Department of Civil and Environmental Engineering Stanford ...zd207gv1593/TR155_Cordova.pdf · The John A. Blume Earthquake Engineering Center was established to promote research

Department of Civil and Environmental Engineering

Stanford University

Report No.

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) [email protected] http://blume.stanford.edu

©2007 The John A. Blume Earthquake Engineering Center

© Copyright by Paul Phillip Cordova 2005

All Rights Reserved

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Abstract

Composite RCS moment frames integrate reinforced concrete columns with structural

steel beams, providing several advantages over conventional steel or concrete moment

resisting frames. Past studies have shown these systems to be efficient in both design and

construction stages while able to maintain sufficient strength and ductility necessary in

seismic applications. Despite this past research, use of this hybrid structural system in

the United States has been limited to non- or low-seismic zones, which is largely due to

the reluctance of the engineering community to accept this “new” system as well as a

lack of comprehensive seismic design criteria in building codes and specifications. In

addition, past studies have acknowledged that there is a fundamental need to test full

structural systems, both analytically and experimentally, in order to (1) substantiate the

knowledge that has been accumulated up to this point and (2) act as a proof of concept

for the composite RCS frames.

The primary goal of this research program is to fill this knowledge gap and facilitate the

greater acceptance and use of composite RCS systems as a viable alternative to

conventional lateral resisting systems. This research synthesizes and interprets some of

the latest provisions and past studies on RCS systems and applies the accumulated

knowledge to (1) develop and validate improved seismic design provisions for RCS

frames, (2) assess and demonstrate the seismic performance of RCS structural systems

through full-scale frame testing and analytical simulations of prototype building systems,

and (3) develop and validate modeling guidelines for nonlinear analysis and performance

simulation. The cornerstone of this study is the planning, design, and testing of a full-

scale 3-story composite RCS moment frame. Using the pseudo-dynamic loading

technique, this specimen is subjected to a series of earthquake motions ranging in hazards

from frequent to extremely rare events. In addition to providing insight into the seismic

performance and design of composite RCS frames, the frame and supporting

subassembly tests also provide a rich data set for the validation of nonlinear analysis and

damage models. This also helps address one of the broader aims of this investigation,

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which is to provide support in the development of performance based earthquake

engineering.

Designed to evaluate the minimum limits of current building code requirements, the full-

scale test frame exhibited excellent seismic performance up through the maximum

considered earthquake intensity level. The damage patterns after each pseudo-dynamic

earthquake event were representative of the performance expected in well-detailed

moment resisting frames designed by current building codes, with no instances of brittle

failure (e.g. fracture). Nonlinear beam-column fiber elements and two-dimensional joint

elements were independently calibrated to multiple subassembly tests and modeling

recommendations are proposed. These models are used to simulate the test frame

conditions and loading protocol. The analytical results correlate well with the

experimental response within interstory drifts up to 3%, beyond which, the physical

damage in the frame exceeds what the analytical models used in this study are expected

to accurately capture.

Using the recommendations presented herein, trial designs of three case study buildings

(3, 6, and 20-stories) are generated, analytically modeled, and subjected to a suite of

earthquake ground motions at a range of hazard levels. The response of these case study

buildings are probabilistically evaluated considering several key engineering demand

parameters. These results, coupled with the response of the test frame, validate the

seismic behavior of composite RCS frames and also help assess and improve several key

design issues that are applicable to this system, as well as others.

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Acknowledgements

First and foremost, I would like to extend my deepest gratitude to my professor, adviser,

and friend, Dr. Greg Deierlein. You have made this experience extremely rewarding and

it would not have been the same without you.

To the rest of the professors in the Structural Engineering and Geomechanics

Department, your role in my development as a researcher and a structural engineer should

not be understated. When I first arrived at Stanford University, I thought I knew

everything; fortunately you all saved me from myself and greatly expanded my horizons

in structural and earthquake engineering.

Special thanks to Dr. Keh-Chyuan Tsai and the rest of the NCREE staff and students that

took me in for over three months during the experimental phase of this project. It was an

amazing experience to work in one of the premier laboratories in the world alongside

with some extremely talented people. In addition to Dr. Tsai, I would like to single out

and thank a few of the most visible people on this project: Chui-Hsin Chen, Wen-Chi Lai,

Kung-Juin Wang, and Wei-Chung Cheng.

I would also like to acknowledge the contribution of Professor Gustavo Parra-Montesinos

and Luis B. Fargier-Gabaldon from the University of Michigan in the development of the

updated RCS joint guidelines.

To my fellow cohorts in the “GGD Quatro” (© Greg Deierlein), Arash Altoontash, Amit

Kanvinde, and Rohit Kaul, you all are an unforgettable group of guys and I wouldn’t

have wanted to share this experience with anyone else. The stories we have together,

both inside and outside the research world, could fill up an entire novel, but for the sake

of all of us, I will refrain.

The Blume Center is a really special place filled with outstanding researchers and

remarkable people and I have truly been blessed to be a part of it throughout the years.

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Unfortunately, there are way too many people to mention here, but I am confident that

those people who deserve thanks do not need to see their name in print in order to know

that I appreciate them. Beyond that, I would like to take a line to thank Racquel Hagen,

the Administrative Associate of the Blume Center, for all her time and effort in keeping

the Blume Center and its inhabitants in order.

I would also like to acknowledge and thank my family. You all have provided me with

my foundation and my wings – two gifts that have helped me persevere through the good

and bad times and accomplish the things I have.

And of course, my unending thanks to my beautiful wife, Mrs. Sylvie Cordova.

Honestly, I didn’t plan for the first four months of our marriage to coincide with the final

months of my Ph.D. – but what a way to start out. Your support and strength throughout

my entire academic career is appreciated.

The research reported herein has been supported by the Pacific Earthquake Engineering

Research (PEER) center, Stanford University (with special thanks to Dr. Noé Lozano),

Earthquake Engineering Research Institute (EERI), National Science Foundation, and the

National Science Council of Taiwan.

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Table of Contents Abstract .............................................................................................................................. iv Acknowledgements ............................................................................................................ vi List of Tables .................................................................................................................... xiv List of Figures .................................................................................................................xvii Chapter 1: Introduction ............................................................................................... 1 1.1 Motivation for this Study .................................................................................. 3 1.2 Objectives.......................................................................................................... 4 1.3 Scope and Organization of Report .................................................................... 5 Chapter 2: RCS System Design ................................................................................... 9 2.1 Background of RCS Composite Moment Frames............................................. 9 2.2 Previous Research ........................................................................................... 12

2.2.1 Beam-Column Composite Joints............................................................... 12 2.2.2 Small-Scale Frame Tests ........................................................................... 14 2.2.3 Trial Design Studies of System Performance............................................ 15

2.3 System and Member Design Guidelines ......................................................... 15 2.3.1 General Building Design Requirements: IBC 2003 and ASCE 7-02.......................................................................................... 16 2.3.2 Member Design Requirements: Part II of the AISC Seismic Provisions .................................................................................... 20

2.3.2.1 Reinforced Concrete Columns ............................................................ 20 2.3.2.1.1 Strong-Column Weak-Beam.......................................................... 21

2.3.2.1.1.1 SEAOC Blue Book Provisions................................................... 23 2.3.2.1.2 Precast RC Column Splice Design................................................ 24

2.3.2.2 Composite Steel Beams....................................................................... 25 2.3.2.2.1 Plastic Strength of Composite Beams ........................................... 27 2.3.2.2.2 Design of Shear Studs ................................................................... 29 2.3.2.2.3 Steel Beam Splices ........................................................................ 31

2.3.2.2.3.1 Bearing versus Slip Design: Bolt Banging................................. 34 2.4 Composite Joint Design Guidelines ................................................................ 36

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2.4.1 Joint Deformations .................................................................................... 37 2.4.2 General Detailing Requirements ............................................................... 37 2.4.3 Effective Joint Width................................................................................. 38 2.4.4 Joint Strength............................................................................................. 40 2.4.5 Inner Panel Shear Strength ........................................................................ 42 2.4.6 Inner Panel Vertical Bearing Strength ....................................................... 43 2.4.7 Outer Panel Shear Strength ....................................................................... 45 2.4.8 Joint Panel Shear and Vertical Bearing Moment Capacity........................ 46

2.4.8.1 Strong-Joint Weak-Beam..................................................................... 46 2.4.9 Detailing Considerations ........................................................................... 47

2.4.9.1 Ties within Beam Depth...................................................................... 47 2.4.9.2 Longitudinal Column Bars .................................................................. 47 2.4.9.3 Face Bearing Plates and Steel Band Plates ......................................... 48 2.4.9.4 Steel Beam Flanges ............................................................................. 49 2.4.9.5 Extended Face Bearing Plates and Steel Column ............................... 49

2.4.10 Model Validation ....................................................................................... 50 2.4.10.1 RCS Joint Tests Considered ................................................................ 50 2.4.10.2 Updated Joint Guidelines Validation Results ...................................... 51 2.4.10.3 Determination of Strength Reduction (f) Factors................................ 51

2.5 Final Recommendations .................................................................................. 54 2.5.1 Reinforced Concrete Columns .................................................................. 54 2.5.2 SCWB Criterion ........................................................................................ 54 2.5.3 Composite Steel Beams............................................................................. 55 2.5.4 Precast Element Splices ............................................................................ 56 2.5.5 Composite Joint Design ............................................................................ 57

Chapter 3: Full-Scale Composite RCS Test Frame ................................................. 76 3.1 Background ..................................................................................................... 76 3.2 Rationale for Full-Scale RCS Frame Test ....................................................... 78 3.3 Design of Full-Scale Test Frame ..................................................................... 78

3.3.1 Plan and Layout of Test Frame.................................................................. 79 3.3.2 General Design Information...................................................................... 80 3.3.3 Strong-Column Weak-Beam...................................................................... 81 3.3.4 Measured Material Strengths..................................................................... 83 3.3.5 Beam and Column Splices ........................................................................ 83

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3.3.6 Shear Studs in Hinge Region..................................................................... 85 3.3.7 Roof Joints................................................................................................. 86

3.4 Description of Test .......................................................................................... 86 3.4.1 Test Setup .................................................................................................. 86 3.4.2 Loading Protocol ....................................................................................... 87

3.5 Construction of Test Frame ............................................................................. 89 3.6 Test Results...................................................................................................... 90

3.6.1 Global Results ........................................................................................... 91 3.6.2 Description of Damage.............................................................................. 94

3.6.2.1 EQ#1 – 50% in 50 year ....................................................................... 95 3.6.2.2 EQ#2 – 10% in 50 year ....................................................................... 96 3.6.2.3 EQ#3 – 2% in 50 year ......................................................................... 98 3.6.2.4 EQ#4 – 10% in 50 year ..................................................................... 100 3.6.2.5 Final Pushover................................................................................... 100

3.6.3 General Observations .............................................................................. 101 3.7 Conclusions ................................................................................................... 103

3.7.1 General Seismic Performance of RCS Frame ......................................... 103 3.7.2 Frame Transient Drift .............................................................................. 104 3.7.3 Frame Residual Drifts ............................................................................. 106 3.7.4 Frame Repair ........................................................................................... 107 3.7.5 Precast System Performance ................................................................... 109

3.7.5.1 Beam Splices ..................................................................................... 109 3.7.5.2 Column Splices ................................................................................. 110

3.7.6 Frame Overstrength................................................................................. 111 3.7.7 Behavior of Composite Beams................................................................ 111

3.7.7.1 Shear Stud Design ............................................................................. 113 3.7.8 Behavior of RC Columns ........................................................................ 113 3.7.9 Strong-Column Weak-Beam Criterion .................................................... 114 3.7.10 Behavior of Composite Joints ................................................................. 116 3.7.11 Differences between Subassembly and Frame Tests............................... 117

Chapter 4: Analytical Modeling and Validation .................................................... 162 4.1 Introduction ................................................................................................... 162 4.2 OpenSees Component Models ...................................................................... 162

4.2.1 Material Models ...................................................................................... 162

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4.2.2 Flexibility-Based Fiber Beam-Column Elements ................................... 164 4.2.2.1 Reinforced Concrete Columns .......................................................... 165 4.2.2.2 Composite Steel Beams..................................................................... 172 4.2.2.3 Convergence issues ........................................................................... 176

4.2.3 Composite Joints Elements ..................................................................... 178 4.3 Test Frame Validation Study ......................................................................... 180

4.3.1 Errors within the Pseudo-Dynamic Testing Method ............................... 182 4.3.2 Comparison to Experimental Global Response ...................................... 183

4.3.2.1 Comparison of First and Second Design Level Event ...................... 186 4.3.3 Comparison to Experimental Local Response ........................................ 187 4.3.4 Residual Drifts......................................................................................... 190 4.3.5 Time Evolution versus Predetermined Analysis...................................... 191 4.3.6 Comments on Analytical Models ............................................................ 192

4.4 Damage Indices ............................................................................................. 195 4.4.1 Damage Model ........................................................................................ 195 4.4.2 Plastic Rotations...................................................................................... 198 4.4.3 Overview of Damage after Each Event................................................... 198 4.4.4 Evolution of Damage Indices and Maximum Plastic Rotations ............. 200

4.4.4.1 Columns ............................................................................................ 200 4.4.4.2 Beams ................................................................................................ 204 4.4.4.3 General Comments ............................................................................ 206

4.5 Summary of Recommendations .................................................................... 207 4.5.1 RC Column Summary ............................................................................. 207 4.5.2 Composite Beam Summary..................................................................... 208 4.5.3 Composite Joint Summary ...................................................................... 209

4.6 Conclusions ................................................................................................... 210 4.6.1 Future Work............................................................................................. 211

Chapter 5: Applications ........................................................................................... 272 5.1 Introduction ................................................................................................... 272 5.2 Case Study Buildings .................................................................................... 272

5.2.1 Beam Design ........................................................................................... 274 5.2.2 Column Design........................................................................................ 275 5.2.3 Composite Joint Design .......................................................................... 276 5.2.4 Drift Limitations...................................................................................... 277

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5.3 Nonlinear Dynamic Time History Analyses.................................................. 277 5.3.1 Ground Motion Scaling Techniques........................................................ 278 5.3.2 Limitations of Analytical Models............................................................ 279 5.3.3 Ground Motion Selection ........................................................................ 280 5.3.4 Weighted 20-story Scaling Technique..................................................... 282

5.4 3-Story Perimeter Frame Results .................................................................. 284 5.4.1 Interpreting the Test Frame Results......................................................... 284 5.4.2 Modeling Variations for Realistic Building Case Study.......................... 288

5.4.2.1 Static Pushover Response.................................................................. 290 5.4.2.2 Derivation of Damping and Effects on Maximum Response............ 290 5.4.2.3 Global Response................................................................................ 293 5.4.2.4 Member Plastic Rotations ................................................................. 294 5.4.2.5 Damage Indices ................................................................................. 296

5.5 6-Story Perimeter Frame Results .................................................................. 299 5.5.1 Static Pushover Response........................................................................ 300 5.5.2 Global Response...................................................................................... 300 5.5.3 Member Plastic Rotations ....................................................................... 301 5.5.4 Damage Indices ....................................................................................... 302

5.6 20-Story Perimeter Frame Results ................................................................ 303 5.6.1 Static Pushover Response........................................................................ 304 5.6.2 Global Response...................................................................................... 304 5.6.3 Member Plastic Rotations ....................................................................... 305 5.6.4 Damage Indices ....................................................................................... 307

5.7 Conclusions ................................................................................................... 308 5.7.1 Seismic Design........................................................................................ 308 5.7.2 General Seismic Performance ................................................................. 309 5.7.3 Drift Criterion.......................................................................................... 309 5.7.4 Composite Joint Performance ................................................................. 310 5.7.5 Strong-Column Weak-Beam Criterion .................................................... 310 5.7.6 Damage Distribution ............................................................................... 311

Chapter 6: Conclusions ............................................................................................ 382 6.1 Summary ....................................................................................................... 382 6.2 Major Findings and Conclusions................................................................... 385

6.2.1 Seismic Performance of Composite RCS Frames................................... 385

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6.2.2 Performance of Precast Splices ............................................................... 386 6.2.3 Structural Period Elongation ................................................................... 386 6.2.4 SCWB...................................................................................................... 386 6.2.5 Top Floor Joints....................................................................................... 387 6.2.6 IBC 2003/ASCE 7-2002 Drift Criterion ................................................. 387 6.2.7 Full-scale System versus Subassembly Test Behavior............................ 387 6.2.8 Validity of Fiber Beam-Column Models ................................................. 388 6.2.9 Mehanny Damage Index ......................................................................... 389 6.2.10 Perspective on the Performance of the Test Frame ................................. 389

6.3 Design and Analytical Modeling Recommendations .................................... 390 6.3.1 Strong-Column Weak-Beam Criterion .................................................... 390 6.3.2 Bolted Beam Splice Design..................................................................... 391 6.3.3 Column Grouted Splice Design............................................................... 391 6.3.4 Composite beams .................................................................................... 392 6.3.5 Updated Joint Guidelines ........................................................................ 392 6.3.6 Bond-Slip in RC Columns....................................................................... 393 6.3.7 Analytical Modeling of Composite RCS Frames.................................... 393

6.4 Future Work................................................................................................... 393 6.4.1 Calibration of Deteriorating Models ....................................................... 394 6.4.2 Investigation of Subassembly Boundary Conditions .............................. 394 6.4.3 Alternative Energy-Based Damage Models ............................................ 395

Bibliography ................................................................................................................. 396

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List of Tables

2.1 Joint width comparisons between ASCE and Updated Guidelines............... 58 2.2 Summary of joint details and dimensions for those in the panel shear

joint group. (Units: kN, mm)......................................................................... 59 2.3 Summary of joint details and dimensions for those in the vertical bearing

joint group. (Units: kN, mm)......................................................................... 60 2.4 Results from Update Guidelines for the joint group failing in panel shear.

