (PB91-1 10312, A08, MF-AOI).
NCEER-90-0012 "Two-Dimensional Two-Phase Elasto-Plastic Seismic Response of Earth Dams," by AN. Yiagos,Supervised by J.H. Prevost, 6/20/90, (PB91-1 10197, AI3, MF-A02).
NCEER-90-00I3 "Secondary Systems in Base-Isolated Structures: Experimental Investigation, Stochastic Response andStochastic Sensitivity," by G.D. Manolis, G. Juhn, M.C. Constantinou and AM. Reinhorn, 7/1190, (PB91110320, A08, MF-AOI).
NCEER-90-0014 "Seismic Behavior of Lightly-Reinforced Concrete Column and Beam-Column Joint Details," by S.P.Pessiki, C.H. Conley, P. Gergely and R.N. White, 8/22/90, (PB91-108795, AI I, MF-A02).
NCEER-90-0015 "Two Hybrid Control Systems for Building Structures Under Strong Earthquakes," by J.N. Yang and ADanielians, 6/29/90, (PB91-125393, A04, MF-AOI).
NCEER-90-0016 "Instantaneous Optimal Control with Acceleration and Velocity Feedback," by J.N. Yang and Z. Li, 6/29/90,(PB91-125401, A03, MF-A01).
NCEER-90-0017 "Reconnaissance Report on the Northern Iran Earthquake of June 21, 1990," by M. Mehrain, 10/4/90,(PB91-125377, A03, MF-AOI).
NCEER-90-0018 "Evaluation of Liquefaction Potential in Memphis and Shelby County," by T.S. Chang, P.S. Tang, C.S. Leeand H. Hwang, 8/10/90, (PB91-125427, A09, MF-A01).
NCEER-90-0019 "Experimental and Analytical Study of a Combined Sliding Disc Bearing and Helical Steel Spring IsolationSystem," by M.C. Constantinou, A.S. Mokha and AM. Reinhorn, 10/4/90, (PB91-125385, A06, MF-A01).This report is available only through NTIS (see address given above).
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NCEER-90-0020 "Experimental Study and Analytical Prediction of Earthquake Response of a Sliding Isolation System with aSpherical Surface," by AS. Mokha, M.C. Constantinou and AM. Reinhom, lOll 1190, (PB9I-I254I9, A05,MF-AOI).
NCEER-90-0021 "Dynamic Interaction Factors for Floating Pile Groups," by G. Gazetas, K. Fan, A Kaynia and E. Kausel,9/10/90, (PB91-170381, AOS, MF-A01).
NCEER-90-0022 "Evaluation of Seismic Damage Indices for Reinforced Concrete Structures," by S. Rodriguez-Gomez andAS. Cakmak, 9/30/90, PB91-171322, A06, MF-A01).
NCEER-90-0023 "Study of Site Response at a Selected Memphis Site," by H. Desai, S. Ahmad, E.S. Gazetas and M.R. Oh,lOll 1190, (PB9I-196857, A03, MF-A01).
NCEER-90-0024 "A User's Guide to Strongmo: Version 1.0 of NCEER's Strong-Motion Data Access Tool for PCs andTerminals," by P.A. Friberg and C.A.T. Susch, 11115/90, (PB91-171272, A03, MF-A01).
NCEER-90-0025 "A Three-Dimensional Analytical Study of Spatial Variability of Seismic Ground Motions," by L-L. Hongand AH.-S. Ang, 10/30/90, (PB91-170399, A09, MF-A01).
NCEER-90-0026 "MUMOID User's Guide - A Program for the Identification of Modal Parameters," by S. Rodriguez-Gomezand E. DiPasquale, 9/30/90, (PB91-171298, A04, MF-A01).
NCEER-90-0027 "SARCF-II User's Guide - Seismic Analysis of Reinforced Concrete Frames," by S. Rodriguez-Gomez, Y.S.Chung and C. Meyer, 9/30/90, (PB91-I71280, A05, MF-AOI).
NCEER-90-0028 "Viscous Dampers: Testing, Modeling and Application in Vibration and Seismic Isolation," by N. Makrisand M.C. Constantinou, 12/20/90 (PB91-190561, A06, MF-A01).
NCEER-90-0029 "Soil Effects on Earthquake Ground Motions in the Memphis Area," by H. Hwang, C.S. Lee, K.W. Ng andT.S. Chang, 8/2/90, (PB91-190751, A05, MF-A01).
NCEER-91-0001 "Proceedings from the Third Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities andCountermeasures for Soil Liquefaction, December 17-19, 1990," edited by T.D. O'Rourke and M. Hamada,2/1/91, (PB91-179259, A99, MF-A04).
NCEER-91-0002 "Physical Space Solutions of Non-Proportionally Damped Systems," by M. Tong, Z. Liang and G.C. Lee,1/15/91, (PB91-179242, A04, MF-A01).
NCEER-91-0003 "Seismic Response of Single Piles and Pile Groups," by K. Fan and G. Gazetas, 1/10/91, (PB92-174994,A04, MF-A01).
NCEER-91-0004 "Damping of Structures: Part 1 - Theory of Complex Damping," by Z. Liang and G. Lee, 10110/91, (PB92197235, A12, MF-A03).
