Department of Civil and Environmental Engineering Stanford University
MODELING OF ASSESSMENT OF SEISMIC PERFORMANCE OF COMPOSITE FRAMES WITH REINFORCED
CONCRETE COLUMNS AND STEEL BEAMS
by
Sameh Samir Mehanny
and
Gregory G. Deierlein
Report No. 135
August 2000
The John A. Blume Earthquake Engineering Center was established to promote research and education in earthquake engineering. Through its activities our understanding of earthquakes and their effects on mankind’s facilities and structures is improving. The Center conducts research, provides instruction, publishes reports and articles, conducts seminar and conferences, and provides financial support for students. The Center is named for Dr. John A. Blume, a well-known consulting engineer and Stanford alumnus. Address: The John A. Blume Earthquake Engineering Center Department of Civil and Environmental Engineering Stanford University Stanford CA 94305-4020 (650) 723-4150 (650) 725-9755 (fax) earthquake @ce. stanford.edu http://blume.stanford.edu
©2000 The John A. Blume Earthquake Engineering Center
MODELING OF ASSESSMENT OF SEISMIC
PERFORMANCE OF COMPOSITE FRAMES
WITH REINFORCED CONCRETE COLUMNS
AND STEEL BEAMS
by
Sameh Samir Fahmy Mehanny
and
Gregory G. Deierlein
Report No. 135
August 2000
ii
iii
iv
Abstract
Composite moment frames consisting of steel beams and reinforced concrete columns (so
called RCS moment frames) are one of several types of hybrid systems gaining
acceptance as cost-effective alternatives to traditional steel or reinforced concrete frames
for seismic design. New design standards for composite moment frames have recently
been introduced in the United States, and composite RCS frames have been one focus
area investigated as part of Phase 5 (Composite and Hybrid Structures) of the US-Japan
Cooperative Earthquake Research Program. This research presents an extensive and
pioneering analytical study whose focus is on the seismic behavior of composite frames
with the objectives to (1) develop and improve existing analytical models and techniques
for the nonlinear inelastic static and time history analyses of composite RCS moment
frames, (2) propose damage indices and performance criteria to assess seismic
performance of such frames, (3) apply accurate nonlinear analysis methods to evaluate
building performance under varying seismic hazards, (4) develop and correlate stability
limit states to performance levels suggested by modern seismic codes, and (5) investigate
response dependency on ground motion parameters so as to reduce the uncertainty in
estimating median response. The ultimate goal is to achieve broader acceptance of RCS
frames in high seismic regions by demonstrating their reliability through a modern
performance-based methodology.
Our approach toward establishing a performance-based design basis for composite RCS
frames involves both evaluation of seismic damage indices with test data on member and
connection response and comparative behavioral studies between RCS and conventional
v
structural steel moment frames. Trial designs of six- and twelve-story RCS and steel
framed buildings are developed to exercise the latest seismic design criteria and standards
in the United States including the recently approved International Building Code (IBC
2000) and the 1997 AISC Seismic Provisions. Nonlinear static and time-history analyses
are run under two sets of earthquake records (general versus near-fault records with
forward directivity) that were selected and scaled to different hazard levels representative
of performance levels ranging from immediate occupancy to near collapse. Peak and
cumulative performance (i.e., damage) indices are then developed, calculated and
compared with structural acceptance criteria established using data from tests and models
of structural components. A new methodology is proposed to quantify system stability
limit states by integrating the destabilizing effects represented by local damage indices
through modified second-order inelastic stability analyses. The proposed method avoids
the need for questionable ad-hoc averaging techniques to relate local to global damage
indices. Correlation parameters between ground motion intensity measures, such as
spectral acceleration, etc., and structural damage are presented, and statistical
performance measures of global response are reported.
Supported by test data on structural components, the analyses demonstrate excellent
seismic performance of composite framed structures when evaluated both on their own
merits and in comparison with steel frames. In particular, by permitting steel beams to
run continuous through the reinforced concrete columns, the composite frames avoid the
fracture critical details that have caused problems with welded steel moment frames. The
design studies do, however, suggest areas for improving current design criteria, in
particular, the minimum strength and stiffness requirements for proportioning beams and
columns to resist seismic loads. By improving understanding of the seismic response of
composite RCS frames this research should lead to their broader utilization for seismic
regions and will contribute towards the development of more transparent and reliable
performance-based design methodologies.
vi
vii
Acknowledgements
This report is based on the PhD thesis of the first author under the supervision of the
second author. The research forms part of the US-Japan Cooperative Earthquake
Research Program Phase 5 - Composite and Hybrid Structures, supported in the United
States by the National Science Foundation under the leadership of Dr. S. C. Liu. The
authors gratefully acknowledge the National Science Foundation support (grant CMS-
9632502) and supplemental support from the Steel Structures Development Center of the
Nippon Steel Corporation. The authors conducted the research at Cornell (1996-98) and
Stanford Universities (1998-2000) and greatly appreciate the advice and support of
faculty, students, and staff of the John A. Blume Earthquake Engineering Center and the
departments of Civil and Environmental Engineering at Cornell and Stanford
Universities.
The authors would express their sincere gratitude to Dr. Hiroshi Kuramoto of the
Building Research Institute of Japan who spent a year in residence with the authors to
work on the project. Special thanks are also due to: Dr. Ryoichi Kanno of the Nippon
Steel Corporation and Dr. Sherif El Tawil of the University of Central Florida for their
participation, help and advice throughout the research; Professors C. Allin Cornell and
Helmut Krawinkler of Stanford University and Dr. Nilesh Shome of EQE, Inc. for their
advice regarding the seismic hazard analyses; Prof. Richard N. White of Cornell
University and Dr. Abdelkader K. Tayebi of Louisiana Tech for sharing their expertise on
modeling reinforced concrete structures; and Prof. Hiroshi Noguchi of Chiba University
and other participants of the US-Japan Cooperative Earthquake Research Program.
x
Table of Contents
Abstract iv
Acknowledgements vii
List of Tables xvii
List of Figures xx
Chapter 1 Introduction 1
1.1 Evolution of Composite Construction …………………………. 3
1.1.1 Pros and Cons of Composite RCS Systems ……………… 5
1.1.2 Background of Experimental and Analytical Work ……… 6
1.1.3 Current Codes and Provisions for Composite Systems ….. 9
1.2 Overview of Recent Developments in Performance-Based
Engineering ……………………………………………………..
11
1.3 Objectives ……………………………………………………… 13
1.4 Scope and Organization ………………………………………... 14
Chapter 2 Analytical Models Using Spread-of-Plasticity Approaches 17
2.1 Overview of Inelastic Analysis Models ………………………... 18
2.2 Review of Bounding Surface Model …………………………... 19
2.2.1 Single-Surface Model ……………………………………. 19
2.2.2 Two-Surface Bounding Model …………………………… 20
2.2.3 Motion of the Bounding Surface …………………………. 22
2.2.4 Plasticity Coefficients ……………………………………. 23
xi
2.3 General Bi-Symmetric Beam-Column Element in DYNAMIX .. 23
2.3.1 Element Formulation ……………………………………... 24
2.3.2 Modeling of Stiffness Degradation with Cycles …………. 29
2.3.3 Calculation of Plastic Rotation …………………………... 32
2.4 Composite Beam Model ……………………………………….. 33
2.4.1 Limitations and Assumptions …………………………….. 34
2.4.2 Element Formulation, Moment-Curvature Skeleton and
Hysteresis Model ………………………………………….
35
2.4.3 Elastic Stiffnesses and Ultimate Strength Calculation for
Composite Beam ………………………………………….
41
2.4.4 Verification Study ………………………………………... 45
2.5 Composite Joint Panel Model ………………………………….. 51
2.5.1 Joint Panel Kinematics …………………………………… 52
2.5.2 Joint Panel Moment-Distortion Hysteresis Models ……… 53
2.6 Modeling of Geometric Nonlinearity ………………………….. 55
2.6.1 Definitions, Assumptions and Limitations ……………….. 56
2.6.2 Total Geometric Stiffness Matrix Based on Hermitian
Shape Functions …………………………………………..
57
2.6.3 Geometric Stiffness Matrix as a Function of Spread-of-
Plasticity …………………………………………………..
58
2.6.4 General Comments ……………………………………….. 59
2.7 Overview of the Scheme of the Numerical Integration of the
Equation of Motion for Time History Analysis ………………...