(Units: kN, mm) ............................................................................................ 61 2.5 Results from Update Guidelines for the joint group failing in vertical

bearing. (Units: kN, mm) .............................................................................. 62 2.6 Summary of values required to compute phi-factor using the beta-

reliability index.............................................................................................. 62

3.1 Rationale for large-scale test ......................................................................... 120 3.2 Design loads summary .................................................................................. 121 3.3 Test frame member properties ....................................................................... 121 3.4 Measured strengths of steel tension coupons ................................................ 122 3.5 Measured crushing strength of concrete cylinders ........................................ 122 3.6 Summary of maximum and minimum drifts during each pseudo-dynamic

event (both absolute drift and with the residual removed)............................ 122

4.1 Summary of RC column specimens used in calibration study...................... 214 4.2 Composite beam validation study ................................................................. 215 4.3 Material properties for composite beam test specimens ............................... 217 4.4 Plastic rotation capacity of test frame components ....................................... 218 4.5 Correlation between the Mehanny damage index and the expected

damage in the component.............................................................................. 218 4.6 Comparison of the simulated to measured maximum plastic rotation in

1st floor interior column................................................................................. 218 4.7 Comparison of the simulated to measured maximum plastic rotation in

1st floor exterior column................................................................................ 219 4.8 Comparison of the simulated to measured maximum plastic rotation in

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2nd floor interior column................................................................................ 219 4.9 Comparison of the simulated to measured maximum plastic rotation in

2nd floor exterior column ............................................................................... 219 4.10 Comparison of the simulated to measured maximum plastic rotation in

1st floor beam................................................................................................. 220 4.11 Comparison of the simulated to measured maximum plastic rotation in

2nd floor beam................................................................................................ 220 4.12 Summary of OpenSees input parameters for definitions of Concrete02

materials (uniaxialMaterial Concrete02)....................................................... 220 4.13 Summary of OpenSees input parameters for definitions of Steel02

materials (uniaxialMaterial Steel02) ............................................................. 221 4.14 Summary of OpenSees input parameters for definitions of Hysteretic

materials (uniaxialMaterial Hysteretic)......................................................... 221

5.1 Summary of design values for each of the case study buildings................... 313 5.2 Member design schedule of 6-story case study building .............................. 313 5.3 Member design schedule of 20-story case study building ............................ 314 5.4 Summary of column and beam strengths with the corresponding SCWB

ratios for the 3-story perimeter frame. (units: kN,mm)................................. 315 5.5 Summary of column and beam strengths with the corresponding SCWB

ratios for the 6-tory perimeter frame (frame line 1 and 7). (units: kN,mm).......................................................................................................... 315

5.6 B Summary of column and beam strengths with the corresponding SCWratios for the 20-story perimeter frame (frame line A and F). (units: kN,mm).......................................................................................................... 316

5.7 Strength of composite joints and the strong-joint weak-beam ratios for the 3-story case study frame. (units: kN,mm) ............................................... 316

5.8 Strength of composite joints and the strong-joint weak-beam ratios for the 6-story case study frame. (units: kN,mm) ............................................... 317

5.9 Strength of composite joints and the strong-joint weak-beam ratios for the 20-story case study frame. (units: kN,mm) ............................................. 317

5.10 Modal properties of 20-story frame and corresponding weights for record scaling ................................................................................................ 318

5.11 Comparison of IDRMAX of two OpenSees models with test frame ............... 318 5.12 Measured strengths of steel tension coupons ................................................ 318

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5.13 Measured crushing strength of concrete cylinders ........................................ 319 5.14 Plastic rotation capacity of 3-story case study frame components................ 3

Correlation between the Mehanny damage index and the expected 19

5.15 damage in the component.............................................................................. 319

5.16 Probability of beam hinges being in a specific damage state given a 10/50 and 2/50 hazard level........................................................................... 320

5.17 Plastic rotation capacity of 6-story case study frame components................ 320 5.18 lastic rotation capacity of 20-story case study frame components............. P . 321

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List of Figures

1.1 Photo of composite RCS frames depicting the steel beam running continuous through the reinforced concrete column ..................................... 8

2.1 Typical construction sequence of composite RCS moment frames............... 63 2.2 RCS precast construction utilizing beam-column modules and column

and beam spliced connection ......................................................................... 63 2.3 Example of precast RCS construction in Japan (Shimizu Corporation)........ 64 2.4 Example of cast-in-place RCS system that replaces steel erection

columns with stiffened reinforcing bar cages. (Shimizu Corporation).......... 64 2.5 Connection between steel beam and reinforced concrete column................. 65 2.6 Schematic diagrams of RCS joint details tested ............................................ 65 2.7 Typical failure modes in RCS beam-column joints (Kanno et al. 2000)....... 66 2.8 Typical hysteretic response of a RCS beam-column test failing in joint

bearing failure (Kanno 1993)......................................................................... 66 2.9 Typical hysteretic response of RCS beam-column test failing in joint

shear (Kanno 1993)........................................................................................ 67 2.10 Typical hysteretic response of RCS beam-column test failing in beam

hinging (Kanno 1993).................................................................................... 67 2.11 Typical configuration of reinforcement bars in RC columns ........................ 68 2.12 (a) Illustration showing the separation of int./ext. columns for the SCWB

criterion and (b) the appropriate load factors with respect to the P-M column curve in order to obtain the lower flexural strength ......................... 68

2.13 SEOAC Blue Book strong-column weak-beam provisions........................... 68 2.14 Details of grouted splice connections for precast RC columns ..................... 69 2.15 Differences between the definitions of effective slab width considering

lateral versus gravity loading......................................................................... 69 2.16 Schematic of a typical bolted flange plate beam splice connection .............. 70 2.17 Assumed moment diagram for composite beam ........................................... 70 2.18 Assumed hinge length and location of beam splice....................................... 71 2.19 Cross-section of the beam splice plates and the concrete slab depicting

the force couple between the lower plates and slab....................................... 71 2.20 Plot of the location of the plastic neutral axis versus the ratio of

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composite to steal beam strength, 76 mm deck and slab. (1 in. = 25.4mm)......................................................................................................... 71

3.14

2.21 Normalized load versus joint distortion response (Parra-Montesinos et al., 2001) ........................................................................................................ 72

2.22 Joint detail showing the band plate, cover plate, and the transverse beam.... 72 2.23 Definition of outer strut width ....................................................................... 73 2.24 Joint Example ................................................................................................ 74 2.25 Predicted versus measured joint shear strength for both ASCE and

Updated model............................................................................................... 74 2.26 Predicted versus measured joint bearing strength for both ASCE and

Updated model............................................................................................... 75

2.27 Ratio of the composite to the bare steel beam strength for typical W-section beams (1in = 25.4mm, 1ksi = 6.89MPa) ........................................... 75

3.1 Plan View of Building.................................................................................... 1233.2 Plan and elevation views of full-scale composite test frame......................... 1233.3 Joint detail showing the transverse beam and placement of ties ................... 1243.4 ΣMc/ΣMg ratios at each joint assuming a) steel beams (nominal), b)

composite beams (nominal) and (c) composite beams and RC columns with measured material properties................................................................. 124

3.5 Schematic of a typical bolted flange plate beam splice connection .............. 1253.6 RC column cantilever tests with the grouted splice located (a) 1-meter up

the column height and (b) flush at the column-footing interface .................. 1263.7 Response of RC column subassembly test with precast splice at (a) 1-

meter above the footing and (b) flush at the column-footing interface. (Tsai 2002) ..................................................................................................... 127

3.8 Top joint option #1. Section AA in Fig. 3.9................................................... 1283.9 Section A-A from Fig. 3.8.............................................................................. 128

3.10 Reinforcement cap plate ................................................................................ 1283.11 Plate to reinforcing bar detail ........................................................................ 1293.12 Schematic of load path between actuators, loading beams, and test frame... 1293.13 Final records scaled at T1 = 1sec to appropriate Taiwanese hazard levels .... 130

Construction photos of (a) a typical pre-cast beam-column module and (b) the completion of the first floor ............................................................... 130

3.15 Roof displacement versus time for the 50/50 ................................................ 131

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3.16 Roof displacement versus time for the 10/50-1 event ................................... 131

32 3.19

133 3.20

133 3.21

134 3.22

134 3.23

137 3.29

139 3.32

140 3.34

140 3.35

141 3.36

. 141 3.37

3.17 Roof displacement versus time for the 2/50 event......................................... 1323.18 Roof displacement versus time for the final 10/50 event .............................. 1

Maximum interstory drift ratios for each floor during each pseudo-dynamic loading event ...................................................................................Maximum story shear for each floor during each pseudo-dynamic loading event..................................................................................................Maximum story shear for each floor during each pseudo-dynamic loading event..................................................................................................Maximum story shear for each floor during each pseudo-dynamic loading event..................................................................................................Maximum story shear for each floor during each pseudo-dynamic loading event in dotted line) .......................................................................... 135

3.24 Hysteretic response of a 1st floor interior column base for the 50/50 event .. 1353.25 Hysteretic response of a 1st floor interior column base for the 10/50-1a

event............................................................................................................... 1363.26 Hysteretic response of a 1st floor interior column base for the 10/50-1b

event............................................................................................................... 1363.27 Hysteretic response of a 1st floor interior column base for the 2/50 event .... 1373.28 Hysteretic response of a 1st floor exterior beam hinge for the 50/50 event ...

Hysteretic response of a 1st floor exterior beam hinge for the 10/50-1a event............................................................................................................... 138

3.30 Hysteretic response of a 1st floor exterior beam hinge for the 10/50-1b event............................................................................................................... 138

3.31 Hysteretic response of a 1st floor exterior beam hinge for the 2/50 event. (Large rotations are due to measurement errors caused by severe local buckling) ........................................................................................................Hysteretic response of a 1st floor beam for the 10/50-2 event ....................... 139

3.33 Hysteretic response of a 1st floor interior beam hinge for the 2/50 event......Total and outer panel hysteretic response of a 1st floor interior joint for the 50/50 event...............................................................................................Total and outer panel hysteretic response of a 1st floor interior joint for the 10/50-1a event..........................................................................................Total and outer panel hysteretic response of a 1st floor interior joint for the 10/50-1b ..................................................................................................Total and outer panel hysteretic response of a 1st floor interior joint for

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the 10/50-1b event ........................................................................................Total and outer panel hysteretic response of a 1st floor interior joint for

. 142 3.38

3.39

145 3.44

146 3.46

3.53

3.55

the 10/50-2 event ........................................................................................... 142Hysteretic response of the 2nd floor upper interior column hinge after the 10/50-1a event ............................................................................................... 143

3.40 Hysteretic response of the 2nd floor upper interior column hinge after the 10/50-1b event ............................................................................................... 143

3.41 Hysteretic response of the 2nd floor upper interior column hinge after the 2/50 event....................................................................................................... 144

3.42 Damage in 1st floor interior column base after the 50/50 event .................... 1453.43 Damage in 1st floor interior column base after the 10/50-1b event ...............

Damage in 1st floor interior column base after the 2/50 event ...................... 1463.45 Damage in 1st floor interior column base after the 10/50-2 event .................

Yielding in 1st floor beam after the 50/50 event ............................................ 1473.47 Yielding and local buckling in 1st floor beam (1B1S) after the 10/50-1b

event............................................................................................................... 1473.48 Yielding and local buckling in 1st floor beam (1B1S, exterior beam

hinge) after the 2/50 event ............................................................................. 1483.49 Yielding and local buckling in 1st floor beam (1B1S, exterior beam

hinge) after the 10/50-2 event........................................................................ 1483.50 Yielding and local buckling in 1st floor beam (1B3N) after the 10/50-1b

event............................................................................................................... 1493.51 Yielding in 1st floor beam (1B1N, interior beam hinge) after the 2/50

event............................................................................................................... 1493.52 Yielding in 1st floor beam (1B1N, interior beam hinge) after the 10/50-2

event............................................................................................................... 150 1st floor splice plate after the 10/50-1b event ................................................ 150

3.54 Joint 1J3 after the 50/50 Chi-Chi event ......................................................... 151Joint 1J3 after the 10/50-1b Loma Prieta event ............................................. 151

3.56 Joint 1J3 after the 2/50 Chi-Chi event ........................................................... 1523.57 Joint 1J3 after the10/50-2 Loma Prieta event ................................................ 1523.58 Damage in upper hinge of 2nd floor interior column hinge after the 10/50-

1b event.......................................................................................................... 1533.59 Damage in upper hinge of 2nd floor interior column hinge after the 2/50

event............................................................................................................... 1533.60 Damage in upper hinge of 2nd floor interior column hinge after the 10/50-

xx

2 event............................................................................................................ 154

155

3.63

3.68 ielding and local buckling in 1st floor beam (1B1S, exterior beam nge) after the final pushover event ............................................................. 158

3

3 3 3

3 161 3.74

2

4.2 ....... 222 4.3

3 4.5

4.8

5 4.9

3.61 Frame at its maximum drift state during static push. IDR in 1st floor:10%, 2nd: 8%, and 3rd: 3%....................................................................................... 154

3.62 Damage in 1st floor exterior column base after the final pushover event ......Damage in 1st floor interior column base after the final pushover event....... 155

3.64 Damage in upper hinge of 2nd floor exterior column hinge after the final pushover event ............................................................................................... 156

3.65 Damage in upper hinge of 2nd floor exterior column hinge after the final pushover event ............................................................................................... 156

3.66 Slab above exterior beam hinge, 1B1S, after the final static push ................ 1573.67 Net section rupture of lower flange plates in 1st floor beam splice ............... 157

Yhi

.69 Yielding and local buckling in 1st floor beam (1B3N, exterior beam hinge after the final pushover event ........................................................................ 158

.70 Spectral acceleration versus displacement for the Loma Prieta event........... 159

.71 Spectral acceleration versus displacement for the Chi-Chi event ................. 159

.72 Spectral acceleration graphs of final records with highlighted spectral values at the elongated periods ...................................................................... 160

.73 RC column base hinges after loose concrete had been chipped away...........Boundary condition in subassembly tests causes slab to pull away from beam............................................................................................................... 161

4.1 Hysteretic response for the OpenSees Steel02 material model ..................... 22Hysteretic response for the OpenSees Concrete02 material model........Backbone and cyclic response of Hysteretic model in OpenSees ................. 223

4.4 Typical tensile softening response of reinforced concrete............................. 22Representation of deformations from bond slip and yield penetration.......... 224

4.6 Idealized backbone response of reinforcing bar pull out. (Fillipou et al. 1983) .............................................................................................................. 224

4.7 RC Column calibration against subassembly test: Tsai 2002-FFH08, base springs included ............................................................................................. 225RC Column calibration against subassembly test: Tsai 2002-FFH08, no base ................................................................................................................ 22RC Column calibration against subassembly test: Tsai 2002-FFL08,

xxi

grouted splice within hinge............................................................................ 226

....... 227 4.13

....... 228 4.14

....... 229 4.15

....... 229 4.16

....... 230 4.17

t ..... 231 4.19

..... 233

4.23 .... 234

4.24 ..... 234

4.25 5

4.26 5

4.27 6

4.28

4.10 RC Column calibration against subassembly test: Tsai 2002-FRL08, grouted splice within hinge zone (OS model with coupler influence shown as backbone)....................................................................................... 226

4.11 RC Column calibration against subassembly test: Tsai 2002-FRL60, grouted splice within hinge zone, high axial load ......................................... 227

4.12 RC Column calibration against subassembly test: Tanaka et al. (1990) test #4......................................................................................................RC Column calibration against subassembly test: Tanaka et al. (1990) test #3......................................................................................................RC Column calibration against subassembly test: Tanaka et al. (1990) test #2......................................................................................................Schematics of the cantilever and double-ended test setup with respect to bond slip and OpenSees modeling..........................................................Definition of effective slab width showing both AISC-LRFD and the column width ..........................................................................................Composite beam subassembly dimensions and cross-section details............ 231

4.18 Composite beam calibration against subassembly test: Uang (1985) tesComposite beam calibration against subassembly test: Bursi and Ballerini (1996) test ....................................................................................... 232

4.20 Composite beam calibration against subassembly test: Tagawa (1989) test.................................................................................................................. 232

4.21 Composite beam calibration against subassembly test: Tagawa (1989) test.................................................................................................................. 233

4.22 Composite beam calibration against subassembly test: Lee (1987) test...Composite beam calibration against subassembly test: Cheng (2002), specimen INUCS- East Beam....................................................................Composite beam calibration against subassembly test: Cheng (2002), specimen INUCS- West Beam..................................................................Composite beam calibration against subassembly test: Cheng (2002), specimen ICLCS- East Beam ........................................................................ 23Composite beam calibration against subassembly test: Cheng (2002), specimen ICLCS- West Beam ....................................................................... 23Composite beam calibration against subassembly test: Cheng (2002), specimen ICLPS- East Beam......................................................................... 23Composite beam calibration against subassembly test: Cheng (2002),

xxii

specimen ICLPS- West Beam........................................................................ 23Schematic of OpenSees joint element used in this study .............................. 237

6 4.29

7 4.31

241 4.38

1 4.39

............. 242 4.40

............. 242 4.41

4.42

4.43 244

4.44

245 4.46

246 4.48

4.30 Panel shear hysteretic model (backbone and cyclic model) .......................... 23Vertical bearing hysteretic model (backbone and cyclic model) ................... 238

4.32 Calibration results for joint specimen OJB1-0, which primarily fails in vertical bearing .............................................................................................. 238




4.36 Calibration results for joint specimen OJS1-1, which primarily fails in panel shear ..................................................................................................... 240

4.37 Calibration results for joint specimen OJS2-0, which primarily fails in panel shear .....................................................................................................Calibration results for joint specimen OJS3-0, which primarily fails in panel shear ..................................................................................................... 24Calibration results for joint specimen OJS4-0, which primarily fails in panel shear ........................................................................................Calibration results for joint specimen OJS5-0, which primarily fails in panel shear ........................................................................................Calibration results for joint specimen OJS6-0, which primarily fails in panel shear ..................................................................................................... 243 Calibration results for joint specimen OJS7-0, which primarily fails in panel shear ..................................................................................................... 243Calibration results for joint specimen HJS1-0, which primarily fails in panel shear .....................................................................................................Calibration results for joint specimen HJS2-0, which primarily fails in panel shear ..................................................................................................... 244

4.45 Contributions from panel shear and vertical bearing spring for joint specimen OJS3-0, OJS4-1, and OJS5-0 ........................................................Schematic of the analytical model of the test frame...................................... 246

4.47 Ramp and hold phases of pseudo-dynamic testing and the concept of force relaxation ..............................................................................................OpenSees versus test frame response for 50/50 event: (a) roof

xxiii

displacement, (b) base shear, (c) peak IDR, and (d) peak story shear...........OpenSees versus test frame response for 10/50-1a event: (a) roof displacement, (b) base shear, (c) peak IDR, and (d) peak story shear........... 248

247 4.49

2 4.54

6 4.62

..... 256 4.63

4.50 OpenSees versus test frame response for 10/50-1b event: (a) roof displacement, (b) base shear, (c) peak IDR, and (d) peak story shear........... 249

4.51 OpenSees versus test frame response for 2/50 event: (a) roof displacement, (b) base shear, (c) peak IDR, and (d) peak story shear........... 250

4.52 OpenSees versus test frame response for 10/50-2 event: (a) roof displacement, (b) base shear, (c) peak IDR, and (d) peak story shear........... 251

4.53 Contours of the power spectral density for the frequency of the analytical response throughout the time history (10/50-1) using a 10-second sliding window .......................................................................................................... 25Contours of the power spectral density for the frequency of the measured response throughout the time history (10/50-1) using a 10-second sliding window ..........................................................................................................