NCEER-91-0005 "3D-BASIS - Nonlinear Dynamic Analysis of Three Dimensional Base Isolated Structures: Part II," by S.Nagarajaiah, AM. Reinhom and M.e. Constantinou, 2/28/91, (PB91-190553, A07, MF-A01). This reporthas been replaced by NCEER-93-0011. .
NCEER-91-0006 "A Multidimensional Hysteretic Model for Plasticity Deforming Metals in Energy Absorbing Devices," byE.J. Graesser and FA CozzarelIi, 4/9/91, (pB92-108364, A04, MF-A01).
NCEER-91-0007 "A Framework for Customizable Knowledge-Based Expert Systems with an Application to a KBES forEvaluating the Seismic Resistance of Existing Buildings," by E.G. Ibarra-Anaya and S.J. Fenves, 4/9/91,(PB91-210930, A08, MF-A01).
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NCEER-91-0008 "Nonlinear Analysis of Steel Frames with Semi-Rigid Connections Using the Capacity Spectrum Method,"by G.G. Deierlein, SoH. Hsieh, Y-J. Shen and J.F. Abel, 7/2/91, (PB92-113828, A05, MF-AOI).
NCEER-91-0009 "Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/30/91, (PB91-212142, A06, MFAOI). This report has been replaced by NCEER-92-0018.
NCEER-91-0010 "Phase Wave Velocities and Displacement Phase Differences in a Harmonically Oscillating Pile," by N.Makris and G. Gazetas, 7/8/91, (PB92-108356, A04, MF-AOI).
NCEER-91-0011 "Dynamic Characteristics of a Full-Size Five-Story Steel Structure and a 2/5 Scale Model," by K.C. Chang,G.C. Yao, G.C. Lee, D.S. Hao and Y.C. Yeh," 7/2/91, (pB93-116648, A06, MF-A02).
NCEER-91-0012 "Seismic Response of a 2/5 Scale Steel Structure with Added Viscoelastic Dampers," by K.C. Chang, T.T.Soong, SoT. Oh and M.L. Lai, 5/17/91, (PB92-110816, A05, MF-AOI).
NCEER-91-0013 "Earthquake Response of Retaining Walls; Full-Scale Testing and Computational Modeling," by S.Alampalli and A-W.M. Elgamal, 6/20/91, to be published.
NCEER-91-0014· "3D-BASIS-M: Nonlinear Dynamic Analysis of Multiple Building Base Isolated Structures," by P.C.Tsopelas, S. Nagarajaiah, M.e. Constantinou and AM. Reinhom, 5/28/91, (PB92-113885, A09, MF-A02).
NCEER-91-0015 "Evaluation of SEAOC Design Requirements for Sliding Isolated Structures," by D. Theodossiou and M.C.Constantinou, 6/10/91, (PB92-114602, All, MF-A03).
NCEER-91-0016 "Closed-Loop Modal Testing of a 27-Story Reinforced Concrete Flat Plate-Core Building," by H.R.Somaprasad, T. Toksoy, H. Yoshiyuki and AE. Aktan, 7/15/91, (PB92-129980, A07, MF-A02).
NCEER-91-0017 "Shake Table Test of a 1/6 Scale Two-Story Lightly Reinforced Concrete Building," by AG. El-Attar, R.N.White and P. Gergely, 2/28/91, (PB92-222447, A06, MF-A02).
NCEER-91-0018 "Shake Table Test ofa 1/8 Scale Three-Story Lightly Reinforced Concrete Building," by AG. El-Attar, R.N.White and P. Gergely, 2/28/91, (PB93-116630, A08, MF-A02).
NCEER-91-0019 "Transfer Functions for Rigid Rectangular Foundations," by AS. Veletsos, AM. Prasad and W.H. Wu,7/31/91, to be published.
NCEER-91-0020 "Hybrid Control of Seismic-Excited Nonlinear and Inelastic Structural Systems," by J.N. Yang, Z. Li and ADanielians, 8/1/91, (PB92-143 171, A06, MF-A02).
NCEER-91-0021 "The NCEER-91 Earthquake Catalog: Improved Intensity-Based Magnitudes and Recurrence Relations forU.S. Earthquakes East of New Madrid," by L. Seeber and J.G. Armbruster, 8/28/91, (pB92-176742, A06,MF-A02).
NCEER-91-0022 "Proceedings from the Implementation of Earthquake Planning and Education in Schools: The Need forChange - The Roles of the Changemakers," by K.E.K. Ross and F. Winslow, 7/23/91, (PB92-129998, A12,MF-A03).
NCEER-91-0023 "A Study of Reliability-Based Criteria for Seismic Design of Reinforced Concrete Frame Buildings," byH.H.M. Hwang and H-M. Hsu, 8/10/91, (PB92-140235, A09, MF-A02).
NCEER-91-0024 "Experimental Verification of a Number of Structural System Identification Algorithms," by R.G. Ghanem,H. Gavin and M. Shinozuka, 9/18/91, (PB92-176577, A18, MF-A04).