62
2.8 Summary ……………………………………………………….. 65
Chapter 3 Stiffness Modeling of Reinforced Concrete Beam-Columns 67
3.1 Introduction …………………………………………………….. 68
3.2 Basic Behavior and Design Issues ……………………………... 70
3.2.1 Beam-Column Behavior …………………………………. 70
3.2.2 Frame Behavior and Design ……………………………… 72
3.3 Inelastic Frame Analysis ……………………………………….. 74
xii
3.4 Review of Stiffness Guidelines ………………………………… 75
3.4.1 ACI-318 Building Code (1995) ………………………….. 77
3.4.2 FEMA 273 ………………………………………………... 78
3.4.3 New Zealand Standard (1995) …………………………… 78
3.4.4 CEB State-of-the-Art Report (CEB 1996) ……………….. 79
3.4.5 Architectural Institute of Japan Standard (1991) ………… 81
3.5 Proposed Stiffness Coefficients ………………………………... 82
3.6 Verification Study ……………………………………………… 83
3.6.1 Description of Test Specimens …………………………... 84
3.6.2 Comparisons and Discussions ……………………………. 84
3.6.3 Cyclic Behavior …………………………………………... 87
3.7 Effective Shear Stiffness (GAeff) ………………………………. 92
3.8 Summary and Concluding Remarks …………………………… 94
Chapter 4 Seismic Damage Indices 96
4.1 Introduction …………………………………………………….. 97
4.2 When Do We Need Damage Indices? …………………………. 98
4.3 Definition of Damage Function and Damage Index …………… 99
4.4 Classification Schemes of Damage Indices and Categorization
of Damage ………………………………………………………
101
4.4.1 Local Versus Global Indices ……………………………... 102
4.4.2 Categorization of Damage ……………………………….. 108
4.5 Proposed Damage Indices ……………………………………… 109
4.5.1 Energy-Based Damage Index …………………………….. 110
4.5.1.1 Some details and advantages of the energy-based
damage model ………………………………………
114
4.5.2 Ductility-Based Damage Index …………………………... 116
4.5.2.1 Some details of the ductility-based damage index …. 117
4.6 Identification of Deformation and Energy Values
Corresponding to Failure ……………………………………….
118
4.6.1 Reinforced Concrete Columns …………………………… 118
xiii
4.6.2 Steel and Composite Beams ……………………………… 123
4.6.2.1 Case of steel beams and composite beams under
hogging bending …………………………………….
125
4.6.2.2 Case of composite beams under sagging bending …. 128
4.6.3 Composite – Reinforced Concrete-Steel – Joint Panels ….. 129
4.7 Calibration and Verification …………………………………… 132
4.7.1 Reinforced Concrete Columns …………………………… 133
4.7.2 Steel and Composite Beams ……………………………… 138
4.7.3 Composite Reinforced Concrete-Steel Joints ……………. 144
4.8 Useful Conclusions and Guidelines for Damage Categorization 150
4.9 Summary ……………………………………………………….. 153
Chapter 5 Case Study Buildings Design and Selection of Records 155
5.1 Overview of Different Seismic-Resistant Design Methods ……. 155
5.1.1 Equivalent Lateral Force Static Procedure ……………….. 156
5.1.1.1 Rationale of the R and Cd factors …………………... 161
5.1.2 Modal Response Spectrum Analysis ……………………... 165
5.1.3 Time History Analysis …………………………………… 166
5.1.4 Static Inelastic Pushover Analysis ……………………….. 167
5.2 Case Study Building Designs ………………………………….. 172
5.2.1 Overview of the ASCE Design Criteria for Composite
Beam-Column Joints ……………………………………...
182
5.2.2 Summary of Design Values and Governing Criteria …….. 185
5.3 Selection of Ground Motion Records ………………………….. 191
5.3.1 General Records ………………………………………….. 194
5.3.2 Near-Fault Records and Directivity Effects ……………… 195
5.4 Summary ……………………………………………………….. 198
Chapter 6 Detailed Performance Study of 6-Story RCS Frame 200
6.1 Modeling and Analysis Assumptions ………………………….. 201
6.1.1 Frame Loading and Mass Characteristics ……………….. 201
xiv
6.1.2 Numerical Models ………………………………………... 201
6.1.3 Modeling of Damping ……………………………………. 203
6.2 Static Inelastic (Push-Over) Analysis ………………………….. 205
6.2.1 Relating Global, IDR, and Local, θp, Responses for Static
Pushover Results ………………………………………….
210
6.3 Nonlinear Dynamic (Time History) Analyses …………………. 214
6.3.1 Incremental Dynamic Analysis (IDA) Concept ………….. 214
6.3.2 Relationship between Spectral Acceleration and
Maximum Interstory Drift Ratio ………………………….
216
6.4 Identification of Collapse Limit State ………………………….. 229
6.4.1 Methodology for the Determination of the State of Global
Collapse …………………………………………………...
229
6.4.1.1 New stiffness and strength values for updating the
damage state of the structure ………………………..
232
6.4.2 Relationship between Spectral Acceleration and Global
Failure Criterion, λu ………………………………………
233
6.4.2.1 Conditional regression of λu ………………………... 240
6.4.3 Relationship between Maximum Interstory Drift Ratio and
Global Failure Criterion, λu ……………………………….
241
6.4.4 Spatial Damage Distribution ……………………………... 246
6.5 Global versus Local Response …………………………………. 254
6.5.1 Relationship between ∆IDRmax and Peak θp,C ……………. 254
6.5.2 Relationship between IDRp,max and Peak θp,B ……………. 260
6.5.3 Estimates of Local Response Given Global Response and
Input Intensity Level – Benefits and Implications ………..
265
6.6 Global Response Dependency on Different Ground Motion
Input Parameters ………………………………………………..
267
6.7 Summary ……………………………………………………….. 275
xv
Chapter 7 Comparative Assessment of RCS and STEEL Moment Frames 282
PART I: 12-Story RCS Special Moment Frame 283
7.1 Modeling of the 12-Story RCS Frame …………………………. 283
7.2 Static Push-Over Analysis ……………………………………... 285
7.3 Incremental Dynamic Analyses ………………………………... 288
7.3.1 Story Incremental Dynamic Analysis Curves ……………. 292
7.4 Global Failure Analysis of the 12-Story RCS Frame ………….. 293
7.4.1 Relationship between Spectral Acceleration and Global
Failure Criterion, λu ………………………………………
296
7.4.2 Relationship between Maximum Interstory Drift Ratio and
Global Failure Criterion, λu ……………………………….
299
7.4.3 Spatial Distribution of Damage …………………………... 302
7.5 Global versus Local Response …………………………………. 308
7.5.1 Relationship between ∆IDRmax and Peak θp,C ……………. 308
7.5.2 Relationship between IDRp,max and Peak θp,B ……………. 309
7.5.3 Estimates of Local Response Given Global Response and
Input Intensity Level ……………………………………...
314
7.6 Global Response Dependency on Different Ground Motion
Input Parameters ………………………………………………..
322
PART II: 6-Story STEEL Special Moment Frame 328
7.7 Modeling of the 6-Story STEEL Frame ……………………….. 328
7.8 Static Push-Over Analysis ……………………………………... 330
7.9 Incremental Dynamic Analyses ………………………………... 334
7.9.1 Story Incremental Dynamic Analysis Curves ……………. 338
7.10 Global Failure Analysis of the 6-Story STEEL Frame ……….. 338
7.10.1 Relationship between Spectral Acceleration and Global
Failure Criterion, λu ……………………………………...
340
7.10.2 Relationship between IDRmax and Global Failure
Criterion, λu ……………………………………………...
343
7.10.3 Spatial Distribution of Damage ………………………… 346
xvi
7.11 Global versus Local Response ………………………………... 349
7.11.1 Relationship between ∆IDRp,max and Peak θp,C …………. 350
7.11.2 Relationship between IDRp,max and Peak θp,B …………... 353
7.11.3 Explanation of Large Dispersion in Beams Plastic
Rotation θp,B Values ……………………………………..