252

4.55 Contours of the power spectral density for the frequency of the analytical response throughout the time history (10/50-1) using a 10-second sliding window .......................................................................................................... 253

4.56 Contours of the power spectral density for the frequency of the measured response throughout the time history (10/50-1) using a 10-second sliding window .......................................................................................................... 253

4.57 Plot of the predominate period of a sliding 10-second window over the displacement time history of the first 10/50 event......................................... 254

4.58 Plot of the predominate period of a sliding 10-second window over the displacement time history of the 2/50 event .................................................. 254

4.59 Plot of the predominate period of a sliding 10-second window over the displacement time history of the second 10/50 event .................................... 255

4.60 Analytical versus experimental comparison of the roof drift versus base shear during the final static pushover of the test frame ................................. 255

4.61 Comparison of the roof displacement response measured from the test frame for the first (1b) and second 10/50 (2) event ....................................... 25Comparison of the roof displacement response predicted by OpenSees for the first (1b) and second 10/50 (2) event ............................................Analytical versus measured response of beams during 50/50 event ............. 257

4.64 Analytical versus measured response of beams during 10/50-1a event ........ 2574.65 Analytical versus 258measured response of beams during 10/50-1b event .. 257

xxiv

4.66 Analytical versus measured response of beams during 2/50 event ............... 258

4.70 4.71

4.73 0 4.74

4.76 1 4.77

262 4.79

3 4.80

4 4.82 4.83 Damage index values (>30%) after 2% in 50 year event .............................. 265 4.84 amage index values (>30%) after final 10% in 50 year event .................... 265 4.85 -d) Photos of damage progression in the 1st floor int. column after each

4

. 267 4.87

4

4.89

4.67 Analytical versus measured response of beams during 10/50-2 event .......... 2584.68 Analytical versus measured response of columns during 50/50 event .......... 2584.69 Analytical versus measured response of columns during 10/50-1b event..... 259

Analytical versus measured response of columns during 10/50-1b event..... 259 Analytical versus measured response of columns during 2/50 event ............ 259

4.72 Analytical versus measured response of columns during 10/50-2 event....... 260Analytical versus measured response of joints during 50/50 event............... 26Analytical versus measured response of joints during 10/50-1a event.......... 260

4.75 Analytical versus measured response of joints during 10/50-1b event ......... 261Analytical versus measured response of joints during 2/50 event................. 26Analytical versus measured response of joints during 50/50 event............... 261

4.78 Comparison of the residual displacements from the analytical (thin line) and experimental (thick line) model after each pseudo-dynamic event ........Calibration results for joint specimen OJB1-0, which primarily fails in vertical bearing .............................................................................................. 26Damage index values (>30%) after 50% in 50 year event ............................ 263

4.81 Damage index values (>30%) after 10% in 50 year 1a event........................ 26Damage index values (>30%) after 10% in 50 year -1b event ...................... 264

D(amain event. Evolution of damage indices using (e,f) OpenSees and (g) measured data ................................................................................................ 266

.86 (a-d) Photos of damage progression in the 1st floor exterior column after each main event. Evolution of damage index using (e) OpenSees and (f) measured data ...............................................................................................(a-d) Photos of damage progression in the 2nd floor interior column after each main event Evolution of damage index using (e) OpenSees and (f) measured data ................................................................................................ 268

.88 (a-d) Photos of damage progression in the 2nd floor exterior column after each main event. Evolution of damage index using (e) OpenSees and measured data ................................................................................................ 269(a-d) Photos of the damage progression in the 1st floor beam after each main event. Evolution of damage index using (e) OpenSees and (f) measured data ................................................................................................ 270

xxv

4

5.1 2

5.3 . 323

5.4

5.5 325

5.6

.... 327

5.8

8 5.10

328 5.11

329 5.12

5.15

.90 (a-d) Photos of the damage progression in the 1st floor beam after each main event. Evolution of damage index using (e) OpenSees and (f) measured data ................................................................................................

271

Typical floor plan of 6-story case study building .......................................... 322

5.2 Typical floor plan of 20-story case study building ........................................ 32IBC 2003 design hazard spectra with the code-defined periods (1.2Ta) for the 3, 6, and 20 story frames labeled on the curve .......................................Schematic of typical transverse reinforcement in RC columns for 6-story perimeter frame.............................................................................................. 324Schematic of typical transverse reinforcement in RC columns for 20-story perimeter frame.....................................................................................Typical plan view of the column section just below the beam and in the beam-column joint. (section A-A and B-B in Figs. 5.7 and 5.8) ................... 326

5.7 Cross-section of typical beam-column joint depicting the location of the joints ties ....................................................................................................Cross-section of typical beam-column joint depicting the location of the joints ties ........................................................................................................ 327

5.9 (a)The traditional cloud approach of nonlinear time history analyses and two alternative concepts for scaling ground motions using (b) incremental scaling of single ground motions and (c) the stripe analysis technique........................................................................................................ 32Magnitude and distance to the rupture pairs for ground motion records used in this study ...........................................................................................Epsilon versus spectral acceleration at a period of 1 second for the 80 ground motions considered in this study .......................................................Epsilon versus spectral acceleration at a period of 1.5 seconds for the 80 ground motions considered in this study ....................................................... 329

5.13 Epsilon versus spectral acceleration at a period of 4 seconds for the 80 ground motions considered in this study ....................................................... 330

5.14 Response spectrum for selected ground motions at (a) 0.05g, (b) 0.09g, (c) 0.2g, (d ) 0.3g, (e) 0.4g, (f ) 0.5g, and (g) 0.6g stripe hazard level for

330-

the 3-story building........................................................................................ 333Response spectrum for selected ground motions at (a) 0.03g, (b) 0.06g, 334(c) 0.1g, (d ) 0.2g, (e) 0.3g, and (f ) 0.4g stripe hazard level for the 6- -

xxvi

story building ................................................................................................. 336 7

5.17

ft

43

5.22 . 343

5.23

346 5.27

5.16 Example of weighted average scaling technique........................................... 33Response spectrum for selected ground motions at (a) 0.01g,(b) 0.02g, 337(c) 0.05g, (d) 0.1g, (e) 0.18g, and (f) 0.2g stripe hazard level for the 20-story building .................................................................................................

-340

5.18 Plot of the measured and simulated maximum IDR from the first four events of the pseudo-dynamic loading protocol ............................................ 340

5.19 Comparison of stripe analysis study and the measured and simulated drifrom the test frame......................................................................................... 341

5.20 Simulate IDA stripe response for selected columns (a,b), beams (c,d), and joints (e,f) compared to the measured response from the frame test ...... 342

5.21 Static pushover curve for 3-story frame using IBC 2003 force distribution . 3IDR profile of 3-story frame during the pushover at the design base shear and selected roof drift ratios .........................................................................Comparison of the median response of 3-story RCS frame with zero damping and 2% damping based on initial and last committed stiffness matrix ............................................................................................................. 344

5.24 Relationship between damping ratio and frequency for the 3-story RCS frame as defined by the Rayleigh equation.................................................... 344

5.25 Stripe analysis plot of maximum interstory drift versus hazard level for the 3-story RCS frame ................................................................................... 345

5.26 Drift profile of 3-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.045g-0.5g)............................................................................................Drift profile of 3-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.6g-1.15g) ............................................................................................................. 347

5.28 Maximum drift at each floor of 3-story frame during each event in the corresponding stripe level (bold lines: median, 16th, and 84th percentile) ..... 348


5.30 Relationship between the maximum plastic rotation in the interior columns and the scaled spectral acceleration ................................................ 350

5.31 Relationship between the maximum plastic rotation in the exterior columns and the scaled spectral acceleration ................................................ 351

5.32 Relationship between the maximum plastic rotation in the beams and the

xxvii

scaled spectral acceleration............................................................................ 352

5.34

5.38

5.39 Relationship between the final value of the damage index for the exterior

..... 358 5.40

..... 359 5.41

360 5.42

361 5.43

. 362 5.44

362 5.45

. 363 5.46

364 5.48

5.49

5.33 Relationship between the maximum positive (left column) and negative (right column) plastic rotation in the beams and the scaled spectral acceleration .................................................................................................... 353Relationship between the maximum rotation for the interior joints and the scaled spectral acceleration...................................................................... 354

5.35 Relationship between the maximum rotation for the exterior joints and the scaled spectral acceleration...................................................................... 355

5.36 Summary of the median and ± standard deviation of plastic rotations of 3-story frame members at the 10%in50year level (Sa = 0.72g)..................... 356

5.37 Summary of the median and ± standard deviation of plastic rotations of 3-story frame members at the 2%in50year level (Sa = 1.08g)....................... 356Relationship between the final value of the damage index for the interior columns and the scaled spectral acceleration ................................................ 357

columns and the scaled spectral acceleration ...........................................Relationship between the final value of the damage index for the beams and the scaled spectral acceleration..........................................................Relationship between the final value of the damage index for the interior joints and the scaled spectral acceleration .....................................................Relationship between the final value of the damage index for the exterior joints and the scaled spectral acceleration .....................................................Summary of the median and ± standard deviation of damage indices of frame members in 3-story frame at the 10%in50year level (Sa = 0.72g) .....Summary of the median and ± standard deviation of damage indices of frame members in 3-story frame at the 2%in50year level (Sa = 1.08g) ........Relationship between damping ratio and frequency for the 6-story RCS frame as defined by the Rayleigh equation...................................................Static pushover curve for 6-story frame using IBC 2003 force distribution . 363

5.47 IDR profile of 6-story frame during the pushover at the design base shear and selected roof drift ratios ..........................................................................Stripe analysis plot of maximum interstory drift versus hazard level for the 6-story RCS frame ................................................................................... 364 Drift profile of 6-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.03g-0.4g) ............................................................................................................... 365

xxviii

5.50

... 366 5.51

... 367 5.52

368 5.53

369 5.54

369 5.55

370 5.56

0 5.57

frame as defined by the Rayleigh equation.................................................... 371 5.58 Static pushover curve for 20-story frame using IBC 2003 force

distribution..................................................................................................... 371 5.59 IDR profile of 20-story frame during the pushover at the design base

shear and selected roof drift ratios................................................................. 372 5.60 Stripe analysis plot of maximum interstory drift versus hazard level for

the 20-story RCS frame ................................................................................. 372 5.61 Drift profile of 20-story frame at the time of maximum drift during each

event scaled to the common hazard level labeled in the x-axis. (Sa=0.01g-0.2g) ............................................................................................................... 373

5.62 Drift profile of 20-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.27g-0.3g) ............................................................................................................... 374

5.63 Maximum drift at each floor of 20-story frame during each event in the corresponding stripe level (bold lines: median, 16th, and 84th percentile) .....

375


5.65 Summary of the median and ± standard deviation of plastic rotations of 20-story frame members at the 10%in50year level (Sa = 0.18g)................... 377

5.66 Summary of the median and ± standard deviation of plastic rotations of

Drift profile of 6-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.48g-

0.8g) ............................................................................................................Maximum drift at each floor of 6-story frame during each event in the corresponding stripe level (bold lines: median, 16th, and 84th percentile) ..Maximum drift at each floor of 6-story frame during each event in the corresponding stripe level (bold lines: median, 16th, and 84th percentile) .....Summary of the median and ± standard deviation of plastic rotations of 6-story frame members at the 10%in50year level (Sa = 0.48g).....................Summary of the median and ± standard deviation of plastic rotations of 6-story frame members at the 2%in50year level (Sa = 0.72g).......................Summary of the median and ± standard deviation of damage indices of 6-story frame members at the 10%in50year level (Sa = 0.48g) ........................Summary of the median and ± standard deviation of damage indices of 6-story frame members at the 10%in50year level (Sa = 0.72g) ........................ 37Relationship between damping ratio and frequency for the 20-story RCS

xxix

xxx

20-story frame members at the 2%in50year level (Sa = 0.27g)..................... 378 5.67 Summary of the median and ± standard deviation of plastic rotations of

20-story frame members at the 2%in50year level (Sa = 0.27g)..................... 379 5.68 Summary of the median and ± standard deviation of damage indices of

20-story frame members at the 2%in50year level (Sa = 0.27g)..................... 380

5.69 Maximum interstory drift response for each case study building at the 10/50 hazard level.......................................................................................... 381

Chapter 1: Introduction

Composite and hybrid structures comprised of reinforced concrete and structural steel

members have gained popularity over the past thirty years, due in large part to the

efficiency that they provide in the design and construction of multi-story buildings.

These systems utilize structural steel and reinforced concrete components, wherein the

intrinsic advantages of each material are optimized in resisting the applied loads. These

composite design concepts also provide flexibility in construction, which can lead to

improved integration of construction trades and reduced construction time. Rapid

advancements in composite systems occurred in a number of cities (e.g., Dallas and

Houston, Texas; Atlanta, Georgia), during a period of rapid growth in the early 1980’s.

To a large extent, the applications of these systems have been limited to regions of low-

to moderate-seismicity, in spite of a number of key advantages these systems can provide

for seismic design.

This research focuses on one type of composite moment frame system, which is

comprised of reinforced concrete (RC) columns and steel (S) beams and is referred to as

composite RCS moment frames. As shown in Fig. 1.1, this system permits the primary

steel beam to run continuous through the reinforced concrete column, thereby allowing

the beam to be spliced away from the location of maximum moments. Through past

studies on beam column subassembly experiments (Sheikh 1987, Deierlein 1988, Kanno

1993, Parra-Montesinos 2000, Liang 2004), this connection detail has been shown to

provide the necessary ductility and toughness required for use in seismic applications. In

addition, splicing the beam outside of the hinging zone avoids the fracture problems

encountered in conventional steel frames during the 1994 Northridge and 1995 Hanshin

earthquakes. Past analytical studies of system performance have demonstrated that the

inelastic dynamic response of these systems is comparable to that of an equivalent steel

moment resisting frame (Mehanny et al., 2000, Bugeja 1999, Noguchi 1998).

With the ultimate goal to facilitate greater acceptance and use of RCS systems for seismic

design, this research extends past studies on RCS systems and applies the accumulated

1

knowledge to (1) develop and validate improved seismic design provisions for RCS

frames, (2) assess and demonstrate the seismic performance of RCS frames through full-

scale frame testing and simulations of prototype building systems, and (3) develop and

validate modeling guidelines for nonlinear analysis and performance simulation. A focal

point of this research is the planning, design and testing of a full-scale composite RCS

moment frame that is pseudo-dynamically loaded to simulate earthquake motions. In

addition to the direct benefits of the test results, the frame and supporting subassembly

tests provide a rich data set for the validation of nonlinear analysis models. The

analytical portion of this study focuses on modeling implementations in the program

OpenSees (Open System for Earthquake Engineering Simulation), which has been

developed by the Pacific Earthquake Engineering Research (PEER) Center (McKenna et

al., 1999). Data from RCS subassembly tests and the full-scale frame test are used to

verify how well the nonlinear OpenSees models can simulate the earthquake-induced

response and damage to RCS building systems.

In addition to validating the seismic performance and design of RCS systems, a parallel

goal of this investigation is to provide data and interpret information that support the

development of performance based earthquake engineering (PBEE). PBEE is a recent

focus of research that has been sparked by the improved knowledge about earthquake

phenomena and the ability to realistically simulate the structural response characteristics.

This methodology provides a tool to inform owners and engineers regarding the trade-

offs of the up front cost of a structure versus the expected performance (i.e. structural and

nonstructural damage) during specific loading events and the costs associated with those

performance levels (Krawinkler and Miranda, 2004). PBEE approaches and enabling

technologies provide the means to accelerate the development and implementation of

new seismic resisting systems, such as provided by RCS moment frames. In this sense,

this investigation provides the opportunity to advance PBEE by contributing to the

development and calibration of tools for performance assessment and an application

(RCS frame design) that is ripe for greater adoption by earthquake engineers.

2

1.1 Motivation for this Study

The advantages of composite RCS systems have been well documented (Griffis 1986)

and are presented in detail in Chapter 2 of this report. Past research has shown that

composite frames can be designed with seismic deformation capacity and toughness at

least equal to traditional steel or reinforced concrete construction. Despite this research,

the use of composite RCS frames remains limited in the United States to low seismic

zones. This can be attributed to the hesitation of structural engineers, contractors, and

building code officials to accept this “new” system, the historical separation of

construction trades in the United States, and the lack of comprehensive earthquake

engineering design criteria in building codes and specifications.

During 1990’s, considerable research on composite construction was conducted through a

cooperative US-Japan Cooperative Earthquake Engineering Research Program on

Composite and Hybrid Structures (Goel 2004, Deierlein and Noguchi 2004). During the

latter stages of this initiative it was recommended to conduct tests and complementary

analyses on full structural systems to validate the knowledge that had been gained

through the program. System testing would also provide a platform to study the 3-

dimensional, indeterminate aspects of complete structure behavior and allow the

investigation of many practical aspects of composite structures, such as economy and

constructability. The scope of this research investigation, which incorporates a full-scale

composite RCS frame test conducted through another international collaboration with

researchers from Taiwan, was devised to address this need. In addition to the planning,

design, analysis and execution of the frame test, this investigation synthesizes much of

the past research on RCS components and systems. An underlining goal is to promote

greater utilization of composite RCS frames in the United States through development of

seismic design guidelines, validation of seismic response, and modeling validation for

nonlinear analyses.

An integral element in the performance assessment of structures is the ability to

accurately model the time history response of a building to an earthquake excitation. The

3

full-scale testing program provides valuable data to validate the analytical models used to

simulate the seismic response of structural systems. This is something of great

importance to the current state of structural engineering; particularly as the push for

performance based earthquake engineering requires the simulation of building response

out to large interstory drifts and damage states.

1.2 Objectives

The main objectives of this work can be summarized in the following points:

1. Synthesize and interpret current design specifications for composite RCS moment

frames and investigate alternative design approaches based on emerging

performance-based design concepts and recommendations from related research

and development studies.