NCEER-91-0025 "Probabilistic Evaluation of Liquefaction Potential," by H.H.M. Hwang and C.S. Lee," 11/25/91, (PB92143429, A05, MF-AOI).
NCEER-91-0026 "Instantaneous Optimal Control for Linear, Nonlinear and Hysteretic Structures - Stable Controllers," by J.N.Yang and Z. Li, 11/15/91, (PB92-163807, A04, MF-AOI).
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NCEER-91-0027 "Experimental and Theoretical Study of a Sliding Isolation System for Bridges," by M.C. Constantinou, A.Kartoum, A.M. Reinhorn and P. Bradford, 11/15/91, (PB92-176973, AIO, MF-A03).
NCEER-92-0001 "Case Studies of Liquefaction and Lifeline Performance During Past Earthquakes, Volume 1: Japanese CaseStudies," Edited by M. Hamada and T. O'Rourke, 2/17/92, (PB92-197243, A18, MF-A04).
NCEER-92-0002 "Case Studies of Liquefaction and Lifeline Performance During Past Earthquakes, Volume 2: United StatesCase Studies," Edited by T. O'Rourke and M. Hamada, 2/17/92, (PB92-197250, A20, MF-A04).
NCEER-92-0003 "Issues in Earthquake Education," Edited by K. Ross, 2/3/92, (PB92-222389, A07, MF-A02).
NCEER-92-0004 "Proceedings from the First U.S. - Japan Workshop on Earthquake Protective Systems for Bridges," Editedby I.G. Buckle, 2/4/92, (PB94-142239, A99, MF-A06).
NCEER-92-0005 "Seismic Ground Motion from a Haskell-Type Source in a Multiple-Layered Half-Space," A.P. Theoharis,G. Deodatis and M. Shinozuka, 1/2/92, to be published.
NCEER-92-0006 "Proceedings from the Site Effects Workshop," Edited by R. Whitman, 2/29/92, (PB92-197201, A04, MFAOl).
NCEER-92-0007 "Engineering Evaluation of Permanent Ground Deformations Due to Seismically-Induced Liquefaction," byM.H. Baziar, R. Dobry and A-W.M. Elgamal, 3/24/92, (PB92-222421, AB, MF-A03).
NCEER-92-0008 "A Procedure for the Seismic Evaluation of Buildings in the Central and Eastern United States," by C.D.Poland and 1.0. Malley, 4/2/92, (PB92-222439, A20, MF-A04).
NCEER-92-0009 "Experimental and Analytical Study of a Hybrid Isolation System Using Friction Controllable SlidingBearings," by M.Q. Feng, S. Fujii and M. Shinozuka, 5/15/92, (PB93-150282, A06, MF-A02).
NCEER-92-001O "Seismic Resistance of Slab-Column Connections in Existing Non-Ductile Flat-Plate Buildings," by A.1.Durrani and Y. Du, 5/18/92, (PB93-116812, A06, MF-A02).
NCEER-92-0011 "The Hysteretic and Dynamic Behavior of Brick Masonry Walls Upgraded by Ferrocement Coatings UnderCyclic Loading and Strong Simulated Ground Motion," by H. Lee and S.P. Prawel, 5/11192, to be published.
NCEER-92-0012 "Study of Wire Rope Systems for Seismic Protection of Equipment in Buildings," by G.F. Demetriades,M.C. Constantinou and A.M. Reinhorn, 5/20/92, (PB93-116655, A08, MF-A02).
NCEER-92-0013 "Shape Memory Structural Dampers: Material Properties, Design and Seismic Testing," by P.R. Witting andFA Cozzarelli, 5/26/92, (PB93-116663, A05, MF-AOl).
NCEER-92-0014 "Longitudinal Permanent Ground Deformation Effects on Buried Continuous Pipelines," by M.l O'Rourke,and C. Nordberg, 6/15/92, (PB93-116671, A08, MF-A02).
NCEER-92-0015 "A Simulation Method for Stationary Gaussian Random Functions Based on the Sampling Theorem," by M.Grigoriu and S. Balopoulou, 6/11/92, (PB93-127496, A05, MF-AOl).
NCEER-92-0016 "Gravity-Load-Designed Reinforced Concrete Buildings: Seismic Evaluation of Existing Construction andDetailing Strategies for Improved Seismic Resistance," by G.W. Hoffmann, S.K. Kunnath, A.M. Reinhomand J.B. Mander, 7/15/92, (PB94-142007, A08, MF-A02).
NCEER-92-0017 "Observations on Water System and Pipeline Performance in the Limon Area of Costa Rica Due to the April22, 1991 Earthquake," by M. O'Rourke and D. Ballantyne, 6/30/92, (PB93-126811, A06, MF-A02).
NCEER-92-0018 "Fourth Edition of Earthquake Education Materials for Grades K-12," Edited by K.E.K. Ross, 8/10/92,(PB93-114023, A07, MF-A02).
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NCEER-92-0019 "Proceedings from the Fourth Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilitiesand Countermeasures for Soil Liquefaction," Edited by M. Hamada and T.D. O'Rourke, 8/12/92, (PB93163939, A99, MF-Ell).