353
7.12 Response Dependency on Ground Motion Parameters ………. 357
7.13 Summary ……………………………………………………… 360
Chapter 8 Conclusions and Recommendations 365
8.1 Summary ……………………………………………………….. 366
8.2 Main Findings and Conclusions ……………………………….. 370
8.2.1 Large Static Lateral Overstrength ………………………... 371
8.2.2 Disaggregation of Response under Near-Fault Ground
Records ……………………………………………………
371
8.2.3 High Collapse Limit Hazard, Sa(λu=1.0) ………………… 372
8.2.4 Relating λu=0.95λuo to λu=1.0 Performance Levels ……… 373
8.2.5 Relating Performance to Hazard Levels …………………. 374
8.2.6 Consistency of Drift versus Stability criterion …………… 375
8.2.7 Spatial Distribution of Damage …………………………... 376
8.2.8 Local versus Global Response Relationships ……………. 377
8.2.9 Reducing the Variability in the Response through a Dual
Earthquake Intensity Index ……………………………….
378
8.3 Suggestions for Future Work …………………………………... 379
Appendix A Selected Ground Records 383
Appendix B Story IDA Curves 416
Bibliography 429
xvii
List of Tables
2.1 Material properties for test specimens ……………………………….. 46
3.1 Effective section properties per New Zealand Standard (NZS 1995) .. 79
3.2 Comparison of measured versus predicted stiffness …………………. 87
4.1 Summary of selected local damage indices ………………………….. 106
4.2 Selected global damage indices ……………………………………… 107
4.3 Useful values for calculation of RC columns damage indices ………. 133
4.4 Value of damage indices at failure state for RC columns ……………. 134
4.5 Values for calculation of damage indices for steel and composite
beams …………………………………………………………………
138
4.6 Combined damage indices at failure for steel and composite beams ... 139
4.7 Values for calculation of damage indices for composite RCS joints ... 144
4.8 Combined damage indices at failure for composite RCS joints ……... 145
4.9 Structural performance levels and damage …………………………... 151
4.10 Correlation of damage index and damage state ……………………… 152
5.1 Main design details and cross-sections dimensions of 6-story RCS
building ……………………………………………………………….
173
5.2 Main design details and cross-sections dimensions of 12-story RCS
building ……………………………………………………………….
174
5.3 Main design details and cross-sections of 6-story STEEL building …. 174
xviii
5.4 Seismic masses for case study frames ……………………………….. 185
5.5 Summary of design parameters for case study buildings ……………. 189
5.6 Comparisons of different Vdesign/W ratios for the case study frames … 189
5.7 Main characteristics of general records ……………………………… 195
5.8 Main characteristics of near-fault records …………………………… 198
6.1 Stiffness and strength values of RC columns ………………………... 202
6.2 Stiffness and strength values of composite and steel beams ………… 203
6.3 Properties of composite joint panels …………………………………. 203
6.4 Modal properties of the 6-story RCS frame ………………………….. 205
6.5 Limiting values of rotation capacity for RC columns ………………... 209
6.6 Limiting values of rotation capacity for composite and steel beams … 210
6.7 Limiting values for composite joints distortion ……………………… 210
6.8 Values of α and β for the regression fit of Equation 6.5 …………….. 218
6.9 Conditional dispersions and coefficient of determination for IDRmax .. 223
6.10 Values of a and ß for Equation 6.7 ………………………………… 239
6.11 Indicative drift values at different performance levels (FEMA 273) ... 245
6.12 Regression equations for local response given global response and
input intensity level …………………………………………………...
266
6.13 aS
R values for different records ……………………………………... 272
6.14 Regression results for IDRmax conditioned on different input
parameters …………………………………………………………….
273
6.15 Regression results for λu conditioned on different input parameters … 274
7.1 Stiffness and strength values of RC columns ………………………... 284
7.2 Stiffness and strength values of composite and steel beams ………… 284
7.3 Properties of composite joint panels …………………………………. 285
7.4 Values of α and β for the regression fit of Equation 7.1 …………….. 288
7.5 Values of a and ß for Equation 7.2 ………………………………… 297
xix
7.6 Regression equations for local response given global response and
input intensity level for the 12-story RCS frame ……………………..
319
7.7 Regression results for IDRmax conditioned on different input
parameters …………………………………………………………….
324
7.8 Regression results for λu conditioned on different input parameters … 325
7.9 Stiffness and strength values of steel columns ………………………. 329
7.10 Stiffness and strength values of composite and steel beams ………… 329
7.11 Properties of joint panels …………………………………………….. 329
7.12 Regression parameters α and β for the 6-story steel frame ………….. 334
7.13 Average regression parameters α and β for near-fault records ……… 337
7.14 Values of a and ß for the 6-story steel frame ……………………… 340
7.15 Average a and ß values for near-fault records ……………………... 343
7.16 Regression results for IDRmax conditioned on various input
parameters …………………………………………………………….
358
7.17 Regression results for λu conditioned on various input parameters ….. 359
8.1 Summary of Sa statistical values at various performance levels ……... 373
xx
List of Figures
1.1 Schematic of typical composite RCS systems ……………………………... 2
2.1 Idealized elasto-plastic material behavior .………………………………… 20
2.2 Kinematics of the two-surface bounding model …………………………… 21
2.3 Beam-column element with distributed plasticity – DYNAMIX ………….. 24
2.4 Schematic curvature distribution along a cantilever beam ………………… 32
2.5 Constitutive model and moment curvature skeleton for composite beam
element ……………………………………………………………………...
40
2.6 Schematic diagram of nested bars movements …………………………….. 40
2.7 Cross-section main dimensions for a typical composite beam …………….. 43
2.8 Plastic stress distribution for a typical composite beam …………………… 44
2.9 Test setup and specimen for verification study problems ………………….. 47
2.10 Experimental and analytical results – specimen Tagawa (1989) …………... 49
2.11 Experimental and analytical results – Bursi and Ballerini (1996) (Specimen
with full shear connection) …………………………………………………
50
2.12 Experimental and analytical results for specimen CG3 – Uang (1985) …… 50
2.13 Experimental and analytical results for specimen EJ-WC – Lee (1987) …... 51
2.14 Panel shear and bearing modes of failure ………………………………….. 53
2.15 Composite joint panel model ………………………………………………. 54
2.16 Constitutive model for joint panel shear …………………………………… 54
2.17 Constitutive model for joint bearing ……………………………………….. 55
xxi
2.18 Comparison between FBSFs and Hermitian shape functions in the presence
of spread-of-plasticity (El-Tawil, 1996) ……………………………………
60
3.1 Behavior of reinforced concrete element in flexure (a) member subjected to
lateral load, (b) moment-curvature response, (c) load-deformation response
71
3.2 Load versus deflection behavior of a reinforced concrete frame …………... 73
3.3 Nonlinear beam-column element models for frame analysis (a)
concentrated-hinge type, (b) spread-of-plasticity type ……………………..
76
3.4 Stress-resultant yield surface model and idealized moment-curvature
response …………………………………………………………………….
76
3.5 Effective secant flexural stiffness per CEB (Filippou and Fardis, 1996) ….. 80
3.6 Proposed EIeff model compared to test data and other models …………….. 85
3.7 Comparative of effective stiffness coefficients with test data ……………... 86
3.8 Test specimen WP9 by Watson and Park (a) variation in EIeff with axial
load, (b) moment-curvature response ………………………………………
88
3.9 Test specimen by Kuramoto (a) variation in EIeff with axial load, (b)
moment-curvature response ………………………………………………...
89
3.10 Comparison of cyclic load behavior for WP9 specimen (a) experimental,
(b) DYNAMIX analysis …………………………………………………….
90
3.11 Comparison of cyclic load behavior for Kuramoto specimen (a)
experimental, (b) DYNAMIX analysis ……………………………………..
91
3.12 Proposed shear stiffness model …………………………………………….. 92
4.1 Definition of PHCs and FHCs and load sequence effects …………………. 112
4.2 Different failure surfaces for different values of γ …………………………. 113
4.3 Stress-strain model for monotonic loading of confined and unconfined
concrete in compression (Paulay and Priestley, 1992) ……………………..
120
4.4 Moment-rotation relationship for steel beams ……………………………... 124
4.5 Idealized moment-rotation relationship for Ef calculation for steel beams ... 125
4.6 Values of cyclic joint panel distortion at failure by least square fit based on
results by Kanno (1993) …………………………………………………….
131
xxii
4.7 Idealized moment-distortion for composite joint panels, Sheikh et al.
(1989) ……………………………………………………………………….