2. Contribute to the development of an updated strength model for composite RCS

beam-column joints. This will be accomplished by reinterpreting the original

tests used to create an earlier set of guidelines (ASCE 1994), examining more

recent subassembly tests that have studied a wider variety of joint details and

configurations, and evaluating the results from the subassembly and full-scale

testing program described below. This portion of the research is part of a broader

collaborative effort that is aimed toward updating the 1994 ASCE “Guidelines for

Design of Joints between Steel Beams and Reinforced Concrete Columns”.

3. In a collaborative project with researchers from the National Center for Research

on Earthquake Engineering (NCREE), develop and implement a testing program

to investigate the design, constructability, and seismic performance of a full-scale

composite RCS moment resisting frame.

4. Investigate differences between the response of beam-column subassembly and

full-scale system testing and evaluate how this affects the interpretations from

these tests.

5. Using the results and observations from both the full-scale test as well as other

subassembly tests, calibrate and validate analytical models for composite RCS

moment frames. These simulation models consist of (a) flexibility-based beam-

4

column elements that integrate fiber sections along the length of the member in

order to capture distributed plasticity and (b) a two-dimensional joint model with

dual springs in series to capture the deformation mechanisms of composite joints.

Modeling recommendations will be proposed to facilitate the accurate simulation

of the behavior of RC columns, composite steel beams, and composite joints.

6. Validate damage indices for use in conjunction with analytical models to correlate

the physical damage of a test specimen to the simulated nonlinear response of the

components.

7. Exercise the recommended design provisions and modeling guidelines in the

design and performance assessment of three case-study buildings under various

seismic hazard levels.

8. Using the information from both the full-scale test and results from analytical

models, validate the current design methods for RCS frames and propose

improved techniques where current methods are found to be insufficient or where

information is unavailable.

1.3 Scope and Organization of Report

In Chapter 2, a brief summary of the background on the rationale and development of

composite RCS systems is provided. Previous research on these systems is discussed,

including beam-column subassembly tests, small-scale frame tests, and trial design

studies of system performance. Building system guidelines are summarized from the

International Building Code (ICC 2003) and the ASCE-7 Standard Minimum Design

Loads for Buildings and other Structures (2002). Member design requirements for the

RC columns and steel (or composite) beams are evaluated from the AISC-LRFD

Specification (1999), the AISC Seismic Provisions for Structural Steel Buildings (2002),

and the ACI-318 code (2002). In addition to these standards and provisions, a review of

the latest research on alternative design recommendations and aspects of component

performance is also provided. A detailed review of the current standard for the design of

the composite RCS joints (ASCE 1994) is provided as well as the concurrent

development of a proposed update to these guidelines. This chapter is concluded with a

5

summary of a recommended methodology for the system and component design of

composite RCS frames.

In Chapter 3, the testing program for a full-scale 3-story composite RCS frame, which

was conducted at the National Center for Earthquake Engineering in Taipei, Taiwan, is

presented. An overview of the design of the test frame along with several of the key

design issues is outlined. The test setup, the pseudo-dynamic loading protocol, and the

final quasi-static pushover are reviewed. A brief overview of the construction process,

which was handled by an outside contractor to provide as much realism to the process as

possible, is also discussed. A description of the test is provided with a discussion on

global and local results, as well as corresponding photos of the damage incurred by the

frame. Conclusions and implications regarding design, construction, and performance

are discussed, as well as some of the observed differences between full-scale frame and

subassembly testing.

Chapter 4 summarizes the modeling recommendation for composite RCS frames and the

corresponding calibration and validation studies. Nonlinear analyses are conducted using

the OpenSees platform and the analytical results are compared to data from subassembly

tests and the full scale test frame. Component models for the RC columns, composite

steel beams, and composite joints are developed and calibrated against subassembly data.

Individual modeling recommendations are proposed for each of these components. These

recommendations are used to create an analytical model of the test frame and simulate the

response of the frame to input earthquake loading. The measured and simulated

responses are compared at the global and local level, and the similarities and differences

are discussed. The analytical models are extended using damage indices to determine the

predicted damage states from the analytical models and then compared to the physical

damage observed in the test frame. Conclusions on the validity and limitations of the

simulation and damage models are presented.

Chapter 5 applies the design recommendations from Chapter 2 and generates the design

for three case study buildings with heights of 3, 6, and 20 stories. These frames are then

6

modeled in OpenSees using the recommendations presented in Chapter 4 and the

structural performance is assessed at multiple seismic hazard levels, which represent

frequent to extremely rare earthquake loading events. This probabilistic study

investigates the response of these frames in terms of three engineering demand

parameters: (1) maximum interstory drift, (2) inelastic component rotations, and (3)

cumulative damage indices. These models are used to assess the performance as well as

investigate some of the design issues raised in other chapters of the report.

An overview and summary of the major findings and conclusions of the study, and ideas

for future research are discussed in Chapter 6.

7

Figure 1.1 – Photo of composite RCS frames depicting the steel beam running continuous

through the reinforced concrete column.

RC Column

Composite Joint

Gravity Bea Steel

Beam m

Bolted Beam Splice

8

Chapter 2: RCS System Design

This chapter begins with a brief discussion of the motivation and development of

composite structures in the United States and Japan. A summary of past research on

composite RCS frames is also presented and will serve as the foundation for the current

study. What follows is a detailed review of the current knowledge for the design of

composite RCS frames in building code provisions, as well as alternate approaches

proposed from recent research. Current joint design guidelines (ASCE 1994) are

reviewed and compared to an updated model that has been developed and validated as

part of this research. A recommended design methodology is summarized in the

conclusion of this chapter.

This research applies and evaluates the provisions of the 2003 International Building

Code (ICC 2003) that are relevant to composite RCS frames. This code, either directly or

indirectly, references the ASCE-7 Standard Minimum Design Loads for Buildings and

other Structures (2002), the AISC-LRFD 1999, AISC Seismic Provisions for Structural

Steel Buildings (2002), and the ACI-318 (2002). The 1994 ASCE Joint Design

Guidelines constitute the current standard for composite joints. While there exists more

current versions of these codes and provisions during the time of publication of this thesis

(IBC 2005, ASCE-7 2005, AISC-LRFD 2005, and AISC Seismic 2005), the earlier codes

mentioned herein were the governing standards when this research was completed.

Where applicable, the newer versions of the code are mentioned when the design method

has had an appreciable change.

2.1 Background of RCS Composite Moment Frames

The RCS composite moment frame systems began to gain popularity in both the United

States and Japan in the late 1970’s and early 1980’s. In the US, this system came about

as an attractive modification of traditional steel moment frames for mid- to high-rise

buildings in relatively low seismic zone (e.g. Houston, Texas). Replacing the heavy

wide-flange columns of a typical steel moment frame with the more cost effective

9

reinforced concrete columns to resist the high axial compressive loads brings about an

economical advantage to the RCS system (Griffis 1992). The economic advantage of RC

columns over steel columns increases as buildings get taller and stiffness (drift) criteria

tend to control the design (Leon and Deierlein, 1995).

In Japan, RCS composite systems were developed as an alternative to low-rise reinforced

concrete moment frames in high seismic zones. Here the goal was to take advantage of

the long-span capabilities of steel beams to provide column-free spaces for the low-rise

office buildings and retail stores. When steel beams were incorporated with a composite

slab, the advantage over typical deep reinforced concrete beams became even more

obvious since the typical depth and weight of a floor could be reduced, resulting in cost

savings in the foundation design. In Japan, the tradition of mixing reinforced concrete

and steel members was already established with the common steel reinforced concrete

(SRC) construction, which is characterized by full concrete encasement of structural steel

frames (columns and beams). In general, composite systems are much more developed in

Japan due to the large amount construction companies that have a longer tradition of

mixing the trades of steel and reinforced concrete, something that is not as common in the

US.

Another important advantage of these composite systems is the ability to accommodate

innovative construction techniques that lower the overall cost and expedite the process of

erecting buildings. In the US, a typical high-rise construction sequence utilizes small

steel erection columns to advance steel framing several floors ahead of placing reinforced

concrete columns (Fig. 2.1). This staggered staging allows for the separation of the steel

and concrete trades (as well as other construction activities), which gives each of the

groups enough space to work independently of each other. For example, a typical

composite frame construction sequence may read as follows if we start from the upper

most floor and work our way down (Griffis 1992):

1. Upper stage: placement of the bare steel frame using small steel erection columns.

2. 2nd tier: Follow with any necessary welding (steel erection columns) and

placement of metal deck for composite slab.

10

3. 3rd tier: Follow with placement of shear studs and slab reinforcement.

4. 4th tier: Pouring of the concrete slab.

5. 5th tier: Placement of the reinforcing bar cage around steel erection columns.

6. 6th tier: Setting of the column formwork and casting of the concrete columns.

This sequence can be further accelerated by the use of innovative jump-form framing

systems. Optimization of this sequence requires close coordination and control of the

overall construction process.

An alternative precast construction method can also be implemented in the erection of

composite frames. In this scheme, the steel beam is cast integral with the RC column and

field spliced a short distance away from the column face. The columns are spliced

together with grouted sleeve couplers and the beams are spliced together with bolted

flange plates and shear tabs to generate a continuous system, as shown in Fig. 2.2 and

2.3. The size of these precast modules can be varied to span several stories and/or bays to

accommodate the optimum configuration for ease of construction. Variations to these

methods, such as utilizing the column reinforcing bar cage as the erection column have

been developed by construction companies in Japan (Fig. 2.4).

Perhaps one of the biggest advantages provided by RCS systems lies within the

composite beam-column joints, an example of which is shown in Fig. 2.5. In these

composite joints the steel beam runs continuous through the concrete column, thereby

eliminating the need to interrupt the beam at the column face. This type of detail avoids

welding or bolting of the beam at the location of maximum moment, which mitigates

some of the fracture problems encountered in conventional steel moment frames during

the 1994 Northridge and 1995 Hanshin earthquakes. The longitudinal reinforcement of

the column is also continuous through the joint and can be spliced away from the joint.

This beam-column joint detail is common to both the cast-in-place and precast forms of

construction.

11

2.2 Previous Research

RCS composite moment frames have been studied for over twenty years, with a primary

focus on understanding the behavior and design of the beam-column joints. In addition

to research on connections, there have also been system design and performance

assessment studies with the intent to evaluate and benchmark the behavior of these

innovative frames against more conventional moment frames. This section will review

some of the important past research that have helped develop the understanding of

composite joints and systems.

2.2.1 Beam-Column Composite Joints

The reinforced concrete column and the steel (or composite) beams are relatively

straightforward to design following provisions for members in conventional steel or

reinforced concrete construction. A primary challenge in the design of RCS frames lies

within the unique connection between the steel beam and the RC columns, and thus, the

primary focus of past research has been on these composite connections. During the

1980’s, over 400 RCS connection subassemblies were tested in Japan, and 17 were tested

in the United States. Many of the early joints tested in Japan were of proprietary details

sponsored by Japanese construction companies with the primary goal being to validate

specific joint details. While the results of these tests are interesting, they are of limited

research value to quantify the internal force transfer mechanisms of the joint. The

contributions from the U.S. consisted of two series of subassembly tests that were

performed at the University of Texas Austin by Deierlein et al. (1989) and Sheikh et al.

(1989). Based on these two investigations, Deierlein (et. al 1989) proposed design

equations to quantify the strength and stiffness of composite connections, which later

came to form the basis of the 1994 ASCE Guidelines for Design of Joints between Steel

Beams and Reinforced Concrete Columns (ASCE 1994).

During the 1990’s, the United States-Japan Cooperative Earthquake Engineering

Research Program on Composite and Hybrid Structures began and provided the impetus

to test about 56 more connection subassemblies (33 in Japan and 23 in the U.S.) with the

12

specific intent of investigating and quantifying the internal joint transfer mechanisms.

Deierlein and Noguchi (2000, 2004) summarize the subassemblies tested under the US-

Japan program. Apart from the formal US-Japan program, Kanno and Deierlein (1993,

1997) tested 19 RCS beam column joint subassemblies and 50 small concrete blocks

loaded with steel bearing plates to investigate the bearing strength in RCS joints above

and below the steel beam. Both the tests covered by the US-Japan program and those by

Kanno (1993, 1997) provided a significant amount of new data to fill knowledge gaps for

various connection configurations and force transfer mechanisms.

Summarized in Fig. 2.6 are several examples of the types of RCS joint details that have

been tested. There are two distinctive types of RCS joints; one is the “through-beam”

detail (details 1-7 in Fig.2.6) where the steel beam runs continuous through the concrete

column, the advantages of which have been already discussed. The second is the

“through-column” detail (details 8-11 in Fig. 2.6) where the beam flanges are interrupted

at the column face to accommodate a variety of reinforcing bar arrangements and to

facilitate the placement of concrete in the joint. Detail 12 in Fig. 2.6 is an example of a

hybrid detail, where the SRC concept of encasing the steel beam in concrete is applied for

a short segment of the beam framing into the joint. While the through-beam type detail is

preferred in the United States, both types are used in Japan particularly among the

proprietary details developed by the construction companies. Other than the through-

beam versus through-column difference, the joint details shown in Fig. 2.7 differ by the

wide variety of stiffeners, cover plates, and bearing plates that are implemented to ensure

adequate force transfer between the steel beam and the concrete column.

Overall, the subassembly tests have shown that when detailed to ensure proper force

transfer between the beam and column, RCS composite joints are capable of providing a

reliable amount of strength and ductility necessary for seismic design. In fact, in order to

investigate joint failure in these subassembly tests, the dimensions of the steel beam had

to be significantly altered from regular practice to ensure that the beam possessed enough

moment strength to avoid beam hinging (large flange thickness), while limiting the joint

panel shear strength (small web thickness). For standard rolled W-shape beams, fairly

13

simple joint details can be provided to ensure that the joints have enough strength to force

plastic hinging to occur in the steel or composite beams.

The beam-column subassembly tests that have been specifically designed to cause failure

in the composite connections generally exhibit either one or a combination of two

primary failure modes (Fig. 2.8). Vertical bearing failure is characterized by rigid body

rotation of the beam through the joint resulting from concrete crushing both above and

below the joint. This localized crushing of the concrete causes gaps to open up between

the steel beam and the concrete column. The deformations caused by this vertical

bearing failure leads to more of a pinched hysteretic response, as shown in Fig. 2.8. The

second type of joint failure is panel shear failure, which is very similar to the

corresponding behavior in joints within conventional all steel or RC moment frames. The

difference in RCS joint shear failure is that the benefit of both steel web yielding and the

development of concrete struts exist within the joint region. Although the deformation

response for this type of failure does contain some slight pinching, it is more associated

with larger, energy dissipating hysteretic loops, as shown in Fig. 2.9. Again, keep in

mind that these specimens were intentionally designed to fail in the joints, whereas in

traditional seismic design it is recommended that the majority of inelastic action occur

within the beam. In a properly detailed RCS joint, it is fairly easy to ensure beam

hinging and the associated response shown in Fig. 2.10. Nevertheless, even if failure

were to occur in the joint, the hysteretic response has proven to be quite stable.

2.2.2 Small-Scale Frame Tests

The US-Japan program included two reduced-scale RCS moment frames – one at the

Osaka Institute of Technology (Baba and Nishirmura 2000) and the second at Chiba

University (Noguchi and Uchida 2004). Both are about 1/3-scale two-bay two-story RCS

frames with through-beam type connections with differences only in the joint details (one

had cover plates and band plates while the other had face bearing plates and band plates).

The frame was designed such that the plastic strength of the beams was nearly equal to

the ultimate shear strength of the joints, so as to provide information on the interaction

14

between frame and connection response. Both test specimens were subjected to reverse

cyclic loading and withstood story drift ratios in excess of 5% without significant

strength or stiffness degradation, thus confirming the reliable seismic behavior of RCS

framing systems.

2.2.3 Trial Design Studies of System Performance

Several groups of researchers have developed trial designs of RCS frames based on a

common theme building devised for the US-Japan program (Mehanny and Deierlein

2000, Bugeja 1999, Noguchi 1998). The goal of these studies were to first apply the

proposed seismic design provisions for RCS systems and then evaluate the seismic

performance of resulting designs using nonlinear analyses and advanced performance

assessment techniques. Traditional steel frames were also investigated in these studies to

benchmark the performance of conventional frames compared to the composite RCS

frames. Using a common floor plan, the building heights varied as well as the

implementation of perimeter versus space frame systems. These design studies have

shown that the steel beam sizes tend to be similar for the RCS and steel system and that

the main differences lie in the column and connection designs. Given the additional

stiffness provided by the RC columns, the RCS frames tended to be controlled more by

the minimum strength requirements whereas the steel frames were restricted by lateral

drift limitations. In general, these investigations have shown that the inelastic dynamic

response of the RCS frames is similar to comparably designed steel moment frames.

2.3 System and Member Design Guidelines

In the United States, the seismic design criteria for composite RCS frames are distributed

over several codes and standards (Deierlein 2000). The first formal seismic design

requirements for composite steel-concrete structure came with the 1994 edition of the

NEHRP (National Earthquake Hazards Reduction Program) Recommended Provision for

the Development of Seismic Regulations for New Buildings (BSSC 1995). The 1994

edition included a new chapter that contained a comprehensive set of design criteria for

composite systems, members, and connections as well as defined the seismic design

15

coefficients (R and Cd) necessary for calculating the design earthquake loads and

deformations. In these provisions, the Building Seismic Safety Council (BSSC) defined a

list of seven composite systems that have the likeliest practical applications; included on

this list was composite special moment frames. The strength and detailing requirements

for the composite members were largely based on the already existing AISC and ACI

standards, but also included clarifications of how they should be applied and

supplementary information when certain issues were not covered. These provisions are

important not only because they were the first of their kind for composite structures, but

they also set the foundation for subsequent “codified” publications.

The current set of documents that control the design of composite RCS structures begins

at the International Building Code (IBC) (ICC 2003) and the ASCE 7 Standard Minimum

Design Loads for Buildings and other Structures (ASCE 2002), both of which specify the

general seismic loading and design requirements, much like that of the 1994 NEHRP

Provisions. ASCE-7 (2002) adopts Part II of the AISC Seismic Design Provisions (2002)

for specific detailing requirements for RCS frames (composite special moment frames),

which again are largely based on the original 1994 and 1997 NEHRP Provisions. Given

that these systems are made up of components of steel and reinforced concrete, the AISC

Seismic Provisions extensively reference both the AISC-LRFD Specifications

(1999/2001) and the ACI 318 Building Code (2002) for guidance in designing the

appropriate members. In the commentary of the AISC Seismic Provisions, users are

referred to the 1994 ASCE RCS Joint Design Recommendations.