NCEER-92-0020 "Active Bracing System: A Full Scale Implementation of Active Control," by A.M. Reinhorn, T.T. Soong,R.c. Lin, M.A. Riley, YP. Wang, S. Aizawa and M. Higashino, 8/14/92, (PB93-1275 12, A06, MF-A02).
NCEER-92-0021 "Empirical Analysis of Horizontal Ground Displacement Generated by Liquefaction-Induced LateralSpreads," by S.F. Bartlett and T.L. Youd, 8/l7/92, (PB93-188241, A06, MF-A02).
NCEER-92-0022 "IDARC Version 3.0: Inelastic Damage Analysis of Reinforced Concrete Structures," by S.K. Kunnath,A.M. Reinhom and R.F. Lobo, 8/3l/92, (PB93-227502, A07, MF-A02).
NCEER-92-0023 "A Semi-Empirical Analysis of Strong-Motion Peaks in Terms of Seismic Source, Propagation Path andLocal Site Conditions, by M. Kamiyama, MJ. O'Rourke and R. Flores-Berrones, 9/9/92, (PB93-150266,A08, MF-A02).
NCEER-92-0024 "Seismic Behavior of Reinforced Concrete Frame Structures with Nonductile Details, Part I: Summary ofExperimental Findings of Full Scale Beam-Column Joint Tests," by A. Beres, R.N. White and P. Gergely,9/30/92, (PB93-227783, A05, MF-A01).
NCEER-92-0025 "Experimental Results of Repaired and Retrofitted Beam-Column Joint Tests in Lightly Reinforced ConcreteFrame Buildings," by A. Beres, S. El-Borgi, R.N. White and P. Gergely, 10/29/92, (PB93-227791, A05, MFA01).
NCEER-92-0026 "A Generalization of Optimal Control Theory: Linear and Nonlinear Structures," by J.N. Yang, Z. Li and S.Vongchavalitkul, 1l/2/92, (PB93-188621, A05, MF-A01).
NCEER-92-0027 "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part I Design and Properties of a One-Third Scale Model Structure," by J.M. Bracci, A.M. Reinhorn and J.B.Mander, 12/l/92, (PB94-104502, A08, MF-A02).
NCEER-92-0028 "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part II Experimental Performance of Subassemblages," by L.E. Aycardi, 1.B. Mander and A.M. Reinhorn, 12/1/92,(PB94-104510, A08, MF-A02).
NCEER-92-0029 "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part III Experimental Performance and Analytical Study of a Structural Model," by 1.M. Bracci, A.M. Reinhom andJ.B. Mander, 12/l/92, (PB93-227528, A09, MF-A01).
NCEER-92-0030 "Evaluation of Seismic Retrofit of Reinforced Concrete Frame Structures: Part I - Experimental Performanceof Retrofitted Subassemblages," by D. Choudhuri, 1.B. Mander and A.M. Reinhom, 12/8/92, (PB93-198307,A07, MF-A02).
NCEER-92-0031 "Evaluation of Seismic Retrofit of Reinforced Concrete Frame Structures: Part II - ExperimentalPerformance and Analytical Study of a Retrofitted Structural Model," by J.M. Bracci, A.M. Reinhom and1.B. Mander, 12/8/92, (PB93-198315, A09, MF-A03).
NCEER-92-0032 "Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental FluidViscous Dampers," by M.C. Constantinou and M.D. Symans, 12/2l/92, (PB93-191435, AlO, MF-A03).
NCEER-92-0033 "Reconnaissance Report on the Cairo, Egypt Earthquake of October 12, 1992," by M. Khater, 12/23/92,(PB93-188621, A03, MF-A01).
NCEER-92-0034 "Low-Level Dynamic Characteristics of Four Tall Flat-Plate Buildings in New York City," by H. Gavin, S.Yuan, J. Grossman, E. Pekelis and K. Jacob, 12/28/92, (PB93-188217, A07, MF-A02).
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NCEER-93-0001 "An Experimental Study on the Seismic Performance of Brick-Infilled Steel Frames With and WithoutRetrofit," by 1.B. Mander, B. Nair, K. Wojtkowski and 1. Ma, 1/29/93, (PB93-22751O, A07, MF-A02).
NCEER-93-0002 "Social Accounting for Disaster Preparedness and Recovery Planning," by S. Cole, E. Pantoja and V. Razak,2/22/93, (PB94-142114, A12, MF-A03).
NCEER-93-0003 "Assessment of 1991 NEHRP Provisions for Nonstructural Components and Recommended Revisions," byT.T. Soong, G. Chen, Z. Wu, R-H. Zhang and M. Grigoriu, 3/1/93, (PB93-188639, A06, MF-A02).
NCEER-93-0004 "Evaluation of Static and Response Spectrum Analysis Procedures of SEAOCIUBC for Seismic IsolatedStructures," by C.W. Winters and M.C. Constantinou, 3/23/93, (PB93-198299, AI0, MF-A03).
NCEER-93-0005 "Earthquakes in the Northeast - Are We Ignoring the Hazard? A Workshop on Earthquake Science andSafety for Educators," edited by K.E.K. Ross, 4/2/93, (PB94-103066, A09, MF-A02).