132
4.8 Ductility-based damage index – Watson and Park (1994), Unit WP4 …….. 135
4.9 Energy-based damage index – Watson and Park (1994), Unit WP4 ………. 135
4.10a Load-displacement relationship – Watson and Park (1994), Unit WP2 …… 136
4.10b Results for combined ductility- and energy-based damage indices –
Watson and Park (1994), Unit WP2 ………………………………………..
136
4.11a Load-displacement relationship – Watson and Park (1994), Unit WP4 …… 137
4.11b Results for combined ductility- and energy-based damage indices –
Watson and Park (1994), Unit WP4 ………………………………………..
137
4.12 Ductility-based damage index – Kanno (1993), Unit OB1-1 ……………… 140
4.13 Energy-based damage index – Kanno (1993), Unit OB1-1 ………………... 140
4.14 Ductility-based damage index – Uang (1985), Unit CG3 …………………. 141
4.15 Energy-based damage index – Uang (1985), Unit CG3 …………………… 141
4.16a Beam-shear drift angle relationship – Kanno (1993), Unit OB1-1 ………… 142
4.16b Results for combined ductility- and energy-based damage indices – Kanno
(1993), Unit OB1-1 …………………………………………………………
142
4.17a Load-displacement relationship – Uang (1985), Unit CG3 ………………... 143
4.17b Results for combined ductility- and energy-based damage indices – Uang
(1985), Unit CG3 …………………………………………………………...
143
4.18 Ductility-based damage index – Kanno (1993), Unit OJS1-1 ……………... 146
4.19 Energy-based damage index – Kanno (1993), Unit OJS1-1 ……………….. 146
4.20 Ductility-based damage index – Kanno (1993), Unit OJS4-1 ……………... 147
4.21 Energy-based damage index – Kanno (1993), Unit OJS4-1 ……………….. 147
4.22a Beam-shear drift angle relationship – Kanno (1993), Unit OJS1-1 ……….. 148
4.22b Results for combined ductility- and energy-based damage indices – Kanno
(1993), Unit OJS1-1 ………………………………………………………...
148
4.23a Beam-shear drift angle relationship – Kanno (1993), Unit OJS4-1 ……….. 149
4.23b Results for combined ductility- and energy-based damage indices – Kanno
(1993), Unit OJS4-1 ………………………………………………………...
149
xxiii
5.1 IBC 2000 Design response spectrum ………………………………………. 157
5.2 Elastic versus inelastic behavior as related by R and Cd factors …………... 159
5.3 Capacity spectrum superimposed over demand response spectra …………. 171
5.4 Architecture Plan of US-Japan Theme Structure …………………………... 172
5.5 Typical structural plan for 6-story RCS building ………………………….. 175
5.6 Elevation of typical frames in both directions – 6-story RCS building ……. 176
5.7 Cast-in-place RC column details …………………………………………... 177
5.8 Precast RC column details …………………………………………………. 178
5.9 Joint details for 6-story RCS building ……………………………………... 179
5.10 Gravity and design lateral loads for the 6-story RCS frame ……………….. 186
5.11 Gravity and design lateral loads for the 12-story RCS frame ……………… 187
5.12 Gravity and design lateral loads for the 6-story STEEL frame ……………. 188
5.13 Comparison of acceleration response spectra of general records and the
2%in50years site response spectrum (IBC 2000) …………………………..
195
5.14 Comparison of acceleration response spectra of near-fault records and the
2%in50years site response spectrum (IBC 2000) …………………………..
198
6.1 Static pushover curve – IBC 2000 load pattern ……………………………. 207
6.2 Distribution of interstory drift ratios up the height of the frame – pushover
results ……………………………………………………………………….
207
6.3 Distribution of damage indices and progression of damage – pushover
results ……………………………………………………………………….
208
6.4 Schematic of different deformed configurations …………………………... 211
6.5 Global, ∆IDR, versus local, θp,C, response – pushover results …………….. 213
6.6 Global, IDRp, versus local, θp,B, response – pushover results ……………... 213
6.7 Schematic of typical Incremental Dynamic Analysis Curves ……………... 215
6.8 Conditional regression relationship of IDRmax for general records ………... 219
6.9 Conditional regression relationship of IDRmax for near-fault records ……... 220
6.10 Spectral acceleration versus IDRmax for bin of general records ……………. 221
6.11 Spectral acceleration versus IDRmax for bin of near-fault records …………. 221
6.12 Story IDACs for general records ………………………………………….. 224
xxiv
6.13 Story IDACs for near-fault records ………………………………………... 226
6.14 Flow chart of the technique for global collapse determination ……………. 231
6.15 Proposed stiffness reduction as a function of the damage index Dθ ……….. 232
6.16 Spectral acceleration - λu relationship ……………………………………... 234
6.17 Schematic of the effect of residual displacements on λu …………………... 239
6.18 Conditional regression of λu given Sa ……………………………………… 243
6.19 IDRmax - λu relationship ……………………………………………………. 244
6.20 Distribution of Dθ at different λu values- Valparaiso (1985) record ……….. 248
6.21 Distribution of Dθ at different λu values- Mendocino (1992) record ………. 249
6.22 Plastic rotation values at λu = 1.0 – Valparaiso (1985) record …………….. 250
6.23 Plastic rotation values at λu = 1.0 – Mendocino (1992) record ……………. 251
6.24 Distribution of Dθ at different λu values – Erzincan (1992) record ………... 252
6.25 Plastic rotation values at λu = 1.0 – Erzincan (1992) record ………………. 253
6.26 Global versus local response (θp,C) for bin of general records at λu=1.0 …... 256
6.27 Global versus local response (θp,C) for bin of near-fault records at λu=1.0 ... 256
6.28 ∆IDRmax-θp,C relationship for general and near-fault records at λu=1.0 …… 257
6.29 ∆IDRmax-θp,C relationship at different levels of damage based on values of
λu ……………………………………………………………………………
258
6.30 Global versus local response (θp,B) for bin of general records at λu=1.0 …... 261
6.31 Global versus local response (θp,B) for bin of near-fault records at λu=1.0 ... 261
6.32 IDRp,max-θp,B relationship for general and near-fault records at λu=1.0 ……. 262
6.33 IDRp,max-θp,B relationship at different levels of damage based on values of
λu ……………………………………………………………………………
263
6.34 Global versus local response at different hazard levels for bin of general
records ………………………………………………………………………
268
6.35 Global versus local response at different hazard levels for bin of near-fault
records ………………………………………………………………………
269
7.1 Static pushover curve – IBC 2000 lateral load pattern …………………….. 286
xxv
7.2 Distribution of interstory drift ratios up the height of the frame – static
pushover results …………………………………………………………….
286
7.3 Spectral acceleration versus IDRmax relationship for bin of general records . 291
7.4 Spectral acceleration versus IDRmax relationship for bin of near-fault
records ………………………………………………………………………
291
7.5 Comparison of regression results of spectral acceleration versus IDRmax
relationship for general and near-fault records ……………………………..
292
7.6 Story IDACs for the 12-story RCS frame under the general record, Cape
Mendocino (1992) at Rio Del Overpass station …………………………….
294
7.7 Story IDACs for the 12-story RCS frame under the near-fault record,
Imperial Valley (1979) at Array 06 ………………………………………...
295
7.8 Spectral acceleration-λu relationship for bin of general records …………… 298
7.9 Spectral acceleration-λu relationship for bin of near-fault records ………… 298
7.10 IDRmax-λu relationship for bin of general records ………………………….. 301
7.11 IDRmax-λu relationship for bin of near-fault records ……………………….. 301
7.12 Distribution of Dθ – Cape Mendocino (1992) record ……………………… 304
7.13 Distribution of Dθ – Loma Prieta (1989) record at Lexington ……………... 306
7.14 Global versus local response (θp,C) for bin of general records at λu=1.0 …... 310
7.15 Global versus local response (θp,C) for bin of near-fault records at λu=1.0 ... 310
7.16 ∆IDRmax-θp,C relationship for general and near-fault records at λu=1.0 …… 311
7.17 ∆IDRmax-θp,C relationship at different levels of damage based on values of
λu ……………………………………………………………………………
312
7.18 Global versus local response (θp,B) for bin of general records at λu=1.0 …... 315
7.19 Global versus local response (θp,B) for bin of near-fault records at λu=1.0 ... 315
7.20 IDRp,max-θp,B relationship for general and near-fault records at λu=1.0 ……. 316
7.21 IDRp,max-θp,B relationship at different levels of damage based on values of
λu ……………………………………………………………………………
317
7.22 Global versus local response at different hazard levels for bin of general
records ………………………………………………………………………
320
xxvi
7.23 Global versus local response at different hazard levels for bin of near-fault
records ………………………………………………………………………
321
7.24 Static pushover curve – 6-story STEEL frame, IBC 2000 load pattern …… 332
7.25 Distribution of IDR up the height of the frame – static pushover results ….. 332
7.26 Comparison of IDR values for 6-story RCS and STEEL frames – static
pushover results …………………………………………………………….