2.3.1 General Building Design Requirements: IBC 2003 and ASCE 7-02

To determine the general system design information, loading, and the seismic design

criteria of a building one must first turn to the IBC 2003. Information such as the source

of dead and live loads, load combination factors, and wind loading is common to all

structural systems. It is not until the determination of the seismic design base shear that

specific seismic system types, such as composite frames, are identified. The 2000 edition

of the IBC was pretty much self-contained in that all of the information necessary to

16

determine the earthquake loading and other seismic design criteria was included in the

structural design chapter (16). In the 2003 edition, most of the detailed criteria have been

removed and are now included by reference to the 2002 edition of the ASCE 7 Standard

Minimum Design Loads for Buildings and other Structures. The IBC 2003 basically

permits the design of a building if it fully adheres to the provisions of ASCE 7-02

Sections 9.1 through 9.6, 9.13, and 9.14.

The seismic design base shear can be determined using the following general equation

defined by ASCE 7 (2002):

( ) ( )

1DS DS SVW R I T R I

= ≤ (2.1)

but the result should not be less than:

0.044 DSV S IW

= (2.2)

where:

V = design base shear

W = weight (based on seismic mass)

SDS, SD1 = 2/3 SMS, 2/3 SM1 where SDS and SD1 are the design spectral accelerations and SMS and

SM1 are the maximum considered earthquake spectral accelerations for

short (0.3 sec) and long (1.0 sec) periods, respectively.

SMS,SM1 = FaSS, FvS1

where Fa and Fv are site soil factors and SS and S1 are the mapped

spectral accelerations for short and long periods, respectively.

T = fundamental (first mode) period

I = importance factor based on building type

R = structural response modification factor

The R-value, coupled with the importance factor, I, adjusts the elastic spectral

acceleration demand (SDS or SD1) to account for the amount of nonlinearity that is

expected to occur in a design level earthquake. Both ASCE 7 and IBC 2003 define the

R-value according to a building’s seismic force resisting system. For larger values of R,

17

the corresponding system should be able to accommodate larger levels of inelastic action.

Special composite moment frames are specifically noted in this section and assigned an

R-value of 8, which is identical to convention steel or reinforced concrete special moment

frames. The fundamental first mode period, T, can be computed by structural analysis or

by the following code defined equation:

xa TT C h= n (2.3)

where:

Ta = approximate fundamental period

CT = building period coefficient (e.g. 0.016 and 0.028 for RC- and steel-

MRFs, respectively)

hn = the height above the base to the highest level of the building (ft)

x = building period coefficient (e.g. 0.9 and 0.8 for RC- and steel-MRFs,

respectively)

For the purpose of calculating the seismic base shear, the maximum period permitted by

ASCE 7 is Cu times the period given by 2.3. The period coefficient, Cu, depends on the

design spectral response acceleration at 1-second period and varies from 1.4 at SD1≥0.3g

to 1.7 at SD1≤0.1g. This cap on the natural period deters users from intentionally

generating a flexible analytical model in order to reduce design level forces. This upper

limit can result in the introduction of additional overstrength in the design (Mehanny et

al. 2000 CCIV).

An additional base shear is superimposed to the lateral resisting system to account for

accidental torsion caused by an assumed 5% offset of the center of mass of each floor.

This is directly added to the design base shear (Eq. (2.1)) and can potentially be an

apparent source of overstrength when evaluating the performance of a 2-dimensional

analytical model (Mehanny et al. 2000 CCIV).

Using the earthquake load, in conjunction with the dead, live, wind, snow, etc., the

structural system must be designed to resist the most critical of the load combinations

specified in Section 1605.2 of the IBC 2003. This stage of the design process can be

18

referred to as the “strength design” and results in the initial sizing of the elements in the

lateral resisting system. For the composite RCS moment frame, this is the stage where the

composite beams, joints, and RC sections are sized to satisfy the strength requirements

specified by the appropriate codes, the details of which will discussed later in this

chapter.

The IBC 2003 also refers to the ASCE 7 (2002) to stipulate a minimum stiffness criterion

that limits the amount of drift that occurs during the design level event. Deflections

calculated by an elastic analysis under the seismic design base shear and are related to the

expected inelastic deflections by the following equation:

( )d designinelastic d elastic

CC R

IΔ

Δ = = Δ (2.4)

where:

Δinelastic = expected inelastic deflection under design earthquake

Δdesign = deflection calculated by elastic analysis under the design base shear, V

Δelastic = deflection assuming elastic response under the design earthquake

Cd = deflection amplification factor

The deflection amplification factor, Cd, is similar to the R-value in that they both are

defined according to the lateral resisting system. For special composite moment frames,

Cd is assigned a value of 5.5. For moment resisting frames, the drift criterion in IBC

2003 states that the inelastic drift computed for each floor by Equation (2.4) should be

less than h/40 if four stories or less in height and h/50 for all other buildings (where h is

the story height). For purposes of the drift analysis only, the seismic design forces (Eq.

(2.1)) used to calculate Δdesign are not subject to the minimum base shear obtained by

Equation (2.2) nor by the upper limit on the period (i.e., ). Both of these

exceptions can greatly impact the drift criterion since it generally allows for the reduction

of forces when computing deflections.

u aT C T≤

For ductile moment frames, it is more common for the design to be controlled by seismic

drift rather than the strength criterion. When the drift unit controls, it is usually most

effective to increase the stiffness of the beams, (which also increases their strength). The

19

resulting increase in beam strength in turn impacts the design of the columns since the

strong-column weak-beam criterion must also be satisfied. This results in a final design

that has a higher capacity than that required by the strength criterion and the seismic

design base shear defined in Equation (2.1).

ASCE 7-02 requires that the design, construction, and quality of the composite steel and

concrete components that comprise the lateral resisting system adhere to the requirements

of the AISC-LRFD (1999), ACI-318 (2002), and the AISC Seismic Provisions (2002).

These are discussed next.

2.3.2 Member Design Requirements: Part II of the AISC Seismic Provisions

Part II of the AISC Seismic Provisions (2002) outlines the requirements for the design

and construction of composite structural steel, reinforced concrete members, and

composite connections. A majority of the requirements are referenced in from other

existing design provisions, but, the Seismic Provisions supplement missing information

and clarify ambiguities on how to combine other published requirements for steel and RC

systems. In this section, the design requirements for each of the components of

composite RCS frames will be discussed.

2.3.2.1 Reinforced Concrete Columns

The AISC Seismic Provisions state that the design of the reinforced concrete columns in

a composite moment frame shall be in accordance with ACI-318, including all of Chapter

21 (Special Provisions for Seismic Design) except for 21.10. For composite RCS frames,

the reinforced concrete columns are generally designed as they would be in a

conventional reinforced concrete moment frame. One of the major differences in these

composite frames is that the longitudinal steel must be arranged such that it can

accommodate the passage of the steel beams through the joint region. A typical

configuration that demonstrates this situation is shown in Fig. 2.11.

20

Another significant issue that needs to be addressed is how the calculation of internal

forces and deformations of composite RCS systems are affected by the relative stiffness

of the reinforced concrete columns and the composite steel beams. Given that the

seismic design is based on elastic analysis, the effective stiffnesses of the elements should

be representative of the conditions at the onset of significant yielding in the building.

This suggests that the stiffness of the reinforced concrete columns should be

appropriately modified to represent the conditions of an effective cracked section. An

effective stiffness for reinforced concrete columns, which accounts for the amount of

axial load present in the member, is given by Mehanny (2000) in the following equation:

,

0.4 0.6 0.92.4

eff

g tr b

EI PEI P

= + ≤ (2.5)

where:

EIeff = effective stiffness of the cracked reinforced concrete section

EIg,tr = transformed stiffness of the gross reinforced concrete section

P = expected axial load in reinforced concrete column

Pb = balance axial load taken from the RC column P-M interaction diagram.

This stiffness modification will influence the distribution of forces throughout the system

and also change the total amount of drift in the building. This is especially important in

composite RCS frames since the stiffness of the composite steel beams are not expected

to change as much as the RC columns. The recommendations on computing the effective

stiffness of the composite steel beams are developed in the following section.

2.3.2.1.1 Strong-Column Weak-Beam

As in all special moment resisting frames, the columns in composite RCS systems must

be designed to meet the strong-column weak-beam (SCWB) criterion in order to

minimize the potential for the development of a story or multi-story mechanism. The

AISC Seismic provisions reference the ACI 318 (2002) document for the design of RC

column, which in turn specifies the following SCWB criterion:

( )6 5c gM M≥∑ ∑ (2.6)

where:

21

ΣMc = sum of nominal flexural strengths of the columns framing into the joint

ΣMg = sum of nominal flexural strengths of the girders framing into the joint

The (6/5)-factor in Equation (2.6) implies that the columns framing into the joint should

be at least 20% stronger than the beams framing into the joint. The column flexural

strength should be calculated considering the factored axial load (according to the load

combinations specified in Section 1605.2 of the IBC 2003) that would result in the lowest

flexural strength. This implies that for columns that are designed below the balance point

(Pbal as shown in Fig. 2.12b), the load combination that would likely control the SCWB

design is that of 0.9D+1.0E, since this would produce the least amount of compression

(or perhaps even tension) and reduce the flexural strength of the column. The opposite is

true for columns designed above the balance point, where the more compression in the

column the lower its flexural strength, implying that the 1.2D+0.5L+1.0E load

combination should control the SCWB design. The best way to approach the SCWB

criteria is to group the design of the interior and exterior columns, as shown in Fig. 2.12a,

since the factored axial loads in the exterior columns are likely to be much different than

those in the interior columns due the overturning moment caused by the lateral loads.

In the development of Equation (2.6), it is assumed by ACI 318 (2002) that both the

columns and beams are reinforced concrete members. While this applies to the RC

columns in composite RCS frames, it is not suitable for the composite steel beams. For

this reason it is also necessary to consider the SCWB criterion for steel structures to

evaluate how the case of a steel (or composite) beam is handled. The AISC Seismic

Provisions (2002) stipulate the following SCWB criterion for steel frames:

( )

( )*

* 1.01.1c yc uc gpc

pb y p v

Z F P AMM R M M

−=

+>

∑∑∑ ∑

(2.7)

where: *pcM∑ = the sum of moments in the column above and below the joint at the

intersection of the beam and column centerlines *pbM∑ = the sum of moments in the beams at the intersection of the beam and

column centerlines.

22

Zc = plastic section modulus of the column

Fyc = specified minimum yield stress of column

Puc = required compressive strength using LRFD load combinations

Ag = gross area of column

Ry = ratio of expected yield strength to minimum specified (1.1 for Grade

50 steel)

Mp = nominal plastic flexural strength of beam section

Mv = additional moment due to shear amplification from the location of the

plastic hinge to the column centerline, based on factored load

combinations.

For beams with grade 50 steel, where Ry=1.1, the resulting ratio of column to beam

strength in Equation (2.7) is approximately 1.2, which is the same as in Equation (2.6).

The AISC Seismic Provisions (2002) do not specify whether one should consider the

composite action of the beam in Equation (2.6), although the beam strength definition of

1.1 y pR M implies that only the steel section be considered. Researchers have recognized

that the current approach in design codes to ignore the contribution of the concrete slab in

the strength and stiffness of the structural system may be unconservative and could shift

hinging from the beams to the columns, causing an undesirable failure mechanism (Leon

and Hajjar 1998). For example, the composite strength of a W27x84 with a 2.5 inch slab

over a 3 inch metal deck can be up to 40% stronger than the bare steel section, which can

ultimately have a great impact on the balance of strengths between the beams and

columns in a moment resisting frame. This issue is addressed in further detail in Section

2.5.1.

2.3.2.1.1.1 SEAOC Blue Book Provisions

The SEAOC Seismology Committee has drafted a proposed Blue Book (Maffei 2004)

provision for the SCWB provision, which recommends a criterion based on the strength

of the beam hinges over an entire floor to the strength of the column hinges below that

23

floor. This proposed SCWB criteria, shown graphically in Fig. 2.13, should be applied to

all floors except at the roof level. This criterion can be summarized by the following

equation:

c bM M≥∑ ∑ (2.8)

where:

cM∑ = sum of nominal moment strength in all columns framing into the

underside of a level, taken at the center of the joints, for all columns

acting to resist lateral forces in the direction under consideration

bM∑ = sum of nominal moment strengths at each end of each beam, taken at

the center of joints, for all girders acting to resist lateral forces in the

direction under consideration

This SCWB provision is more transparent than those defined in Equations (2.6) and (2.7)

in that it is trying to prevent a story mechanism by ensuring that the strength of the

columns over the entire floor can provide the strength to cause hinging in the steel beams.

The major difference between this and the previously described SCWB criteria is that

only the columns below a joint are considered in the design check. If two consecutive

floors have the same column design, this new provision will essentially increase the

previously defined column to beam strength ratios from 1.2 to 2.0. Support for this

provision can be found in research by Dooley and Bracci (2001), which recommends a

minimum SCWB ratio of 2.0 to provide a significantly high probability of preventing

story mechanisms under design basis seismic loading.1

2.3.2.1.2 Precast RC Column Splice Design

RC column splices are required when the precast method of construction is used. These

grouted splices with mechanical reinforcement bar couplers are common in conventional

precast RC moment frames, an example of which is shown in Fig. 2.14. The high

1 The SEAOC Blue Book Provision for the SCWB criterion (Equation (2.8)) shows promise by capturing the ultimate two-story failure mechanism in the 3-story, 3-bay test frame (Chapter 3), whereas the traditional SCWB criteria (Equations (2.6) and (2.7)) were unsuccessful in protecting the frame from a story mechanism.

24

strength grout is pumped under high pressure into the couplers and splice region and is

designed to develop full plastic strength of the reinforcement bars.

The location of these splices along the length of the column is also an important design

variable. In Japan, it is common to locate these splices directly above the floor level, as

is shown previously in Fig. 2.3. From a structural performance point of view, this

practice is risky considering the potential for severe hinging in this region of the column.

It seems logical to move these splices out of the possible hinging zones and into the mid

height of the column to avoid any adverse effects in the inelastic response of the

columns. 2 The author has consulted with industry engineers regarding this precast

composite RCS system, and they have agreed that mid-height splices are preferable from

a structural point of view. They have also argued that the mid-height splices make the

constructability of the system easier since construction workers will not have to crouch

down to work with the splice. The precedence for this mid-height splice location exists

since it is also common in steel columns.

2.3.2.2 Composite Steel Beams

The beams in a composite RCS moment can be either designed as bare steel or composite

beams. It is recommended that one take advantage of the many benefits incorporating the

composite slab, especially considering that even bare steel beams will require shear studs

to transfer seismic shears between the beam and slab. The focus in this section will be on

composite steel beams, since the design of bare steel beams is fairly straightforward and

well documented. The AISC Seismic Provisions require that the design of the composite

steel beams shall be in accordance with the AISC-LRFD Specification Chapter I. In

order to ensure an adequate amount of ductility in the steel beam prior to crushing of the

2 These precast grouted splices were implemented and tested in the full-scale composite RCS moment frame and performed exceptionally well up through severe levels of inelastic action. The location of the splices were also evaluated in the test frame and in preliminary subassembly tests, with results indicating that both the splice within the hinge zone (Japanese practice) and sufficiently out of the hinge zone performed quite well, although there was a bit more strength deterioration during repeated cycles with the splice in the hinge zone. These tests have shown that these splices are very reliable for use in precast systems in high seismic zones.

25

concrete slab, the Provisions also set the following limit on the distance from the top of

the concrete slab to the plastic neutral axis:

1700

1

con b

y

s

Y dF

E

+⎛ ⎞

+ ⎜ ⎟⎝ ⎠

(2.9)

where:

Ycon = distance from the top of the steel beam to the top of the concrete slab, in.

Db = depth of the steel beam, in.

Fy = specified minimum yield strength of steel beam, ksi.

Es = elastic modulus of the steel beam, ksi.

The AISC Seismic Provisions also provide a more stringent width to thickness ratio for

the steel beam flanges ( 52 yb t F≤ , ksi) than those defined by AISC-LRFD. This is

meant to ensure that the steel sections are able to achieve ductilities up to 6 or 7 without

the occurrence of severe local buckling.

The composite slab provides a significant amount of restraint to the upper flange of the

steel beam and largely prevents the occurrence of large local buckles. This behavior has

been observed in several subassembly tests, including Liang et al. (2004) and Civjian et

al. (2000). When the flutes of the metal deck are oriented parallel to beam (where the

slab is in constant contact with the beam), as in the tests by Liang et al. (2004), local

buckling occurs only in the lower flange of the beam while the upper flange remains

intact as the slab provides full restraint. There is slightly less restraint provided by the

slab if the flutes of the metal deck are perpendicular to the beam, since the slab is only in

contact every other flute width. This was the case in the tests reported by Civjian et al.

(2000), where local buckles were observed in both the upper and lower flanges, but those

in the upper flange are not nearly as significant due to the presence of the slab. 3

Regardless of the orientation of the flutes, the presence of the composite slab minimizes

the amount of local buckling in the upper flange, thereby increasing the level of ductility

that can be achieved by the member. 3 In the RCS test frame, where the flutes of the metal deck were oriented parallel to the steel beam, the slab provided full restraint to the upper flange and therefore local buckling was limited to the lower flange and, in severe excursions, the lower portion of the web panel.

26

While the effective stiffness of the RC columns are dependent on the axial load and the

percentage of section that is considered cracked, the effective stiffness of the composite

steel beams for the elastic analyses used for design purposes should consider what

portions of the beam are in positive moment (i.e., composite section bending) and

negative moment (i.e., steel section only). Under earthquake loading, it is typically

assumed that the beams in a moment frame system will predominately remain in double

curvature. For this reason, it is reasonable to assume that the effective stiffness of

composite steel beams can be taken as the average stiffness of the composite and steel

section, which presumes that approximately one-half of the beam is in negative bending

while the other half is in positive bending. The effective width of the slab for this

stiffness calculation should be determined from Section I3 in the AISC-LRFD (1999),

which states that beff is equal to the sum of the widths for each side of the beam

centerline, each of which shall not exceed:

(2.10) (1) one-eighth of the beam span, center-to-center of supports(2) one-half the distance to the center-line of the adjacent beam(3) the distance to the edge of the slab

This definition of composite beam stiffness, coupled with the effective stiffness for the

RC columns presented in Section 2.3.2.1, is a reasonable assumption for modeling the

stiffness of the frame at the onset of significant yielding and to determine the distribution

of forces and deflections in the structural frame.