NCEER-93-0006 "Inelastic Response of Reinforced Concrete Structures with Viscoelastic Braces," by R.F. Lobo, 1.M. Bracci,K.L. Shen, AM. Reinhorn and T.T. Soong, 4/5/93, (PB93-227486, A05, MF-A02).
NCEER-93-0007 "Seismic Testing ofInstallation Methods for Computers and Data Processing Equipment," by K. Kosar, T.T.Soong, K.L. Shen, l.A. HoLung and Y.K. Lin, 4/12/93, (PB93-198299, A07, MF-A02).
NCEER-93-0008 "Retrofit of Reinforced Concrete Frames Using Added Dampers," by A Reinhorn, M. Constantinou and C.Li, to be published.
NCEER-93-0009 "Seismic Behavior and Design Guidelines for Steel Frame Structures with Added Viscoelastic Dampers," byK.C. Chang, M.L. Lai, T.T. Soong, D.S. Hao and Y.C. Yeh, 5/1/93, (PB94-141959, A07, MF-A02).
NCEER-93-0010 "Seismic Performance of Shear-Critical Reinforced Concrete Bridge Piers," by 1.B. Mander, S.M. Waheed,M.T.A. Chaudhary and S.S. Chen, 5/12/93, (PB93-227494, A08, MF-A02).
NCEER-93-0011 "3D-BASIS-TABS: Computer Program for Nonlinear Dynamic Analysis of Three Dimensional Base IsolatedStructures," by S. Nagarajaiah, C. Li, AM. Reinhorn and M.C. Constantinou, 8/2/93, (PB94-141819, A09,MF-A02).
NCEER-93-0012 "Effects of Hydrocarbon Spills from an Oil Pipeline Break on Ground Water," by 0.1. Helweg and H.H.M.Hwang, 8/3/93, (PB94-141942, A06, MF-A02).
NCEER-93-0013 "Simplified Procedures for Seismic Design of Nonstructriral Components and Assessment of Current CodeProvisions," by M.P. Singh, L.E. Suarez, E.E. Matheu and G.O. Maldonado, 8/4/93, (PB94-141827, A09,MF-A02).
NCEER-93-0014 "An Energy Approach to Seismic Analysis and Design of Secondary Systems," by G. Chen and T.T. Soong,8/6/93, (PB94-142767, All, MF-A03).
NCEER-93-0015 "Proceedings from School Sites: Becoming Prepared for Earthquakes - Commemorating the ThirdAnniversary of the Lorna Prieta Earthquake," Edited by F.E. Winslow and K.E.K. Ross, 8/16/93, (PB94154275, A16, MF-A02).
NCEER-93-0016 "Reconnaissance Report of Damage to Historic Monuments in Cairo, Egypt Following the October 12, 1992Dahshur Earthquake," by D. Sykora, D. Look, G. Croci, E. Karaesmen and E. Karaesmen, 8/19/93, (pB94142221, A08, MF-A02).
NCEER-93-0017 "The Island of Guam Earthquake of August 8, 1993," by S.W. Swan and S.K. Harris, 9/30/93, (PB94141843, A04, MF-AOl).
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NCEER-93-0018 "Engineering Aspects of the October 12, 1992 Egyptian Earthquake," by A.W. Elgamal, M. Amer, K.Adalier and A. Abul-Fadl, 10/7/93, (PB94-141983, A05, MF-AOI).
NCEER-93-0019 "Development of an Earthquake Motion Simulator and its Application in Dynamic Centrifuge Testing," by I.Krstelj, Supervised by J.H. Prevost, 10/23/93, (PB94-181773, A-IO, MF-A03).
NCEER-93-0020 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of a Friction Pendulum System (FPS)," by M.C. Constantinou, P.Tsopelas, Y-S. Kim and S. Okamoto, 11/1/93, (PB94-142775, A08, MF-A02).
NCEER-93-0021 "Finite Element Modeling of Elastomeric Seismic Isolation Bearings," by LJ. Billings, Supervised by R.Shepherd, 11/8/93, to be published.
NCEER-93-0022 "Seismic Vulnerability of Equipment in Critical Facilities: Life-Safety and Operational Consequences," byK. Porter, G.S. Johnson, M.M. Zadeh, C. Scawthorn and S. Eder, 11/24/93, (PB94-181765, A16, MF-A03).
NCEER-93-0023 "Hokkaido Nansei-oki, Japan Earthquake of July 12, 1993, by P.I. Yanev and C.R. Scawthorn, 12/23/93,(PB94-181500, A07, MF-AOI).
NCEER-94-0001 "An Evaluation of Seismic Serviceability of Water Supply Networks with Application to the San FranciscoAuxiliary Water Supply System," by I. Markov, Supervised by M. Grigoriu and T. O'Rourke, 1/21/94,(PB94-204013, A07, MF-A02).
NCEER-94-0002 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of Systems Consisting of Sliding Bearings, Rubber Restoring ForceDevices and Fluid Dampers," Volumes I and II, by P. Tsopelas, S. Okamoto, M.C. Constantinou, D. Ozakiand S. Fujii, 2/4/94, (PB94-181740, A09, MF-A02 and PB94-181757, A12, MF-A03).