333
7.27 Sa-IDRmax relationship for bin of general records ………………………….. 336
7.28 Sa-IDRmax relationship for bin of near-fault records ……………………….. 336
7.29 Comparison of regression results of Sa-IDRmax relationship for 6-story RCS
and STEEL frames ………………………………………………………….
337
7.30 Story IDACs for the 6-story steel frame under the Cape Mendocino (1992)
record at Rio Del Overpass station – general record ……………………….
339
7.31 Story IDACs for the 6-story steel frame under the Erzincan (1992) record
in Turkey – near-fault record ……………………………………………….
339
7.32 Spectral acceleration-λu relationship for bin of general records …………… 341
7.33 Spectral acceleration-λu relationship for bin of near-fault records ………… 341
7.34 IDRmax-λu relationship for bin of general records ………………………….. 345
7.35 IDRmax-λu relationship for bin of near-fault records ……………………….. 345
7.36 Distribution of Dθ at different λu values – Mendocino (1992) record ……... 347
7.37 Distribution of Dθ at different λu values – Erzincan (1992) record ………... 348
7.38 ∆IDRp,max-θp,C relationship for general records at λu=1.0 ………………….. 352
7.39 ∆IDRp,max-θp,C relationship for near-fault records at λu=1.0 ……………….. 352
7.40 IDRp,max-θp,B relationship for general records at λu=1.0 …………………… 354
7.41 IDRp,max-θp,B relationship for near-fault records at λu=1.0 ………………… 354
7.42 Results from time history analysis under LP89-WAHO at λu=1.0 ………… 356
A.1 Miyagi-oki 1978 ground record – Ofuna station …………………………... 384
A.2 Response Spectra (5% Damping) for Miyagi-oki (1978) record – Ofuna …. 385
A.3 Valparaiso 1985 ground record – Llol station ……………………………... 386
xxvii
A.4 Response Spectra (5% Damping) for Valparaiso (1985) record – Llol
station ……………………………………………………………………….
387
A.5 Loma Prieta 1989 ground record – Hollister City Hall ……………………. 388
A.6 Response Spectra (5% Damping) for Loma Prieta (1989) record – Hollister
City Hall …………………………………………………………………….
389
A.7 Loma Prieta 1989 ground record – Hollister South & Pine ………………... 390
A.8 Response Spectra (5% Damping) for Loma Prieta (1989) record – Hollister
South & Pine ………………………………………………………………..
391
A.9 Loma Prieta 1989 ground record – WAHO ………………………………... 392
A.10 Response Spectra (5% Damping) for Loma Prieta (1989) record – WAHO . 393
A.11 Cape Mendocino 1992 ground record – Rio Del Overpass ………………... 394
A.12 Response Spectra (5% Damping) for Cape Mendocino (1992) record – Rio
Del Overpass ………………………………………………………………..
395
A.13 Landers 1992 ground record – Yermo Fire Station ………………………... 396
A.14 Response Spectra (5% Damping) for Landers (1992) record – Yermo Fire
Station ………………………………………………………………………
397
A.15 Mendocino 1992 ground record – Petrolia station …………………………. 398
A.16 Response Spectra (5% Damping) for Mendocino (1992) record – Petrolia
station ……………………………………………………………………….
399
A.17 Imperial Valley 1979 ground record – Array 06 …………………………... 400
A.18 Response Spectra (5% Damping) for Imperial Valley (1979) record –
Array 06 …………………………………………………………………….
401
A.19 Loma Prieta 1989 ground record – Los Gatos station ……………………... 402
A.20 Response Spectra (5% Damping) for Loma Prieta (1989) record – Los
Gatos station ………………………………………………………………..
403
A.21 Loma Prieta 1989 ground record – Lexington station ……………………... 404
A.22 Response Spectra (5% Damping) for Loma Prieta (1989) record –
Lexington station …………………………………………………………...
405
A.23 Erzincan 1992 ground record – Erzincan station …………………………... 406
A.24 Response Spectra (5% Damping) for Erzincan (1992) record – at Erzincan
station ……………………………………………………………………….
407
xxviii
A.25 Northridge 1994 ground record – Newhall station ………………………… 408
A.26 Response Spectra (5% Damping) for Northridge (1994) record – Newhall
station ……………………………………………………………………….
409
A.27 Northridge 1994 ground record – Rinaldi station ………………………….. 410
A.28 Response Spectra (5% Damping) for Northridge (1994) record – Rinaldi
station ……………………………………………………………………….
411
A.29 Northridge 1994 ground record – Sylmar station ………………………….. 412
A.30 Response Spectra (5% Damping) for Northridge (1994) record – Sylmar
station ……………………………………………………………………….
413
A.31 Kobe 1995 ground record – JMA station …………………………………... 414
A.32 Response Spectra (5% Damping) for Kobe (1995) record – JMA station … 415
B.1 Story IDA curves for Miyagi-oki (1978) record – 12-story RCS frame …... 417
B.2 Story IDA curves for Valparaiso (1985) record – 12-story RCS frame …… 417
B.3 Story IDA curves for LP89-HCA record – 12-story RCS frame …………... 418
B.4 Story IDA curves for LP89-HSP record – 12-story RCS frame …………… 418
B.5 Story IDA curves for LP89-WAHO record – 12-story RCS frame ………... 419
B.6 Story IDA curves for CM92-RIO record – 12-story RCS frame …………... 419
B.7 Story IDA curves for LA92-YER record – 12-story RCS frame ………….. 420
B.8 Story IDA curves for Mendocino (1992) record – 12-story RCS frame …... 420
B.9 Story IDA curves for IV79-A6 record – 12-story RCS frame ……………... 421
B.10 Story IDA curves for LP89-LG record – 12-story RCS frame …………….. 421
B.11 Story IDA curves for LP89-LX record – 12-story RCS frame …………….. 422
B.12 Story IDA curves for EZ92-EZ record – 12-story RCS frame …………….. 422
B.13 Story IDA curves for NR94-NH record – 12-story RCS frame …………… 423
B.14 Story IDA curves for NR94-RS record – 12-story RCS frame ……………. 423
B.15 Story IDA curves for NR94-SY record – 12-story RCS frame ……………. 424
B.16 Story IDA curves for KB95-JM record – 12-story RCS frame ……………. 424
B.17 Story IDA curves for Miyagi (1978) record – 6-story STEEL frame ……... 425
B.18 Story IDA curves for Valparaiso (1985) record – 6-story STEEL frame ….. 425
B.19 Story IDA curves for LP89-HCA record – 6-story STEEL frame ………… 425
xxix
B.20 Story IDA curves for LP89-HSP record – 6-story STEEL frame …………. 425
B.21 Story IDA curves for LP89-WAHO record – 6-story STEEL frame ……… 426
B.22 Story IDA curves for CM92-RIO record – 6-story STEEL frame ………… 426
B.23 Story IDA curves for LA92-YER record – 6-story STEEL frame ………… 426
B.24 Story IDA curves for Mendocino (1992) record – 6-story STEEL frame …. 426
B.25 Story IDA curves for IV79-A6 record – 6-story STEEL frame …………… 427
B.26 Story IDA curves for LP89-LG record – 6-story STEEL frame …………... 427
B.27 Story IDA curves for LP89-LX record – 6-story STEEL frame …………... 427
B.28 Story IDA curves for EZ92-EZ record – 6-story STEEL frame …………… 427
B.29 Story IDA curves for NR94-NH record – 6-story STEEL frame ………….. 428
B.30 Story IDA curves for NR94-RS record – 6-story STEEL frame …………... 428
B.31 Story IDA curves for NR94-SY record – 6-story STEEL frame …………... 428
B.32 Story IDA curves for KB95-JM record – 6-story STEEL frame …………... 428
1
Chapter 1
Introduction
Recent trends in the construction of moment-framed buildings show the increased use of
steel, reinforced concrete, and composite steel-concrete members functioning together in
what are termed composite, mixed and/or hybrid systems. Such systems make use of each
type of member in the most efficient manner to maximize the structural and economic
benefits. As shown in Figure 1.1, one example of a composite system consists of
reinforced concrete columns (with small steel erection columns for construction
purposes) and steel or composite beams. This system is also known as RCS system and it
is the focus of this research.