2.3.2.2.1 Plastic Strength of Composite Beams

The plastic strength of composite beams can be defined in different ways depending on

the loading and boundary conditions. Figure 2.15 depicts two of the most common

conditions in moment frames: (1) lateral side-sway where the plastic moment develops in

the hinge zone adjacent to the column and (2) gravity conditions where the maximum

moment is reached somewhere in the middle of the span of the beam. Under gravity

conditions, the effective width and stress in the slab are described by the AISC-LRFD

(2002) recommendations for beff (2.10) and 0.85 . For the lateral sway case, the 'cf

27

boundary conditions are very different than the gravity conditions and it is unclear

whether or not the same effective width and stress should be applied to compute the

capacity of the composite section.

Several researchers have studied the effective width and stress of the slab in the lateral

sway case in order to correctly model the ultimate moment capacity of a composite beam

section. It has been reported by du Plessis (et al.1972) that the effective width of the slab

at the ultimate strength of the section can be related to the slab area that is in direct

contact with the column flange. This recommendation is logical considering the high

stiffness in the region of the slab and column interface and that localized crushing in the

slab along the width of the column is often observed in subassembly tests (Liang et al.

2004).4

It has also been verified that the concrete compressive strength can reach an effective

stress of greater than 'cf due to the high confinement of the slab near the column flange.

Researchers have shown that the concrete within this region can attain an ultimate

effective stress in the range 0.85 to 1.8 'cf (du Plessis et al. 1972, Tagawa 1989, Lee

1987, Civjan et al. 2001, and Cheng et al. 2002). The reason for the large amount of

variation can be largely attributed to whether or not the shear studs in the subassembly

tests were designed for full composite action. If the studs are designed for a partially

composite section, then the strength and ductility of the composite section is governed by

the behavior of the studs. This issue is investigated more in detail in the calibration study

of composite beams in Chapter 4. Final recommendations on computing the plastic

strength of composite beams for sway frames are withheld until the conclusion of this

chapter.

4 Local slab crushing along the width of the column was also observed after the conclusion of the final pushover of the RCS test frame, as discussed in Chapter 3.

28

2.3.2.2.2 Design of Shear Studs

The design of the shear studs to provide composite action between the concrete slab and

the steel beam is covered by the AISC-LRFD Specifications. The nominal shear strength

of headed shear studs is defined by the following equation:

', 0.5n stat sc c c sc uQ A f E A= ≤ F

(2.11)

where:

Qn,stat = nominal strength of a single shear stud embedded in concrete

Asc = cross-sectional are of shear stud connector

Ec = modulus of elasticity of concrete

Fu = specified minimum tensile strength of a shear stud connector.

This equation for shear stud capacity, which is based on work by Ollgaard et al. (1971), is

intended for studs subjected to static shear loading. There are two reduction factors, Rg

and Rp, applied to the upper limit of the shear strength (i.e., the last term in Eq. (2.11))

which account for (1) whether the steel deck ribs are oriented parallel or perpendicular to

the steel beam, (2) how many studs are placed within each perpendicular rib, and (3)

whether the studs are welded through the steel deck or directly to the steel beam. What

Eq. (2.11) does not account for is the cyclic loading of shear studs under seismic loads.

Given the poor performance of shear studs in composite beams witnessed in numerous

subassembly tests (Cheng 2002, Civjan et al. 2001, Bugeja et al. 2000, Leon and

Flemming 1997), it is evident that the current design provisions seem to overestimate the

capacity of shear studs under inelastic cyclic loading.

The AISC Seismic Provisions acknowledge that the effects of reverse cyclic loading on

the strength and stiffness of the shear studs should be considered in the design of

composite beams and recommend that the strength of headed shear studs should be

reduced by 25% unless a higher strength is substantiated by cyclic testing.5 Based on this

recommendation, this would lead to the following modification of Equation (2.11) with

αcyc assumed as 0.75:

5 This requirement has remained unchanged in the newer version of the AISC Seismic Provisions (2005).

29

( )', , 0.5n cyc cyc n stat cyc sc c c sc uQ Q A f E Aα α= = ≤ F

(2.12)

where:

αcyc = cyclic strength reduction factor

It is later recommended in the commentary of the Provisions that an inspection and

quality assurance plan be implemented to insure the proper placement of the shear studs

on the steel beam and that the use of additional shear studs beyond that required in AISC-

LRFD may be necessary to ensure composite action. These provisions, as well as FEMA

350 (2000), do not allow the placement of shear studs from the column face to one half

the beam depth beyond the theoretical hinge point to avoid the introduction of any

imperfections to the beam flange that may lead to early fracture.6

Civjan (2003) performed a series of experimental and analytical tests on modified

composite push-out specimens and bare steel studs to investigate the behavior of shear

studs subjected to reverse cyclic loading. He found that a cyclic loading history resulted

in an approximate reduction in shear strength capacity of 40% as compared to the static

case proposed by Equation (2.11). This reduction is a result of low-cycle fatigue in the

shear stud and weld materials as well as local concrete degradation in the proximity of

the stud. Based on the recommendations from Civjan (2003), the αcyc defined in

Equation (2.12) would be further reduced to 0.60.7

Whereas fully composite beams cause plastification of the steel beam and/or crushing of

the concrete slab, partially composite beams rely on the strength of the studs for the

strength and ductility of the member. Based on the previous discussion, the reliability of

shear studs under seismic loading is questionable; and, if a composite beam is designed

with the studs as the weak link, one must recognize that the probability of early stud

failure and loss of force transfer between the slab and the beam is likely to occur. One

6 This recommendation was inadvertently put to test in the 3-story composite RCS moment frame tested at the National Center for Research in Earthquake Engineering in Taipei, Taiwan (Chapter 3). No fractures occurred despite the repeated inelastic cycles experienced in the regions where studs were placed. This may be due to the fact that upper flange yielding was limited due to composite action of the section. 7 The shear studs in the 3-story composite RCS test frame, which will be described later in Chapter 3, adhered to the recommendations of Civjian (et al 2003) and exhibited excellent behavior throughout large levels of repeated inelastic excursions and experienced no instances of shear stud fracture.

30

may argue that even if composite action is lost because of failure of the studs, the steel

beam is still capable of resisting the seismic loads. While this may be true, one must also

keep in mind that the earthquake loads are transmitted through the slab and into the beam

via the shear studs and direct bearing on the RC column. Loss of the force transfer

between the slab and the beam could result in other types of failures as the slab attempts

to drag the force into the moment resisting frame. Therefore, this becomes a complicated

issue that must be addressed if the beams are designed as partially composite.

2.3.2.2.3 Steel Beam Splices

In either the precast or cast in place method of construction, there will be a need to splice

the steel beams together and ensure the continuity of force transfer. Obviously there are

several ways to splice steel beams together, but here the focus will be on a typical bolted

beam splice using flange plates and a shear tab, an example of which is shown in Fig.

2.16. This bolted beam splice is attractive in that it is easy to construct and avoids field

welding.

Just as it was an issue for the RC column splices, the location of the beam splice raises

several questions. From a structural performance standpoint, it is better to locate the

splice as far away from the expected hinging zones as possible to avoid any unwanted

effects on the plastification of the composite steel beam. For the cast-in-place method,

this is fairly easy to accomplish since the steel beams are shipped to the site as signle

(straight pieces) and their length can easily be managed to provide mid-span splices. For

precast construction, the issue is less straightforward since the precast beam-column

modules are prefabricated and shipped to the site. From a constructability point of view,

the closer the beam splice is to the column the easier it is to transport from the

prefabrication plant to the construction site. Beam-column modules with long steel

beams may be more difficult to ship and handle than those with short beam stubs

protruding from the columns. This is entirely a constructability issue and the ultimate

decision may vary from job to job, especially considering that one may find it more

economical to have precast modules that span multiple stories and/or bays. Nevertheless,

31

it is important that the splice not be located within the expected hinging zone, and

therefore it is recommended that the edge of the splice should be at least two times the

depth of the beam ( 2 ) away from the face of the column. bd

The beam splice should be designed to develop the expected plastic moment (1.1 y pR M )

of the steel beam. The moment demand on the splice under lateral loading can be

determined from Fig. 2.17a, assuming a linear moment diagram between the two

theoretical hinge zones. The moment demand on the splice due to gravity loading is

dependent on the location of the splice and the distribution of gravity load, but the

general shape of this moment diagram is shown in Fig. 2.17b. When these two loading

cases are superimposed, the resulting demand on the beam splice is likely to be close to

the expected plastic moment of the beam (1.1 y pR M ). The fact that the slab is neglected

in the required splice demand (i.e. ignoring composite action) is thought to be reasonable

since the additional capacity at the splice location provided by the slab is also neglected.

The location of the edge of the splice is at least two times the depth of the steel beam

away from the RC column face, assuming that the hinge zone of the steel beam is fully

contained within one beam depth from the face of the column (Fig. 2.18). This

accommodates at least one full beam depth between the end of the severe hinging zone

and the edge of the splice plate. The design of the beam splice is based on methods

described in the AISC-LRFD (2001) with the following steps:

1. Design Force: The splice should be designed to develop the expected plastic

moment of the steel beam (1.1 y pR M ).

2. Plate Thickness: Assuming that the upper and lower flange plates resist the full

moment demand, the thickness of these plates can be determined based on tension

element design concepts using the appropriate phi-factor, 0.9φ = . It is possible

to use a single or double plate configuration, as shown in Fig. 2.16, to

accommodate the design forces. The tension force carried in the flange plates can

be determined from the following equation:

1.1 y p

FlangePlatesb f

R MT

d t=

− (2.13)

32

3. Bolt Design: The size and number of bolts should be determined according to the

bearing strength, as opposed to slip-critical. Further discussion on this topic is

presented in Section 2.3.2.2.3.1.

4. Bolt Shear: The bolts should be checked against bolt shear failure, per the

Specifications for Structural Joints (2000), by assuming either single or double

shear planes (depending on the plate configuration) and the appropriate phi-factor,

0.75φ = .

5. Net Section: Both the flange plates and the beam flange should be checked

against fracture along a net section accounting for the bolt holes. The ultimate

tensile stress, Fu, and a phi-factor of 0.75φ = should be used in this design check.

6. Bearing Strength at Bolt Holes: The stresses in the interface between a bolt and

the connected material should be checked against the design moment according to

the Specifications for Structural Joints (2000), which will limit excessive bolt

elongation from occurring during the life of the bolted connection

( 2.4 ud tF ). n bR ≤

7. Block Shear: All appropriate cases of block shear must be considered in both the

flange plates and the beam flanges.

An alternative approach to design the beam splice is to consider the composite strength of

the beam and the splice. This would imply that in step 1, the required design force

should consider the additional strength provided by the composite slab in positive

bending according to the recommendations in AISC-LRFD (1999), which implies an

effective width equal to Equation (2.10) and an effective stress of 0.85 . This

definition of composite strength controls given that the splice location is sufficiently

away from the column face. The design force in the plates can be determined by

computing the required force couple between the slab and the lower flange plates, as

shown in Fig. 2.19, in order to develop plastic moment of the composite beam. This

simplifies the design approach by neglecting the contribution of the upper flange plates

and the shear tab to the strength of the splice in positive bending. This is a reasonable

simplification of the design process given that when composite action is significant

'cf

33

enough to affect the design of the splice plates (large ratios of Mp,comp/Mp,steel), the

expected location of the plastic neutral axis (PNA) in the region of the beam splice is

close to the upper flange plates, which would limit the amount of strain in these elements.

Figure 2.20 shows the location of the PNA for W-flange beams within the groups of W21

through W44 assuming that the effective slab width is equal to about 1525mm, which is

calculated by the AISC-LRFD provisions for span lengths of about 6.4 meters long. This

figure shows that for beams with large ratios of Mp,comp/Mp,steel (≥1.3), the PNA is

relatively close to the location of the upper flange plates (≥80% height of steel beam).

When the PNA is closer to the mid-height of the beam, then the influence of the

composite slab is lessened and the design of the splice plates reverts back to the steel

beam design. This figure tends to support the assumption to ignore the contribution of

upper flange plates in the design.8 Once the required force couple is determined (Fig.

2.19), then the plates and bolts can be appropriately proportioned according to the

previously defined steps 2-6. Despite the fact that the upper flange plates are ignored in

positive bending, they still contribute to the negative bending strength of the splice. One

option is to simply use the same design as the lower flange plates to avoid unnecessary

confusion during the construction process. The second option is to design the upper

flange plates to develop the expected plastic moment of the steel beam, 1.1 y pR M − , at the

column face, which could achieve savings in both the number of bolts used and plate

size.

2.3.2.2.3.1 Bearing versus Slip Design: Bolt Banging

The AISC Seismic Provisions (2005) state that all bolts should be design using bearing

strength values, but that the bolts should be fully tensioned with faying surfaces prepared

as for Class A or better slip-critical conditions. This implies that even thought the bolts

are designed for bearing resistance, there should be a minimum amount of slip-critical

resistance ( 0.33μ = ) to limit slip in moderate earthquakes. This concedes that above 8 In the test frame, discussed in Chapter 3, there was physical evidence that very little yielding occurred in the upper flange plates due to the presence of the composite slab, and is the reason why it is chosen to ignore the contribution of these plates in the design.

34

certain earthquake intensities (or other types of extreme loading) the bolts will slip and

activate bearing against the edge of the bolt hole. This slip will result in a loud and sharp

noise, often described as sounding like a high-powered rifle shot. While this “bolt

banging” phenomenon is generally benign to the connection, it can raise the concern of

building occupants as to the safety of the building (Schwein 1999, Tide 1999). In the

precast composite RCS system, where the splices are generally located close to the

location of high moment reversals, this “bolt banging” phenomenon would occur

repeatedly during an earthquake.9

This brings about the question as to whether steel beam splices such as those in RCS

frames should be designed to avoid or at least minimize the occurrence of “bolt banging”.

A standard slip-critical beam splice would double the amount of bolts required for a

typical bearing connection, and therefore double the length of the splice itself. In

addition to the increase in cost and time of construction, the location of the beam splice

would have to be reconsidered to ensure that the flange plates and bolts do not interfere

with the expected hinging zone. There are alternatives that would make this connection

more attractive, such as the “Hyper Splice” plates produced by Nippon Steel that doubles

the coefficient of friction and therefore significantly reduces the amount of bolts required

to provide a slip-critical connection. Perhaps one of the more attractive solutions may be

to design the splice not to full slip-critical conditions, but rather to some intermediate

level that would minimize the occurrence of slip during events less than the design level

earthquake (i.e. 10% in 50 year hazard). This design methodology would ensure that

during more frequent events (i.e. 50% in 50 year hazard, immediate occupancy) “bolt

banging” would be much less of a problem and likely would not alarm the building

occupants.

9 As will be discussed in Chapter 3, the composite RCS test frame, which was a precast system with splices approximately 2db away from the column face, experienced a significant amount of “bolt banging” even during the immediate occupancy (50% in 50 year hazard) event. The bolt slippage did not cause any detrimental effects on the performance of the building, but it was clear to the lab participants that during a real time earthquake the cannon-like sound generated during each of the hundreds of slips would undoubtedly frighten the building occupants. The moment at which the splices slipped was calculated to be approximately 0.5Mp,steel, which implies that slip could potentially begin at very frequent events of the order of 50% in 5 years.

35

This issue is not unique to RCS systems, but rather all steel framing systems with bolted

connections similar to what is presented here (Schwein 1999, Tide 1999, Committee on

Steel Structures 1992, Mann 1984). Ultimately, this is more of a comfort issue for the

building occupants since it does not cause any negative effects to the structural system.

Nevertheless, design engineers should be aware of this issue and may consider to

minimize the occurrence of “bolt-banging” during lower intensity earthquakes.

2.4 Composite Joint Design Guidelines

The 1994 ASCE Guidelines for Design of Joints between Steel Beams and Reinforced

Concrete Columns is referenced by the AISC Seismic Provisions (2002) as the

recommended design methodology for composite RCS joints. While the 1994 ASCE

Guidelines represent the culmination of research on these joints prior to 1990, there have

been several key studies since then that have further developed the state of art for the

design of these composite joints. These recent studies have lead to several important

improvements to the original 1994 ASCE guidelines, some of which include:

1. They have since been validated and extended for use in high seismic zones.

2. Reduced requirements for transverse ties within joint height.

3. Extend the original model to cover a wider variety of joint details.

4. Modifications to address the differences between interior and exterior joints.

5. Allowance for the use for high strength concrete

6. Performance-based requirements to limit the expected deformation and damage.

Since the 1994 ASCE guidelines have been published, there have been several other

proposals made which incorporate these improvements and better capture the expected

strength and stiffness of composite joints (e.g., Parra-Montesinos et al. 2001a, 2003;

Kanno et al. 1993, 1997, 2002; Kuramoto and Nishiyama 2004; Kuramoto 1996). Based

on the work that has been accomplished since the development of the ASCE Guidelines,

an updated RCS joint design guidelines is currently being developed by a group of

researchers (including the author) that is meant to replace the current ASCE Guidelines

and will likely be implemented within the year of 2005. This section will discuss both

36

the 1994 ASCE Guidelines and the Updated Guidelines as well compare and contrast

some of the major differences between the two.

2.4.1 Joint Deformations

The ASCE guidelines instruct users to account for joint deformations by one of three

typical approaches: (1) neglecting finite joint size and computing member stiffnesses

based on centerline dimensions, (2) employing a modified finite joint dimension (i.e.

50% rigid joint), or (3) adjusting the beam and column stiffnesses to account for the

effect of the joint. All of these are common techniques used for other types of moment

frames and were recommended given the lack of conclusive data on the actual

deformation response at the time of publication. The Updated Guidelines improve upon

the original recommendations by defining an idealized joint shear force versus total joint

distortion envelope response (Parra-Montesinos et al. 2001), as shown in Fig. 2.21, which

has been calibrated with test results of interior and exterior connections, failing in both

shear and bearing (Kanno 1993, Parra-Montesinos and Wight 2000, Parra-Montesinos et

al. 2003, Liang et al. 2003). This idealized force-deformation response is intended for use

in modern frame analysis programs that allow the explicit modeling of connection

behavior.