NCEER-94-0003 "A Markov Model for Local and Global Damage Indices in Seismic Analysis," by S. Rahman and M.Grigoriu, 2/18/94, (PB94-206000, A12, MF-A03).
NCEER-94-0004 "Proceedings from the NCEER Workshop on Seismic Response of Masonry Infills," edited by D.P. Abrams,3/1/94, (PB94-180783, A07, MF-A02).
NCEER-94-0005 "The Northridge, California Earthquake of January 17, 1994: General Reconnaissance Report," edited byJ.D. Goltz, 3/11/94, (PBI93943, AIO, MF-A03).
NCEER-94-0006 "Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part I - Evaluation of SeismicCapacity," by G.A. Chang and J.8. Mander, 3/14/94, (PB94-219185, Al I, MF-A03).
NCEER-94-0007 "Seismic Isolation of Multi-Story Frame Structures Using Spherical Sliding Isolation Systems," by T.M. AIHussaini, V.A. Zayas and M.e. Constantinou, 3/17/94, (PBI93745, A09, MF-A02).
NCEER-94-0008 "The Northridge, California Earthquake of January 17, 1994: Performance of Highway Bridges," edited byI.G. Buckle, 3/24/94, (PB94-193851, A06, MF-A02).
NCEER-94-0009 "Proceedings of the Third U.S.-Japan Workshop on Earthquake Protective Systems for Bridges," edited byI.G. Buckle and I. Friedland, 3/31/94, (PB94-195815, A99, MF-A06).
NCEER-94-0010 "3D-BASIS-ME: Computer Program for Nonlinear Dynamic Analysis of Seismically Isolated Single andMultiple Structures and Liquid Storage Tanks," by P.C. Tsopelas, M.C. Constantinou and A.M. Reinhorn,4/12/94, (PB94-204922, A09, MF-A02).
NCEER-94-0011 "The Northridge, California Earthquake of January 17, 1994: Performance of Gas Transmission Pipelines,"by T.D. O'Rourke and M.C. Palmer, 5/16/94, (PB94-204989, A05, MF-AOI).
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NCEER-94-0012 "Feasibility Study of Replacement Procedures and Earthquake Performance Related to Gas TransmissionPipelines," by T.D. O'Rourke and M.C. Palmer, 5/25/94, (PB94-206638, A09, MF-A02).
NCEER-94-0013 "Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part II - Evaluation of SeismicDemand," by GA Chang and 1.B. Mander, 6/1/94, (PB95-18106, A08, MF-A02).
NCEER-94-0014 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of a System Consisting of Sliding Bearings and Fluid RestoringForcelDamping Devices," by P. Tsopelas and M.C. Constantinou, 6/13/94, (PB94-219144, AI0, MF-A03).
NCEER-94-0015 "Generation of Hazard-Consistent Fragility Curves for Seismic Loss Estimation Studies," by H. Hwang andJ-R. HilO, 6/14/94, (PB95-181996, A09, MF-A02).
NCEER-94-0016 "Seismic Study of Building Frames with Added Energy-Absorbing Devices," by W.S. Pong, C.S. Tsai andG.C. Lee, 6/20/94, (PB94-219136, AlO, A03).
NCEER-94-0017 "Sliding Mode Control for Seismic-Excited Linear and Nonlinear Civil Engineering Structures," by 1. Yang,1. Wu, A Agrawal and Z. Li, 6/21194, (PB95-138483, A06, MF-A02).
NCEER-94-0018 "3D-BASIS-TABS Version 2.0: Computer Program for Nonlinear Dynamic Analysis of Three DimensionalBase Isolated Structures," by AM. Reinhom, S. Nagarajaiah, M.C. Constantinou, P. Tsopelas and R. Li,6/22/94, (PB95-182176, A08, MF-A02).
NCEER-94-0019 "Proceedings of the International Workshop on Civil Infrastructure Systems: Application of IntelligentSystems and Advanced Materials on Bridge Systems," Edited by G.C. Lee and K.C. Chang, 7/18/94, (PB95252474, A20, MF-A04).
NCEER-94-0020 "Study of Seismic Isolation Systems for Computer Floors," by V. Lambrou and M.e. Constantinou, 7/19/94,(PB95-138533, AlO, MF-A03).
NCEER-94-0021 "Proceedings of the U.S.-Italian Workshop on Guidelines for Seismic Evaluation and Rehabilitation ofUnreinforced Masonry Buildings," Edited by D.P. Abrams and G.M. Calvi, 7/20/94, (PB95-138749, A13,MF-A03).
NCEER-94-0022 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of a System Consisting of Lubricated PTFE Sliding Bearings and MildSteel Dampers," by P. Tsopelas and M.C. Constantinou, 7/22/94, (PB95-182184, A08, MF-A02).
NCEER-94-0023 "Development of Reliability-Based Design Criteria for Buildings Under Seismic Load," by Y.K. Wen, H.Hwang and M. Shinozuka, 8/1194, (PB95-211934, A08, MF-A02).
NCEER-94-0024 "Experimental Verification of Acceleration Feedback Control Strategies for an Active Tendon System," bySJ. Dyke, B.F. Spencer, Jr., P. Quast, M.K. Sain, D.C. Kaspari, Jr. and T.T. Soong, 8/29/94, (pB95-212320,A05, MF-AOl).