Over the past fifteen years, composite RCS moment frame systems have been used in the
US and Japan. Extensive research is currently underway to better understand the behavior
of such frames. Much of this research aims at experimentally investigating the
characteristics of joints between steel and reinforced concrete members and at
understanding the behavior of mixed sub-assemblies. System behavior on the other hand
has been much less researched and is not yet well understood. In most instances, system
2
design provisions are extrapolated from corresponding traditional steel or reinforced
concrete systems.
Steel Beam
RC Column
Erection Column
Beam Splice Composite JointRegion withThrough Beams
Figure 1.1 Schematic of typical composite RCS systems.
3
In view of the growing popularity and use of composite systems, there is the need for
rational nonlinear analysis tools suitable for better understanding the behavior of such
systems, especially when subjected to dynamic excitation, and for evaluating design
codes and procedures. Unfortunately, many of the available nonlinear analysis programs
are only suitable for modeling traditional steel or reinforced concrete systems and are not
directly applicable to composite frames. Part of the research presented herein is a
continuation of previous work at Cornell University (El-Tawil and Deierlein, 1996)
aimed at improving this situation by developing nonlinear analysis tools. Among the first
objectives of this research is to further the development of existing nonlinear inelastic
dynamic analytical models and techniques for composite systems. Using these analytical
tools, the next objective is to apply nonlinear static and dynamic analyses to evaluate the
performance of composite RCS frames under multi-level earthquake hazards. Efficient
“dual purpose” local damage indices detecting peak and cumulative type of damage of
various structural components are suggested. A newly proposed technique, which
integrates the local damage effects with system stability analysis, offers a reliable tool to
quantify “near collapse” performance. It further provides insight to relate the degradation
of global stability to performance and hazard levels suggested by seismic codes. This
investigation should lead to the improvement of current seismic codes requirements and
help the development of performance-based design methodologies for such composite
systems.
1.1 Evolution of Composite Construction
In the United States, composite RCS moment frames have been used in several high-rise
office buildings constructed during the 1980’s and 1990’s (Griffis, 1992, Heinge, 1992,
and Leon, 1990). These systems have evolved as a variation of traditional structural steel
framing systems where the floor framing is essentially the same as in a steel framed
structure, but where reinforced concrete columns have replaced steel columns. Among
the main reasons behind that evolution are economics and advances in concrete
technology that made it more cost effective for columns. The economics are simply the
4
relative price of concrete and steel, coupled with a construction industry that was willing
to try new schemes. Concurrent advances in concrete technology made higher strength
concrete commercially available and practical for use in tall buildings. There were also
some construction technologies that helped make concrete more viable in tall buildings
such as concrete pumping, flying forms, etc… Furthermore, as building heights increased
and framing systems became lighter in the last two decades, the required lateral stiffness
of the structural systems under service loads began to impose large penalties on the size
of columns in traditional steel moment frames (Leon and Deierlein, 1995). All of that
leads US designers to stiffening the steel columns by encasing them in concrete, while
the beams and braces are still steel. Further evolution of the mixed construction leads to
the replacement of composite columns by reinforced concrete columns into which the
steel beams frame (so-called RCS systems). Most applications of RCS frames have been
used almost exclusively in high rise construction (Sheikh 1995) in the central and eastern
US where wind forces control the lateral design and detailing of the frames. However,
there is now considerable interest in applying them to low- and mid-rise construction in
high-seismic zones.
In Japan, composite systems have also been used, however, they evolved differently
compared to the US because of differences in the construction practices in both countries.
Composite RCS moment frames have been applied in low-rise construction where they
are replacing traditional reinforced concrete (RC) and structural steel reinforced concrete
(SRC) construction (Kanno, 1993). This form of construction has then expanded because
of the perceived advantages it has in high seismic zones (Griffis, 1995).
Aside from construction sequence differences between the US and Japan (e.g. the
absence of steel erection columns in the Japanese practice), another difference is that in
Japan the composite RCS frames are usually space frames with beams framing into the
column in two directions, whereas in the US most systems have been built with planar
perimeter frames.
5
1.1.1 Pros and Cons of Composite RCS Systems
In general, since composite systems realize the most efficient use of steel, reinforced
concrete, and composite members in a structural system, this type of construction is often
more economical than traditional either all-steel or all-reinforced concrete construction.
Among main advantages of RCS frames are the efficiency of concrete (versus steel) in
carrying large column loads at much lower cost per unit strength and stiffness (Griffis,
1992), and the reduction in total construction time. Speed of construction may be
achieved through separation of trades. Accordingly, construction activity can be spread
vertically, with the help of the erection columns, thus allowing different trades to engage
simultaneously in the construction of the building.
Moreover, steel and composite beams in a floor system lead to reduced floor depth, and
lighter overall floor weights. This in turn leads to lower building mass and more
economical foundations. Furthermore, having steel beams running continuous through
the reinforced concrete columns offers stable hysteretic behavior of the joint region due
to the presence of the steel web. This construction detailing permits the elimination of
field welding at beam-column connections. This helps avoid fracture problems
experienced with welded steel connections that were observed after the Northridge
earthquake.
Among the drawbacks of the RCS construction is the congestion in the connections
regions with ties passing through steel beam webs or welded to them. In addition, more
on site activities are required, although prefabrication techniques may alleviate this
problem. Because of possible congestion, concrete mixes have to be highly workable. In
addition, differential creep and shortening effects and slip between concrete and
structural steel are other drawbacks of composite systems (Griffis, 1987). Yet, even with
these considerations, mixed construction remains a viable and efficient alternative to all-
steel or all-reinforced concrete construction.
6
In spite of the economic and practical advantages of composite systems, their use has
been constrained by the lack of information on the behavior and design of composite
members and connections (Goel et al., 1992), and the lack of accurate and efficient
computational tools for the analysis of such systems. This is particularly crucial for
regions of moderate to high seismicity where there is concern about structural
performance in the inelastic range. This research is a contribution towards improving this
situation.
1.1.2 Background of Experimental and Analytical Work
As recently as ten years ago there was practically no information on the behavior and
design of connections between steel beams and reinforced concrete columns. Since then,
there has been extensive testing of composite beam-column connections which is now
resulting in the development of design guidelines in the US and Japan. In the US,
pioneering experimental work aimed at understanding composite joint behavior was
undertaken at the University of Texas at Austin (Deierlein et al., 1989, and Sheikh et al.,
1989) and at Cornell University (Kanno, 1993). Based on this research, proposed design
guidelines for composite RCS joints have been developed through ASCE (1994). More
extensive testing of various configurations, with the slab effect, is underway at the
University of Michigan (Wight, 1997,1998) and at Texas A&M University (Bugeja et al.,
1999). As discussed by Kanno (1993), research in this field has also been carried out in
Japan by universities, government research institutes, and private construction
companies.
Analytical work for modeling the behavior of either composite sub-assemblies or overall
composite systems is not abundant in the literature. For modeling the behavior of
composite joint panels, Sheikh et al. (1989) proposed a multi-linear relationship for
modeling the force-deformation of the joint. The model is only applicable to
monotonically increasing loading. Kanno (1993) proposed a more detailed model
differentiating between panel shear and bearing modes of deformation which are
characteristic of composite joints. However, as with Sheikh et al. (1989) model, Kanno’s
7
(1993) model is still only applicable to monotonically increasing loads. El-Tawil et al.
(1996) extended Kanno’s (1993) idea of separating joint deformations into shear panel
and joint bearing parts and proposed a joint panel model suitable for cyclic loading. The
model is implemented in DYNAMIX (the analysis software used in this research) and a
detailed explanation of the model is given in Chapter 2.