2.4.2 General Detailing Requirements

As in the 1994 ASCE Guidelines, the Updated Guidelines will focus only on the

“through-beam” type of connection, where the steel beam runs continuous through the

RC column. The 1994 ASCE Guidelines were also limited in scope to the following joint

details: the face bearing plate (FBP), extended face bearing plate (E-FBP), small column,

vertical joint reinforcement, and headed stud details. There have been numerous other

details proposed by researchers, industry engineers, and construction companies since the

development of the original guidelines, some of which have been developed to facilitate

construction and others that have improved the joint strength and performance. The

Updated Guidelines will be extended to include design provisions for the following new

details:

37

1. Transverse beam (Fig. 2.22): this is required detail when one utilizes RCS joints

in a space frame system.

2. Steel band plate (Fig. 2.22): this has emerged as one of the most effective details

for increasing the bearing strength and providing confinement above and below

the beam.

3. Cover plate (Fig. 2.22): this replaces the joint ties and can act as formwork for the

joint when casting the concrete during the construction phase. This joint detail

came about as a logical extension of the face bearing plates in a two-way space

frame joint, but can also be used in a one-way joint as shown in Fig. 2.22

As in the 1994 ASCE Guidelines, it is assumed that all RCS joints will, as a minimum,

have face bearing plate stiffeners within the beam depth, with a width at least equal to the

flange width. These FBPs have proven to significantly increase the joint strength and

improve the overall joint performance by increasing joint stiffness, delaying the onset of

localized cracking and crushing, and providing the necessary confinement to develop the

inner concrete strut.

2.4.3 Effective Joint Width

The effective joint width, bj, is equal to the summation of the inner and outer panel

widths (bi and bo):

j ib b bo= + (2.14)

where:

bj = effective joint width

bi = inner panel width

bo = outer panel width

While the 1994 ASCE guidelines considers the inner panel width equal to the width of

the FBP pb even if it is wider than the beam flange fb , the updated guidelines does not

acknowledge this extra width and sets the inner panel width equal to the beam flange

width, bf:

38

1994 ASCE Guidelines Updated Guidelines

(2.15)max( , )i pb b= fb f (2.16)ib b=

where:

bp = width of FBP

bf = width of beam flange

The outer panel width bo should be calculated according to the shear keys used to

mobilize the concrete outside of the width of the steel beam flanges (i.e. steel columns,

steel band plates, extended FBPs, etc.) and the connection geometry. The updated

guidelines assume that when steel columns or extended FBPs are used, the outer panel

width can be determined by assuming a 1:3 slope projecting from the edges of the shear

key, as shown in Fig. 2.23 and defined in Equation (2.18)a, with dimensions defined by x

and y. For the band plate detail, the assumption is that x = h and y = bf, except that where

the band plate replaces the ties within the bearing region, then the maximum outer panel

width is controlled by the stiffness of the band plate and should be taken as bo = 12tbp (tbp

= thickness of band plate), regardless of the other shear keys present. The reason for this

reduction in the outer panel joint width is based on strain measurements from

subassembly tests (Parra-Montesinos 2000) that indicate the band plates transfer shear

force to the outer concrete regions primarily through direct bearing on the concrete over

the width of the beam flange, as opposed to the formation of a horizontal strut and tie

mechanism. If no shear keys are provided, a minimum outer panel width is allowed by

assuming x = 0.7h and y = 0 in Equation (2.18)a to account for the outer strut formation

between the joint ties and friction in the regions of beam flange subjected to high bearing

stresses (there is also likely a strut developed between the FBPs and the joint ties).

The 1994 ASCE Guidelines define the outer joint width as a ratio of the average of the

beam flange width and the column width according to the types of shear key used in the

joint. If no shear keys are provided, the 1994 ASCE guidelines recommend that the outer

panel width be taken as zero. Both of these definitions for outer panel width are

compared to the new guidelines equations below:

39


( ) 0.5o m ib C b b d= − ≤ b (2.17)a 2 3o fb y x b b bf= + − ≤ − (2.18)a

( ) 2 1.m f fb b b b h b= + ≤ + ≤ 75 f (2.17)b band plates w/no joint hoops

( )( )fC x h y b= (2.17)c 12o bpb t b fb= ≤ − (2.18)bwhere:

C = joint mobilization coefficient

bm = maximum effective width of joint region

db = depth of beam

b = width of concrete column measured perpendicular to the beam

h = height of the concrete column measured parallel to the beam

x,y = effective dimensions of shear keys defined in Fig. 2.24

tbp = thickness of the band plate

In order to compare the differences in joint width for each method, consider a typical

joint with a steel column and FBPs, as shown in Fig. 2.24. The calculated joint widths

summarized in Table 2.1 show that the Updated Guidelines predict an outer panel width

about 2.6 times larger than the ASCE Guidelines. This difference reflects the fact that

the joint width determination from the ASCE Guidelines was largely based criteria for

reinforced concrete joints, whereas more recent research has shown that the composite

RCS joints create internal stress transfer mechanisms with larger effective joint regions.

2.4.4 Joint Strength

Joint panel shear strength is handled the same way in both models and is defined as the

summation of the contribution of the: (1) inner panel strength, Vin, which includes the

capacity of both the steel web panel and inner concrete strut, and (2) the outer concrete

panel strength, Von. Each of the individual components making up the total shear strength

have been refined in the Updated Guidelines, reflecting the most recent test data

available. These changes are discussed in detail in the following sections. The phi-factor

for the shear strength (φs) has also been increased in the new model to 0.85 from the

original value of 0.7. The rationale for the updated phi-factors will be discussed later in

40

Section 2.4.10.3. A new strength reduction factor, k = 0.85, has also been introduced into

the design check to control joint distortions such that joint damage is limited to moderate

cracking with web panel yielding under ultimate loads. Shear design checks for each set

of guidelines are shown in Equations (2.19) and (2.20), respectively.

In the 1994 ASCE Guidelines, joint bearing strength is treated as a total joint failure,

separate from joint shear, and is computed and checked against the appropriate design

forces, as shown in Equation (2.21). The Updated Guidelines assumes that vertical

bearing failure occurs only over the inner panel width, bi, and that the outer panel is more

likely to fail in outer panel shear. Test data has shown that latter approach is more

representative of the true behavior in these composite RCS joints. Kanno (1993)

observed that the outer panel fails in relatively the same manner regardless of whether the

inner panel fails in joint shear or vertical bearing. Therefore, the Updated Guidelines

limits the amount of shear that can be developed in the inner panel by the vertical bearing

strength, as shown in Equation (2.20)b. In the Updated Guidelines, the φ factor in

Equation (2.20)a depends on the governing mode of failure, φs = 0.85 for shear and φb =

0.70 for bearing. These differences in phi-factors reflect the fact that it is more desirable

to design the joint to fail in shear to avoid the undesirable pinched response associated

with bearing failure.

ASCE Guidelines Updated Guidelines

( )j s in onV V Vφ≤ + (2.19)a ( )j in s onV k V Vφ φ≤ + (2.20)a

in spn icnV V V= + (2.19)b ( ) ( )b vb bin s spn icn

j

M V hV V V

dφ

φ φ−

= + ≤ (2.20)b

bj

j

MV

d= −∑

cV (2.19)c bj c

j

MV V

d= −∑ (2.20)c

0.35c b b vbM h V Mφ+ Δ ≤∑ (2.21)

where:

Vj = joint shear demand imposed by adjacent beams and columns

φs = joint shear phi-factor (ASCE: 0.7, Updated: 0.85)

41

φb = joint bearing phi-factor (ASCE: 0.7, Updated: 0.75)

Vin, Von = inner and outer panel shear strength

Vspn = steel web panel shear strength

Vicn, Von = inner and outer concrete panel strength

ΣMb, ΣMc = summation of beam or column moments transferred into the joint

dj = depth of joint equal to distance between beam flange centerlines

Vc = average column shear

ΔVb = difference in beam shears

Mvb = moment derived from vertical bearing strength of joint

k = deformation-based strength reduction factor, set to 0.85

2.4.5 Inner Panel Shear Strength

The shear strength of the inner panel, Vins, is simply summation of the capacities of the

steel web panel, Vspn, and the inner diagonal concrete strut, Vicn. This can be described as

follows:

ins spn icnV V V= + (2.22)

where:

Vins = nominal horizontal shear strength of inner panel

The horizontal shear strength provided by the steel web panel is defined by the ASCE

and Updated Guidelines as follows:


0.6spn ysp spV F t= jh h (2.23) 0.6spn ysp spV F t α= (2.24)

where:

Fysp = nominal yield strength of steel web panel

tsp = thickness of steel web panel

jh = horizontal distance between bearing force resultant (found by

iteration, ≤0.7h)

α = coefficient differentiating interior (0.9) and exterior joints (0.8)

42

Test data was used to simplify Equation (2.23) by removing the iteratively determined jh-

term and replacing with constants that account for the differences in strain distribution for

interior versus exterior configurations. As a result, even if it assumed that 0.7jh h= in

Equation (2.23), the Updated Guidelines (Equation (2.24)) predict a stronger steel panel

zone by approximately 29% (reduced to 14% for exterior joints).

The capacity of the inner diagonal concrete strut is defined by each of the guidelines as

follows:


' '1.7 0.5icn c p c p wV f b h f b= ≤ d (2.25) ' '0.5icn i c i c f jV k f b h f bβ= ≤ d (2.26)

where: '

cf = nominal compressive strength of concrete (MPa)

bp = effective width of FBP: 5 1.5p f pb b t bf≤ + ≤

tp = thickness of FBP

β = strength factor depending on connection type (1.0 interior, 0.6

exterior)

ki = strength factor set to 1.7

dw = depth of the beam web

For interior joints, both the 1994 ASCE and Updated guidelines yield the same strength

for the inner concrete strut. Test data has shown that this strut is less effective for

exterior joints, therefore the strength factor, β, reduces the nominal strength to 60% of

interior joints. To prevent bearing failure at the ends of the strut, both models limit the

amount of shear developed in the concrete strut by a bearing stress of '2.5 cf over an area

at the top and bottom of the FBPs equal to 0.25 f jb d

2.4.6 Inner Panel Vertical Bearing Strength

The 1994 ASCE and Updated Guidelines define the vertical bearing strength of the inner

panel of the joint as follows:

43


( )(

11 2vb cn

vr vrn vrn

M C h

h T C

β= −

+ )+

(2.27)a ( )

( )

*, 11 2vb i cn

vr vrn vrn

M C h

h T C

β= − +

+ (2.28)a

( )1 2cn b jC f b hβ= (2.27)b ( )*1 2cn b fC f b hβ= (2.28)b

'2.0b cf f= (2.27)c '

'

2.0 (w/min. tie reinf.)

2.5 (w/min. band plate reinf.)b c

b c

f f

f f

=

= (2.28)c

where:

Ccn = nominal compression strength of bearing zone

β1* = stress block depth coefficient taken as the 0.85 for ≤ 27.6MPa, and

reduced by 0.05 for every 6.9MPa increase in strength, with a

minimum limit of 0.65.

'cf

fb = effective bearing stress block intensity

The biggest difference between the models is the effective joint width over which the

effective bearing stress acts. The ASCE Guidelines assume that the bearing stress acts

over the entire effective width of the joint, bj, where on the other hand, the Updated

Guidelines assume that the bearing stress is effective only over the inner panel width, bf,

of the joint. As previously discussed, this latter approach has been confirmed in the

subassembly tests (Kanno 1993) and is a better way to model the joint failure

mechanisms. The ratio of the Updated bearing strength to the ASCE bearing strength

yields the following result:

( )( )

* *1 1, , ,

, , 1

1 2

1 2vb i Updated b Updated f

vb ASCE b ASCE j

M f bM f b

β β

β β

−= × ×

− 1

(2.29)

If the joint contains standard joint hoops above and below the beam, then the first ratio

(fb) in Equation (2.29) will simply be unity. If steel band plates are present, then this ratio

will be 2.5. The second ratio in Equation (2.29) will typically be less than 1; with the

only exception being equal to 1 if no shear keys are provided to mobilize the outer

concrete strut. If we take the example developed in Section 2.4.3 (Fig. 2.24) and assume

that only joint hoops are provided for confinement in the bearing zone and

44

' 41.3 (6 )cf MPa ksi= , then the result of Equation (2.29) is 0.81, indicating that the

Updated Guidelines predicts a bearing strength that is about 20% less than the 1994

ASCE prediction. This is expected since the difference in effective joint width in bearing

is considerable. However, the net effort on the joint design is minimal since the Updated

Guidelines include the outer panel shear strength in the total joint bearing strength, as

shown in Equation (2.20).

2.4.7 Outer Panel Shear Strength

The ASCE and Updated Guidelines define the strength of the outer concrete strut as

follows:


'1.7on c oV f= b h (2.30) '

on o c oV k f bβ= h (2.31) where:

ko = confinement strength factor for outer concrete strut

= 1.5 (cover plate or joint hoops and band plates)

= 1.25 (all other cases with either joint hoops or band plates)

Unlike the 1994 ASCE Guidelines, the Updated model varies the strength factor

depending on the type of details in the joints and also accounts for the differences due to

interior versus exterior joint configuration. The ratio of the predicted strengths from the

Updated to the 1994 ASCE Guidelines yields the following results for interior joints:

,

, ,

(0.74 or 0.88)on Updated o Updated

on ASCE o ASCE

V bV b

= , (2.32)

Again, if we take the example joint from Section 2.4.3 (Fig. 2.24), then Equation (2.32)

would yield a ratio of 1.95 to 2.32, depending on the joint details used. For exterior

joints, these ratios are reduced by an additional 40%. Nevertheless, this shows that the

Updated Guidelines predict a much larger contribution from the outer panel concrete strut

compared to the original 1994 ASCE Guidelines.

45

2.4.8 Joint Panel Shear and Vertical Bearing Moment Capacity

Up to this point, the strength of the joint has been represented by joint shear and divided

between the inner and outer joint panels. It is often necessary to combine each of these

contributions to obtain an equivalent joint moment capacity for panel shear and vertical

bearing mechanism. This information can be used to compare with the moment

capacities of the surrounding beams and columns or in analytical models of these

composite joints, such as those described in Chapter 4. The shear strength provided by

the inner concrete strut, the steel web panel, and the outer concrete strut can be combined

in the following equation to compute the moment capacity of the joint in panel shear:

1.25ps spn w icn j on jM V d V d V d= + + (2.33)

where:

Mps = equivalent joint panel shear moment capacity

The inner vertical bearing strength can be combined with the outer panel shear strength to

obtain the equivalent joint vertical bearing moment capacity:

, 1.25vb vb i on jM M V d= + (2.34)

where:

Mvb,total = equivalent joint vertical bearing moment capacity

The smaller of these two moment capacities will control the design strength of the joint.

2.4.8.1 Strong-Joint Weak-Beam

For the seismic design of composite joints, the nominal moment strength of the joint must

be at least equal to the summation of the nominal strengths of the beams framing into the

joint. The nominal strength of the beam in positive bending should consider the

composite strength of the beam, with nominal steel properties and an effective slab stress

of 1.3 . This is referred to as the strong-joint weak-beam criterion and is found in the

AISC Seismic Provisions (2002).

'cf

46

2.4.9 Detailing Considerations

In this section, the design requirements of each of the joint details are proposed to

provide the capacity to develop the full strength of the composite joint.

2.4.9.1 Ties within Beam Depth

Several studies (Kanno 1993, Parra-Montesinos et al. 2000, and Liang et al. 2004) have

shown that the requirements for the horizontal reinforcing bar ties within the depth of the

steel beam can be relaxed from the requirements specified by the 1994 ASCE Guidelines

(Equation (2.35)). Based on these tests, the Updated Guidelines have decreased the tie

requirements to Equation (2.36), which is similar to the minimum requirements for

reinforced concrete joints (ACI 318).


'sh ysha c

h

A Fk f b

s≥ o s (2.35)a 0.01ρ ≥ (2.36)a

0.004sh hA bs≥ (2.35)b min(0.25 ,0.25 )h js d h= (2.36)b

where:

Ash = cross-sectional area of reinforcement parallel to beam with spacing sh.

Fysh = nominal yield strength of column ties

sh = center to center spacing of column ties

ka = strength factor set to 1.89 if joint is subject to tension force, 1.44 if no

tension

ρs = volumetric ratio of hoop volume within beam depth to joint volume

( ) jd hb

2.4.9.2 Longitudinal Column Bars

The limitation on the size of the longitudinal bars passing through the joint is unchanged

from the 1994 ASCE Guidelines, and is specified in Equation (2.37). This requirement is

47

meant to limit the amount of bar slip in the joint associated with possible large changes in

bar forces due to the transfer of moments through the joint (ACI-ASCE 352).

( )420

20 20j

baryr

d dd

F≤ ≤ j (2.37)

where:

dbar = diameter of the longitudinal column bar

Fyr = yield strength of longitudinal column bars in MPa

2.4.9.3 Face Bearing Plates and Steel Band Plates

The requirements on the thickness of the FBPs did not change from the original ASCE

guidelines. The FBP thickness should be sized to for the capacity to resist the nominal

shear strength of the inner concrete strut, Vicn.

(3p in f w

f up

t V b tb F

≥ − )ywF (2.38)

32

icnp

f up

Vtb F

≥ (2.39)

0.20 ic fp

yp w

V bt

F d≥ (2.40)

where:

Fyp, Fup = nominal yield strength and ultimate strength of bearing plate

dw, tw = depth and thickness of beam web

Equations (2.38)-(2.40) are semi-empirical formulas developed from joint tests by Sheikh

et al. (1987). The following minimum thickness requirement should also be adhered to:

22p ft b≥ (2.41)

The Updated Guidelines also specify thickness requirements for the steel band plates,

which were derived from the FBPs requirements given the similarities in behavior.