NCEER-94-0025 "Seismic Retrofitting Manual for Highway Bridges," Edited by I.G. Buckle and I.F. Friedland, published bythe Federal Highway Administration (PB95-212676, A15, MF-A03).
NCEER-94-0026 "Proceedings from the Fifth U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities andCountermeasures Against Soil Liquefaction," Edited by T.D. O'Rourke and M. Hamada, 11/7/94, (PB95220802, A99, MF-E08).
NCEER-95-0001 "Experimental and Analytical Investigation of Seismic Retrofit of Structures with Supplemental Damping:Part 1 - Fluid Viscous Damping Devices," by AM. Reinhom, C. Li and M.C. Constantinou, 113/95, (PB95266599, A09, MF-A02).
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NCEER-95-0002 "Experimental and Analytical Study of Low-Cycle Fatigue Behavior of Semi-Rigid Top-And-Seat AngleConnections," by G. Pekcan, 1.B. Mander and S.S. Chen, 1/5/95, (PB95-220042, A07, MF-A02).
NCEER-95-0003 "NCEER-ATC Joint Study on Fragility of Buildings," by T. Anagnos, C. Rojahn and AS. Kiremidjian,1/20/95, (PB95-220026, A06, MF-A02).
NCEER-95-0004 "Nonlinear Control Algorithms for Peak Response Reduction," by Z. Wu, T.T. Soong, V. GattuIli and R.C.Lin, 2/16/95, (PB95-220349, A05, MF-A01).
NCEER-95-0005 "Pipeline Replacement Feasibility Study: A Methodology for Minimizing Seismic and Corrosion Risks toUnderground Natural Gas Pipelines," by R.T. Eguchi, H.A. Seligson and D.G. Honegger, 3/2/95, (PB95252326, A06, MF-A02).
NCEER-95-0006 "Evaluation of Seismic Performance of an l1-Story Frame Building During the 1994 NorthridgeEarthquake," by F. Naeim, R. DiSulio, K. Benuska, A Reinhorn and C. Li, to be published.
NCEER-95-0007 "Prioritization of Bridges for Seismic Retrofitting," by N. Basoz and AS. Kiremidjian, 4/24/95, (PB95252300, A08, MF-A02).
NCEER-95-0008 "Method for Developing Motion Damage Relationships for Reinforced Concrete Frames," by A Singhaland AS. Kiremidjian, 5/11/95, (PB95-266607, A06, MF-A02).
NCEER-95-0009 "Experimental and Analytical Investigation of Seismic Retrofit of Structures with Supplemental Damping:Part II - Friction Devices," by C. Li and AM. Reinhorn, 7/6/95, (PB96-128087, All, MF-A03).
NCEER-95-0010 "Experimental Performance and Analytical Study of a Non-Ductile Reinforced Concrete Frame StructureRetrofitted with Elastomeric Spring Dampers," by G. Pekcan, 1.B. Mander and S.S. Chen, 7/14/95, (PB96137161, A08, MF-A02).
NCEER-95-0011 "Development and Experimental Study of Semi-Active Fluid Damping Devices for Seismic Protection ofStructures," by M.D. Symans and M.C. Constantinou, 8/3/95, (PB96-136940, A23, MF-A04).
NCEER-95-0012 "Real-Time Structural Parameter Modification (RSPM): Development of Innervated Structures," by Z.Liang, M. Tong and G.C. Lee, 4/11/95, (PB96-137153, A06, MF-A01).
NCEER-95-0013 "Experimental and Analytical Investigation of Seismic Retrofit of Structures with Supplemental Damping:Part III - Viscous Damping Walls," by AM. Reinhorn and C. Li, 10/1/95, (PB96-176409, All, MF-A03).
NCEER-95-0014 "Seismic Fragility Analysis of Equipment and Structures in a Memphis Electric Substation," by J-R. Huoand H.H.M. Hwang, (PB96-128087, A09, MF-A02), 8/10/95.
NCEER-95-0015 "The Hanshin-Awaji Earthquake ofJanuary 17, 1995: Performance of Lifelines," Edited by M. Shinozuka,11/3/95, (PB96-176383, A15, MF-A03).
NCEER-95-0016 "Highway Culvert Performance During Earthquakes," by T.L. Youd and C.J. Beckman, available asNCEER-96-0015.
NCEER-95-0017 "The Hanshin-Awaji Earthquake of January 17, 1995: Performance of Highway Bridges," Edited by I.G.Buckle, 12/1/95, to be published.
NCEER-95-0018 "Modeling of Masonry Infill Panels for Structural Analysis," by AM. Reinhorn, A Madan, R.E. Valles, Y.Reichmann and J.B. Mander, 12/8/95.
NCEER-95-0019 "Optimal Polynomial Control for Linear and Nonlinear Structures," by AK. Agrawal and 1.N. Yang,12111/95, (PB96-168737, A07, MF-A02).
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NCEER-95-0020 "Retrofit of Non-Ductile Reinforced Concrete Frames Using Friction Dampers," by R.S. Rao, P. Gergelyand R.N. White, 12/22/95, (PB97-133508, AIO, MF-A02).