Several researchers have suggested various analytical models for composite beams
subassemblies (i.e., steel beam with a concrete slab and a metal deck). In general,
composite beams can show complex behavior due to slip between the reinforced concrete
slab and the steel beam, and the variation of longitudinal stress across the width of the
slab, which is dependent of the joint details and the loading pattern. In order to capture
this complex behavior, a three-dimensional finite element analysis may be needed.
However, some researchers (Lee 1987, Tagawa et al 1989, Engelhardt et al 1995)
developed two-dimensional discrete member models as a compromise between simplicity
and accuracy. In these models, it is assumed that the effect of slip and the variation of
longitudinal membrane stress on the behavior of composite beams can be implicitly
included in the constitutive moment-rotation relationships. Alternatively, a fiber beam-
column model, with continuously distributed springs along the interface between the
concrete slab and the steel beam to represent shear connectors (studs), has been
developed by Salari et al (1996) to model the composite beam behavior in a more
accurate, but computationally much more expensive way.
Utilizing available information, a composite beam element is developed through this
research using a spread-of-plasticity flexibility formulation that tracks inelastic moment-
curvature cross-section response along the member. This model aims to capture the
overall behavior of a composite beam, particularly differences in the member’s stiffness
and strength under positive versus negative bending, while maintaining computational
efficiency. The element does not explicitly model detailed behavior associated with
cracking in the slab, slip between the slab and beam, etc., but it accounts for these
behavioral characteristics empirically. Development of this model is explained in detail in
Chapter 2 of this thesis.
8
Throughout the literature, very few researchers have developed analytical models or
carried out inelastic analyses aiming at studying the overall system performance of
composite frames. Among these researchers are Elnashai and Elghazouli (1993) who
developed an advanced nonlinear model for the analysis of composite steel/concrete
frame structures subjected to cyclic and dynamic loading. Their formulation consists of
beam-column cubic finite elements accounting for geometric nonlinearities and material
inelasticity. The nonlinear cyclic concrete model considers confinement effects and the
constitutive relationship for steel includes the effect of local buckling and variable
amplitude cyclic degradation. Broderick and Elnashai (1996a,b) used this model to
evaluate the seismic response of moment-resisting composite frames with partially
encased columns sections through the application of nonlinear dynamic analysis
techniques.
El-Tawil and Deierlein (1996) developed a computer program, DYNAMIX – for the
DYNamic Analysis of MIXed (steel-concrete) structures, which is an extension of other
analysis programs from previous research at Cornell University dealing with inelastic
static and dynamic nonlinear analysis of steel structures. Employing a bounding surface
stress-resultant plasticity model, inelastic section behavior (i.e., moment-curvature
response captured through the bounding surface model) is integrated to simulate overall
member response through a flexibility element formulation. The resulting element
accounts for the interaction of axial loads and biaxial bending moments in steel, RC, and
composite beam-columns with bi-symmetric cross-sections, including the effects of
spread-of-plasticity, geometric nonlinearities (P-∆ and P-δ effects), and cyclic stiffness
degradation. A more detailed overview of the element formulation and capabilities is
presented in Chapter 2 of this thesis.
Building on El-Tawil and Deierlein (1996) work, the present research is a pioneering
analytical study aimed at improving available analytical models for composite structures,
and investigating the overall system behavior of composite RCS moment frames under
multi-level earthquake hazards using such reliable and efficient analytical models. It
9
further deals with cumulative damage modeling at the structural components level and
integrates such local damage effects through global collapse analysis techniques for
better seismic simulation and enhanced interpretation of response to random ground
motions. Such study is needed for the improvement of our understanding of the behavior
of such composite systems leading to their broader acceptance by demonstrating their
reliability through a modern performance-based methodology.
1.1.3 Current Codes and Provisions for Composite Systems
Given that composite RCS frames include both structural steel and reinforced concrete
members, many design provisions from the ACI-318 (1995) and AISC-LRFD (1993)
Specifications are directly applicable to composite frames. In certain instances, however,
there are differences in the treatment of fundamental issues in these specifications that
can lead to inconsistencies in design (Leon and Deierlein, 1995). For example, in the
AISC-LRFD Specification, frame stability and the design of beam-columns are handled
through the use of semi-empirical interaction equations which is different from the
approach taken in ACI-318. In large part, the differences are due to the ACI-318 and
AISC-LRFD Specifications treating the design of composite columns through extensions
to provisions for reinforced concrete and structural steel columns, respectively. Thus, for
composite frames with both steel and concrete members, it is not clear how to combine
the different approaches. Beyond this, there are shortcomings in each specification
related to the design and detailing of composite members and connections.
In much the same way that ACI-318 and AISC-LRFD treat composite members by
extension of reinforced concrete and steel provisions, the new IBC 2000 Standards and
the AISC Seismic Provisions (1997), although adopting new recommendations for
composite steel-concrete structures, treat these composite systems as extensions of
traditional steel or reinforced concrete systems. For instance, response modification and
displacement amplification factors (such as the R and Cd factors) are selected, based on
consensus opinion, from corresponding factors for comparable all-steel and/or all-
reinforced concrete systems. These extrapolations are necessitated by a lack of
10
information regarding the behavior of composite systems. Two reasons contribute to this:
(1) lack of relevant experimental research; and (2) most available inelastic analysis tools
handle only steel or only reinforced concrete members. It is generally recognized that
there is considerable room for improvement in current seismic design methods that are
based largely on such empirical factors (R and Cd) for determining seismic loads,
inelastic drifts, stability limits, etc. Not only do such methods greatly oversimplify the
underlying aspects of inelastic behavior under dynamic loads, but they do not provide the
means to accurately evaluate damage and structural limit states under various level
earthquakes.
Furthermore, while composite frames bear many similarities to traditional steel or
reinforced concrete structures, there are important differences that can change their
behavior but yet ignored by current seismic codes. For example, the relative proportions
of strength, stiffness, damping and mass of RCS composite frame buildings are different
than in pure steel or reinforced concrete construction. Thus, it is not known whether
member ductility demands are comparable to those for steel and concrete frames and
whether the same detailing rules should be applied.
The IBC and AISC provisions for composite construction are still new and largely
untried and will require further verification before being fully accepted by other model
codes and standards and the profession. By accurately modeling the inelastic dynamic
behavior of several prototype composite RCS structures under multi-level earthquake
hazards, the present work will help identify areas in seismic codes and earthquake
engineering practice that need improvement and will provide data and suggestions for
such improvements.
11
1.2 Overview of Recent Developments in Performance-Based Engineering
In recent years, a new design philosophy for building codes has been discussed among
the engineering community, namely performance-based design (Vision 2000, 1995). The
goal of any performance-based design procedure is to produce structures that have
predictable seismic performance. Additionally, performance-based design approaches
should be more transparent than current code provisions. Within the context of
performance-based design, a structure is designed such that, under a specified level of
ground motion, the performance of the structure is within prescribed bounds. These
bounds depend mainly on the importance of the structure. In order to evaluate structural
performance, the following information is required (Bertero, 1996):
1. Sources of excitation during service life of structure
2. Definition of performance levels
3. Definition of excitation intensity
4. Types of failures (limit states) of components
5. Cost of losses and repairs.
One of the first requirements of performance evaluation is the selection of one or more
performance objectives, i.e.: select desired performance level and associated seismic
hazard level. Since the evaluation relies on analysis rather than experimentation, the
criteria should be stated in terms of a response that can be calculated. Depending on the
intensity of the ground motion, a different performance objective will be desired.
According to the expected intensity, the designer must analyze whether achieving the
desired objective will be economically feasible. For frequent events, the designer will
probably desire that the structure remains operational. For rare events, ensuring
prevention against collapse may be the only realistic goal. Ultimately, performance-based
design methods and codes will only be accepted if they improve the quality and cost-
effectiveness of constructed facilities. Significant work has been performed in the
development of performance-based design and evaluation, and good discussions on the
subject can be found in Bertero (1996), Cornell (1996), and Krawinkler (1996). Recent
guidelines, such as those in Vision 2000 (SEAOC 1995) and FEMA 273 (BSSC 1997),
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provide a framework for the performance-based design and evaluation of structures under
seismic loads, including both qualitative and quantitative definitions for seismic hazard
and structural performance.
In the recently published FEMA 273 and ATC 40 guidelines, and similar to ideas
proposed in SEAOC’s Vision 2000, it is anticipated that three performance levels
(immediate occupancy, life safety, near collapse) would form the basis of seismic loading
and acceptance criteria for a performance-based design code. However, only two specific
levels of performance are adopted by the SAC Design Criteria, as mentioned by
Hamburger et al. (2000), which are subtly different from those adopted by FEMA 273.
The first, termed Collapse Prevention, is a state of incipient local or global collapse,
whereas the second, termed Incipient Damage, is that state in which structural damage
initiates. Structural acceptance criteria for each performance level are established through
FEMA 273 in terms of response quantities for individual components, assuming that the
demands on local elements are faithfully represented by the global structural analysis.
Structural analyses would be one of four types: linear static, linear dynamic, nonlinear
static (pushover), and nonlinear dynamic.
Acceptance criteria are generally distinguished between force and deformation controlled
based on the available ductility, and it is presumed that system design rules would be
applied to restrict inelastic action to deformation-controlled components. For linear
analyses, acceptance criteria for deformation-controlled components are expressed in
terms of limits on the calculated demand to capacity ratios. For nonlinear analyses,
criteria are described in terms of component deformations and/or generalized strains (e.g.,
curvature). Researchers should undertake a critical review of such acceptance criteria and
the source material upon which they are based, and further check their accuracy and
applicability to new structures. Furthermore, some shortcomings and challenges to
current proposals are yet to be addressed. For example, a key shortcoming of the
acceptance criteria is their reliance on a single peak deformation limit that does not
consider strong motion duration of ground records and other cumulative effects. More
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importantly, current methods are totally lacking in providing techniques to reliably
address near collapse performance level from a system point of view.
Among other unresolved issues yet required to develop a performance-based design code
is the extent to which prescriptive system design requirements in current codes would
apply in performance based design. For example, to what extent should a performance-
based design code attempt to categorize system types like “ordinary”, “intermediate”, and
“special”? Or, to what degree should capacity design principles be enforced? Much work
has yet to be done before finding accurate and convincing answers to these questions.
1.3 Objectives
This research is part of Phase 5 of the US-Japan Cooperative Earthquake Research
Program on Composite and Hybrid Structures. This thesis presents an extensive
analytical design and assessment study whose focus is on the seismic behavior of
composite RCS moment frames. The main objectives of the present work can be
summarized in the following points:
1. Further develop and improve existing analytical models and techniques for the
nonlinear inelastic static and time history analyses of composite RCS moment-
framed buildings.
2. Synthesize and review existing knowledge on members and composite connections
design and behavior.
3. Exercise and evaluate current seismic design provisions for composite construction.
4. Develop accurate damage indices and performance criteria to assess seismic
performance of RCS moment frames.
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5. Apply nonlinear analysis methods to evaluate building performance under varying
seismic hazards.
6. Develop and correlate stability limit states to performance levels suggested by
modern seismic codes.
7. Investigate correlation of structural response to various ground motion parameters so
as to reduce the uncertainty in estimating median response due to limited sample
size (i.e., limited number of ground records or limited number of time history
analyses).
8. Assess composite RCS moment frames through comparisons to well-established
steel moment-framed systems which will put into perspective all the issues that
should be addressed for improving the seismic performance of such new systems.
The ultimate goal is that by improving our understanding of the seismic response of
composite RCS frames under multi-level earthquake hazards, this investigation should
lead to their broader utilization for seismic regions and will contribute towards the
development of more transparent and reliable performance-based design methodologies.
1.4 Scope and Organization
This research is mainly divided into two parts. Part I deals with further development and
improvement of existing analytical tools and models for inelastic dynamic analysis of
composite RCS frames as well as development of performance acceptance criteria (i.e.,
seismic damage indices). Part II investigates the seismic performance of these composite
moment frames under multi-level earthquake hazards and compares their response to
traditional steel moment frames.
Chapter 2 describes analytical models implemented in the software DYNAMIX –
DYNamic Analysis of MIXed (steel-concrete) structures developed through this and
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previous research (El-Tawil and Deierlein, 1996) with capabilities to perform inelastic
static and dynamic analyses of three-dimensional steel and RCS frames. Employing a
stress-resultant plasticity model, beam-column elements implemented in DYNAMIX
account for the interaction of axial loads and biaxial bending moments, including the
effects of spread-of-plasticity, geometric nonlinearities (P-∆ and P-δ), and cyclic stiffness
degradation. A new model for composite beams (i.e., composite floor decks on steel
beams) developed as part of this research is presented. The composite beam model is a
one-dimensional version of the 3-D bounding surface model used for general beam-
columns, including kinematic hardening for cyclic loading and stiffness degradation as a
function of the accumulated plastic energy in the member. Calibration and comparisons
to experimental results are provided. The chapter also summarizes a model for composite
connections between RC columns and steel beams which accounts for finite joint size and
inelastic panel shear and bearing deformations with cyclic stiffness/strength degradation.
Chapter 3 reviews various guidelines for flexural stiffness modeling of reinforced
concrete beam-columns for frame analysis. A formula is proposed to determine effective
initial flexural stiffness of reinforced concrete members, taking into account modest
degrees of cracking, amount of reinforcement, and stiffening effect of axial compression
load in the member. The flexural stiffness model has been verified by test results from
several beam-column specimens for a wide range of axial load ratios.
A brief literature review of seismic damage indices is presented in Chapter 4. Two new
local damage indices are proposed; a ductility-based index and an energy-based index.
The two damage indices are based on the idea of primary and follower half cycles in a
formulation that takes into consideration the ‘temporal’ effect of loading (i.e., loading
sequence) and cumulative damage. Results are compared to selected experimental data
including reinforced concrete columns, steel and composite beams, and composite RCS
joint sub-assemblages. Finally, data is reviewed to correlate the physical damage to the
value of the damage index.
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Chapter 5 first provides an overview of various earthquake-resistant design methods
proposed by recent seismic codes and provisions. Full descriptions of the design of three
case study buildings (6-story RCS, 12-story RCS, and 6-story STEEL) are then
presented. All controlling design criteria are discussed in detail. The chapter also explains
the selection of earthquake records for the time history analyses of the case study
buildings. General characteristics and seismic properties of the records relevant to their
likely effect on the buildings are provided.
A detailed performance study of the 6-story RCS case study frame is described in
Chapter 6. Nonlinear static and time-history analyses results under two sets of earthquake
records (general versus near-fault records with forward directivity) are presented.
Incremental Dynamic Analyses are performed where the records are scaled to different
hazard levels representative of performance levels ranging from immediate occupancy to
near collapse. A new methodology is proposed to quantify system stability limit states by
integrating the destabilizing effects represented by local damage indices through
modified second-order inelastic stability analyses. These stability limit states are then
correlated to performance levels suggested by modern seismic codes. Relating local
(members plastic rotations) to global (interstory drift ratio) response has been also
investigated so as to estimate median local response at a given value of the global
parameter and compare it to acceptance criteria from ATC 40 or FEMA 273. Finally,
correlation parameters between ground motion intensity measures and structural damage
are presented, and statistical performance measures of global response are reported.
Chapter 7 presents a detailed comparative assessment study of RCS and STEEL moment
frames comparing the response of the 6-story RCS frame in Chapter 6 to that of the 12-
story RCS and the 6-story STEEL case study frames. All issues dealt with in Chapter 6
are revisited herein to confirm or modify the findings previously reported.
Finally, in Chapter 8, the main contributions and the general conclusions from this work
are discussed, and recommendations for future work are suggested.
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Chapter 2
Analytical Models Using Spread-of-Plasticity
Approaches
One of the main objectives of this research is to develop efficient and accurate analytical
models for simulating the nonlinear behavior of composite RCS moment frames
subjected to static, cyclic or dynamic loading. This effort started by the development of
the frame analysis interactive program DYNAMIX for DYNamic Analysis of MIXed
systems (El-Tawil and Deierlein, 1996) which evolved from earlier versions used for
dynamic analysis of steel structures (CU-QUAND, Searer, 1994, and Zhao, 1993). As
part of this research further refinement of the analytical models implemented in
DYNAMIX with addition of a new element for composite beams has been accomplished.
In this chapter, analytical models for representing the inelastic beam-column elements
and composite joint panels under cyclic loading are described. These are all based on a
multi-dimensional force-space bounding surface model adopting a flexibility formulation,
which can model both the phenomena of gradual plastification and the interaction
between axial forces and moments. The models are also capable of capturing sp