NCEER-95-0021 "Parametric Results for Seismic Response of Pile-Supported Bridge Bents," by G. Mylonakis, A Nikolaouand G. Gazetas, 12/22/95, (PB97-100242, A12, MF-A03).
NCEER-95-0022 "Kinematic Bending Moments in Seismically Stressed Piles," by A Nikolaou, G. Mylonakis and G.Gazetas, 12/23/95.
NCEER-96-0001 "Dynamic Response of Unreinforced Masonry Buildings with Flexible Diaphragms," by AC. Costley andD.P. Abrams," 10/10/96.
NCEER-96-0002 "State of the Art Review: Foundations and Retaining Structures," by I. Po Lam, to be published.
NCEER-96-0003 "Ductility of Rectangular Reinforced Concrete Bridge Columns with Moderate Confinement," by N.Wehbe, M. Saiidi, D. Sanders and B. Douglas, 11/7/96, (PB97-133557, A06, MF-A02).
NCEER-96-0004 "Proceedings of the Long-Span Bridge Seismic Research Workshop," edited by LG. Buckle and LM.Friedland, to be published.
NCEER-96-0005 "Establish Representative Pier Types for Comprehensive Study: Eastern United States," by J. Kulicki and Z.Prucz, 5/28/96.
NCEER-96-0006 "Establish Representative Pier Types for Comprehensive Study: Western United States," by R. Imbsen, R.ASchamber and T.A. Osterkamp, 5/28/96.
NCEER-96-0007 "Nonlinear Control Techniques for Dynamical Systems with Uncertain Parameters," by R.G. Ghanem andM.1. Bujakov, 5/27/96, (PB97-100259, A17, MF-A03).
NCEER-96-0008 "Seismic Evaluation of a 30-Year Old Non-Ductile Highway Bridge Pier and Its Retrofit," by lB. Mander,B. Mahmoodzadegan, S. Bhadra and S.S. Chen, 5/31/96.
NCEER-96-0009 "Seismic Performance of a Model Reinforced Concrete Bridge Pier Before and After Retrofit," by lB.Mander, IH. Kim and C.A. Ligozio, 5/31/96.
NCEER-96-0010 "IDARC2D Version 4.0: A Computer Program for the Inelastic Damage Analysis of Buildings," by R.E.Valles, AM. Reinhorn, S.K. Kunnath, C. Li and A Madan, 6/3/96, (PB97-100234, A17, MF-A03).
NCEER-96-0011 "Estimation of the Economic Impact of Multiple Lifeline Disruption: Memphis Light, Gas and WaterDivision Case Study," by S.E. Chang, H.A. Seligson and R.T. Eguchi, 8/16/96, (pB97-133490, All, MFA03).
NCEER-96-0012 "Proceedings from the Sixth Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities andCountermeasures Against Soil Liquefaction, Edited by M. Hamada and T. O'Rourke, 9/11/96, (pB97133581, A99, MF-A06).
NCEER-96-0013 "Chemical Hazards, Mitigation and Preparedness in Areas of High Seismic Risk: A Methodology forEstimating the Risk of Post-Earthquake Hazardous Materials Release," by H.A. Seligson, R T. Eguchi, K.lTierney and K. Richmond, 11/7/96.
NCEER-96-0014 "Response of Steel Bridge Bearings to Reversed Cyclic Loading," by IB. Mander, D-K. Kim, S.S. Chenand G.J. Premus, 11113/96, (PB97-140735, A12, MF-A03).
NCEER-96-0015 "Highway Culvert Performance During Past Earthquakes," by T.L. Youd and C.l Beckman, 11/25/96,(PB97-133532, A06, MF-AOI).
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NCEER-97-0001 "Evaluation, Prevention and Mitigation of Pounding Effects in Building Structures," by RE. Valles andA.M. Reinhorn, 2/20/97, (PB97-159552, A14, MF-A03).
NCEER-97-0002 "Seismic Design Criteria for Bridges and Other Highway Structures," by C. Rojahn, R Mayes, D.G.Anderson, 1. Clark, 1.H. Hom, RV. Nutt and MJ. O'Rourke, 4/30/97, (PB97-194658, A06, MF-A03).
NCEER-97-0003 "Proceedings of the U.S.-Italian Workshop on Seismic Evaluation and Retrofit," Edited by D.P. Abrams andG.M. Calvi, 3/19/97, (PB97-194666, A13, MF-A03).
NCEER-97-0004 "Investigation of Seismic Response of Buildings with Linear and Nonlinear Fluid Viscous Dampers," byAA Seleemah and M.C. Constantinou, 5/21/97.
NCEER-97-0005 "Proceedings of the First Workshop on Earthquake Engineering Frontiers in Transportation Facilities,"Edited by G.C. Lee and I.M. Friedland, 8/29/97.
NCEER-97-0006 "Cumulative Seismic Damage of Reinforced Concrete Bridge Piers," by S.K. Kunnath, A EI-Bahy, ATaylor and W. Stone, 9/2/97.
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NATIONALCENTER FOREARTHQUAKEENGINEERINGRESEARCH
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