48

3 12p

up bp f

tF d b

⎛ ⎞⎛ ⎞≥ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟+⎝ ⎠⎝ ⎠

onV (2.42)

4

0.20 on bpbp

ybp

V dt

F h≥ (2.43)

where:

dbp, tbp = depth and thickness of the band plate

Fybp, Fubp = nominal yield strength and ultimate strength of band plate

2.4.9.4 Steel Beam Flanges

Requirements for the thickness of the steel beam flanges have remained the same from

the original ASCE guidelines. These requirements are in place to ensure that the flanges

are able to resist the vertical bearing force associated with the joint shear in the steel

panel. The flange thickness requirement is as follows:

0.30 f sp yspf

yf

b t dFt

hF≥ (2.44)

where:

Fyf = nominal yield strength of the beam flanges

2.4.9.5 Extended Face Bearing Plates and Steel Column

The extended FBPs and/or the steel columns should be designed to resist a force equal to

the joint shear carried by the outer concrete compression strut, Von. The average concrete

bearing stress against these elements is assumed to be approximately 2.5 'cf , which acts

over a height of 0.2dj. These elements may be considered capable of resisting the joint

shear forces if their thicknesses adhere to the following equation:

'

0.120.25

on pf

j y

V bt

d F≥ (2.45)

where:

49

'pb = the flange width of steel column or width of extended FBP

Fy = nominal yield strength of plate

In addition to this, the thickness of the extended FBPs should not be less than that of the

FBPs.

2.4.10 Model Validation

In this section, data are summarized to validate the Updated Guidelines against RCS

beam-column subassembly tests. For each of the applicable tests, both the 1994 ASCE

and Updated Guidelines will be computed and compared to the actual measured strength

of the joint specimen.

2.4.10.1 RCS Joint Tests Considered

The following joint test series were considered in this validation study: (1) Sheikh 1989,

(2) Deierlein 1989, (3) Kanno 1993, (4) Parra-Montesinos and Wight 2000, and (5)

Liang et al. 2003. This includes a total of forty-nine RCS joint tests, which of these,

thirty-eight are of interior configuration and eleven are exterior configurations. Since it is

a requirement of both guidelines, all of the joints that did not have FBPs were not

considered in this study (five in total: Sheikh 1, 3, 9 (1989) and Deierlein 12, 14 (1989)).

The joints were separated into the following failure mechanisms: (1) joint panel shear, (2)

joint vertical bearing, and (3) other (i.e. column failure, beam failure, etc.). There are a

total of twenty-one joints in the joint shear failure group and six in the joint bearing

failure group. The details for these joint tests are summarized in Tables 2.2 and 2.3. For

further details on each of these tests, please refer to the original references (Sheikh et al.

1989; Deierlein et al. 1989; Kanno 1993, 1997; Parra-Montesinos et al. 2000; and Liang

et al. 2003).

50

2.4.10.2 Updated Joint Guidelines Validation Results

Using the information presented in Tables 2.4 and 2.5, the predicted strengths of each of

the subassemblies are computed in terms of beam shear (Vbc) using the 1994 ASCE and

Updated Guidelines and are then compared to the maximum beam shear reached during

the test (Vbe). The results of this procedure for the joint panel shear and joint bearing

failure groups are shown in Figs. 2.25 and 2.26, respectively. The filled circles in these

figures represent the predicted to measure ratio using the Updated Guidelines, while the

unfilled circles are the results from the 1994 ASCE Guidelines. In the joint shear

validation (Fig. 2.25), one can see an overall increase in the ratios from the 1994 ASCE

values to the Updated values. The average values of predicted to measured strengths for

the joint shear group are 0.96 and 0.80 for the Updated and 1994 ASCE Guidelines,

respectively, indicating that the Updated model is more accurately picking up the

measured strength of these specimens. The coefficient of variation from the Updated

Guidelines (13.8%) is also slightly better than the 1994 ASCE guidelines (16.0%).

The predicted to measured ratios for those joints failing in vertical bearing are shown in

Fig. 2.25. The Updated Guidelines greatly improve the accuracy of the strength model,

increasing the mean strength ratios from 0.76 to 0.92. The consistency of the strength

prediction for the vertical bearing model is also improved, as shown by the decrease in

the coefficient of variation from 15.4% to 8.0%.

This validation study shows that for both the joint shear and joint bearing failure modes

the proposed changes incorporated into the Updated Guidelines improves both the

accuracy and the consistency of the original ASCE strength model.

2.4.10.3 Determination of Strength Reduction (φ) Factors

The strength reduction (φ) factors for the two strength models are intended to account for

the variability in the capacity due to (1) discrepancies between the nominal and measured

material properties, (2) differences in fabrication and erection, and (3) inconsistency of

51

the design equations. The phi-factor used for the original ASCE joint guidelines was

taken conservatively as 0.7, since at the time of the publication there was only limited

data to validate the provisions. Given that more experimental results are available, the φ-

factors can now be determined using the beta-reliability method, which is the technique

used to develop the φ-factors for the AISC-LRFD (2002). Using this method, the

expression for the φ-factor can be derived as follows:

( )exp mR

n

RVR

φ αβ= (2.46)

where:

α = linearization approximation constant used to separate the resistance

and demand uncertainties, taken as 0.55.

β = beta reliability or safety index defined as the number of standard

deviations from the mean

2 2ln( / )

ln ln m

mm

R Q R Q

R RQ Q

V Vσ

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟

⎝ ⎠⎣ ⎦ ⎝ ⎠= ≈+

where Rm and Qm are the mean values of the resistance and load effect

and VR and VQ are the corresponding coefficients of variations.

VR = coefficient of variation of the resistance variable

2 2 2M F PV V V= + +

VM, VF, VP = coefficient of variation representing the material strength,

uncertainties in fabrication, and uncertainties in assumptions (i.e., the

professional factor)

m

n

RR

= ratio of the means of the measured to the nominal resistance.

Traditionally, the target beta-value is assumed to be 3.0 for members and 4.5 for

connections. A larger value is traditionally targeted for connections, given that the

ductility of members in is more reliable than that of connections. Using the same

rationale for composite joints, the joint panel shear check is assigned a beta-value of 3.0

52

while vertical bearing check is assigned a value of 4.5. The coefficient of variation

accounting for the material strengths and the uncertainties in fabrications are presented in

Table 2.6, following the assumptions used by Ravindra and Galambos (1978) to develop

φ-factors for the AISC-LRFD (2002). The coefficient of variation that accounts for the

uncertainties in assumptions is largely related to the confidence in the strength model that

was developed in Section 2.4.4 through 2.4.7. This value can be assumed as the

coefficient of variation found in the predicted to measured data presented in Section

2.4.10.2 and is summarized again in Table 2.6. The measured to nominal resistance term

( ) in Equation /mR Rn

n

(2.46) is simply the inverse of the predicted to measured ratios

presented in Section 2.4.10.2 multiplied by the ratio of the expected to nominal material

strengths. The latter ratio is necessary since the predicted strengths in Section 2.4.10.2

are based on measured material properties, whereas the term requires the ratio of

measured to nominal mean resistance. The expected to nominal material strength ratio

will be assumed as 1.1, which is equivalent to the assumed value for Grade 50 steel (Ry).

/mR R

Using the values summarized in Table 2.6 and Equation (2.46), the phi-factors for the

panel shear and vertical bearing strength models are computed as 0.84 and 0.85,

respectively. While this process seems reasonable, there are some reservations about

recommending such a high φ-factor for the vertical bearing strength model, given the

limited amount of available data on which this is based (only 6 data points for bearing

model). The limited data set for the vertical bearing strength reduces the level of

confidence in the low coefficient of variation (0.08), which has a large impact on the

calculated φ-factor. A reasonable approach may be to assume that the coefficient of

variation of the bearing model would be roughly equivalent to the panel shear model

(0.138) if a larger data set was available. If the vertical bearing phi-factor is recalculated

using this assumption, then the phi-factor is decreased to 0.77 (as shown in italics in

Table 2.6). Given the limited data set and the low confidence in the coefficient in

variation, this assumption is considered reasonable and the decreased phi-factor is

accepted for the vertical bearing model. For the sake of consistency with current codes,

53

the final recommended phi-factors for the panel shear and vertical bearing model are

assumed to be 0.85 and 0.75, respectively.

2.5 Final Recommendations

This chapter has reviewed the current knowledge in design standards for composite RCS

frames as well as some of the latest research that can have an impact on these systems.

This section will summarize the recommended design methods that will be used and

validated through the rest of this study. In addition to the recommendations presented in

this section, the general building design requirements presented in Section 2.3.1 from the

IBC 2003 and the ASCE 7 (2002) will be adopted in this study.

2.5.1 Reinforced Concrete Columns

The design of the RC columns follows the conventional seismic design as recommended

in Chapter 21 of ACI 318 (2002). The only special consideration is to arrange the

longitudinal reinforcement bars to accommodate the passage of steel beam (and

potentially a cross-beam for a two way joint). The recommendations of Mehanny (2000)

are adopted to model the effective stiffness of the RC columns, as presented in Equation

(2.5).

2.5.2 SCWB Criterion

The SCWB criteria from ACI 318 (2002) and the AISC Seismic Provisions (2002) were

introduced in Section 2.3.2.1.1. When applying either of these to composite RCS frames,

problems arise with these criteria since they are written for applications to all-concrete or

all-steel moment resisting frames. A natural extension would be to combine the

applicable portions of each of the SCWB criterions into one that could be applied to the

design of composite RCS frames. The updated SCWB criterion is proposed as follows:

* 1.0c

g

MM

>∑∑

(2.47)

54

where:

cM =∑ sum of nominal flexural strengths of the RC columns framing into the

joint, as defined per Equation (2.6) *gM =∑ sum of the expected beam strengths, where applicable, considering the

composite section of the beam.

Equation (2.47) uses the definition of column strengths from the ACI 318 (2002)

(Equation (2.6)) as described in Section 2.3.2.1.1. The sum of the beam strengths in

Equation (2.47) now requires that the strength of the composite beams also be included in

the SCWB check, recognizing that the beam in positive bending will attain the full

composite strength while the beam in negative bending will achieve the expected plastic

moment of the bare steel beam (1.1 y pR M ).10 Calculation of the plastic strength of the

composite section should follow the recommendations presented in Section 2.3.2.2.1.

This proposed SCWB criterion is used for the design of the frames presented within this

study.

While the SCWB provision proposed by the SEOAC Blue Book (Equation (2.8)) is not

used for design in this study, this provision will be investigated with respect to the

seismic performance of the frames.

2.5.3 Composite Steel Beams

As mentioned in Section 2.5.1, it is recommended that the composite strength of the steel

beams be considered in the seismic design of composite RCS systems. The amount of

overstrength that a composite slab provides to a bare steel beam is significant enough to

disrupt the intended sway mechanism of a moment frame and therefore should not be

ignored. This is clearly shown in Fig. 2.27, which shows the increase in capacity that a

composite slab provides for typical W-section beams. In addition to the SCWB criteria,

the composite strength and stiffness should also be considered in the strength design of

10 This conclusion is supported by the results of the full-scale test frame, discussed in Chapter 3, which shows the durability and performance of the slab significantly impacted the specimen behavior.

55

the beams and in meeting the drift limitations. Recommendations on modeling the

stiffness of composite beams have been proposed in Section 2.3.2.2.

It is recommended that the shear studs be designed to provide a fully composite section

according to the recommendations from the AISC Seismic Provisions (2002) described in

section 2.3.2.2.2. Partially composite sections are not recommended given the limited

ductility of shear studs, particularly under cyclic loading. For a fully composite section,

the maximum plastic strength of a composite section can be modeled according to the

recommendations of du Plessis (et al. 1972) with an effective concrete stress of 1.3

acting over an effective width equal to the column width.

'cf

11 To remain consistent with

the recommendations for a bare steel beam, the plastic force of steel beam should

consider the expected yield strength, including strain hardening, of the steel, which is

as 1.1defined y yR F .

2.5.4 Precast Element Splices

Design recommendation for the steel beam splices were presented in section 2.3.2.2.3. It

is sufficient to consider the simplified version of the splice design by ignoring the

composite slab since it factors into both the demand and capacity. It is suggested that the

location of the beam splice be at least twice the depth of the beam away from the column

face to avoid any interaction with the hinging zone of the steel beam, which is likely to be

contained within one depth of the beam away from the column face. The slip capacity of

these bolted connections and the “bolt banging” phenomenon will be investigated further

in Chapter 3, but for the time being, it is recommended that the bolts be designed for

bearing capacity

The RC columns are spliced using the common precast construction technique of grouted

splices with mechanical reinforcement bar couplers. These splices are typically designed

by the construction company to develop the entire plastic moment of the RC column

11 Both the effective width and effective stress of the composite slab presented within this section are investigated and validated in the calibration study presented in Chapter 4.

56

section. It is suggested that these splices be located in the middle-third of column height

to avoid any interaction with potential hinging regions at the column ends and also to

make the workability of the splice more convenient for construction workers.

2.5.5 Composite Joint Design

The proposed updates to the 1994 ASCE Joint Design Guidelines, as presented in Section

2.4, are recommended for the design of composite RCS joints. As shown in Section

2.4.10.2, this new model has been shown to be more accurate and consistent in predicting

both the panel shear and vertical bearing strength of these joints. The updated provisions

now cover a wider variety of joint details that have proven to be effective in maintaining

the strength and stiffness of composite joints as well as improving the constructability.

New phi-factors have been proposed using the beta-reliability method, which is the same

technique used to develop the phi-factors for the AISC-LRFD (2002) design approach.

57

Table 2.1 – Joint width comparisons between ASCE and Updated Guidelines. Joint Dimension ASCE Guidelines Updated Guidelines

bi 266 mm 266 mm bo 102 mm 269 mm

bj = bi + bo 368 mm 535 mm

58

Table 2.2 – Summary of joint details and dimensions for those in the panel shear joint group. (Units: kN, mm)

Name h b bf db tf tsp f'c Fysp Tvrn Cvrn hvr Lc Lb Joint Details

KANNO OJS1-1 406 406 127 355 10.21 6.5 41.20 379.0 0 0 0 3391 3048 JH

KANNO 0JS2-0 406 406 102 229 19.55 6.66 42.60 407.0 0 0 0 3391 3048 JH,SC

KANNO OJS3-0 406 406 153 355 25.93 6.66 42.60 407.0 324.9 324.9 305 3391 3048 JH,DB,E-FBP (d=102,t=13.45,w=153)


KANNO OJS5-0 406 406 153 355 25.25 6.53 48.30 393.0 324.9 324.9 305 3391 3048 JH,DB,BP (dbp=102,tbp=13.45)


KANNO 0JS7-0 406 406 153 355 25.25 6.53 48.30 393.0 324.9 324.9 305 3391 3048 JH,TB,DB,E-FBP (d=102,t=13.45,w=153)

KANNO HJS1-0 406 406 153 355 25.93 6.66 102.00 407.0 0 0 0 3391 3048 JH,E-FBP (d=102,t=13.45,w=153)

KANNO HJS2-0 406 406 153 355 25.93 6.66 102.00 407.0 0 0 0 3391 3048 JH,ST,E-FBP (d=102,t=13.45,w=153)

DEIERLEIN 10 508 508 203.2 450.9 22.4 6.68 32.41 249.6 0 0 0 3708 4877 JH

DEIERLEIN 11 508 508 203.2 450.9 22.4 13.39 32.41 249.6 433.9 433.9 381 3708 4877 JH,DB

DEIERLEIN 13 508 508 203.2 450.9 22.4 6.68 34.47 249.6 0 0 0 3708 4877 JH,ST

DEIERLEIN 15 508 508 203.2 450.9 22.4 6.68 28.27 249.6 0 0 0 3708 4877 JH,SC

DEIERLEIN 17 508 508 203.2 450.9 22.4 6.68 26.89 249.6 433.9 433.9 381 3708 4877 JH,SC,DB

SHEIKH 4 508 508 203.2 444.5 19.05 6.35 29.65 247.5 0 0 0 3708 4877 JH

SHEIKH 5 508 508 203.2 444.5 19.05 6.35 29.65 247.5 0 0 0 3708 4877 JH

SHEIKH 7 508 508 203.2 444.5 19.05 6.35 25.6 247.5 0 0 0 3708 4877 JH

SHEIKH 8 508 508 203.2 444.5 19.05 6.35 24.8 247.5 0 0 0 3708 4877 JH,E-FBP (d=101.6,t=22.23,w=203.2)

PARRA 1 400 400 203 241 32 12.7 43.40 279.0 0 0 0 2240 2440 JH,SC

PARRA 6 400 400 172 390 29.08 7.94 29.60 381.0 0 0 0 2240 2440 JH,SC

PARRA 9 400 400 172 390 29.08 7.94 29.00 320.0 0 0 0 2240 2440 TB,SC,BP (dbp=100,tbp=13)

59

Table 2.3 – Summary of joint details and dimensions for those in the vertical bearing joint group. (Units: kN, mm)

Name h b bf db tf tsp f'c Fysp Tvrn Cvrn hvr Lc Lb Joint Details

KANNO OJB1-0 406 406 153 355 16.1 25.93 48.70 345.0 0 0 0 3391 3048 JH,SC

KANNO OJB4-0 406 406 153 355 16.1 25.93 48.50 345.0 0 0 0 3391 3048 JH,SC

KANNO OJB5-0 406 406 153 355 16.1 25.93 46.00 345.0 228.8 228.8 305 3391 3048 JH,SC,DB

KANNO OJB6-1 406 406 153 355 16.1 25.93 46.00 345.0 0 0 0 3391 3048 JH,SC

SHEIKH 2 381 381 101.6 304.8 11.11 6.35 24.48 383.4 0 0 0 2743 2438 JH

SHEIKH 6 508 508 203.2 444.5 19.05 6.35 27.58 247.5 0 0 0 3708 4877 JH

60

Table 2.4 – Results from Update Guidelines for the joint group failing in panel shear. (Units: kN, mm)

NameUpdated

Vmeas/Vpred

ASCE Vmeas/Vpred

bo Vspn Vicn Vohn Mvb Ccn x Vb,PanelShear Vb,Bearing

KANNO OJS1-1 0.69 0.60 0 540.1 562.6 0 362200 1275 284.2 136.8 132.3

KANNO 0JS2-0 0.86 0.65 177.7 594.3 455.1 588.5 300800 1058 284.2 126.7 159.1

KANNO OJS3-0 0.89 0.76 253.0 594.3 689.2 838.0 649400 1588 284.2 273.1 361.2

KANNO OJS4-1 0.83 0.70 253.0 594.3 689.2 838.0 649400 1588 284.2 273.1 361.2

KANNO OJS5-0 0.75 0.81 161.4 562.6 733.9 683.1 837700 2250 284.2 252.5 406.8

KANNO OJS6-0 1.01 0.71 253.0 562.6 733.9 892.3 709800 1800 284.2 283.9 391.6

KANNO 0JS7-0 0.80 0.67 253.0 562.6 733.9 892.3 709800 1800 284.2 283.9 391.6

KANNO HJS1-0 1.04 0.87 253.0 594.3 1067.0 1297.0 1080000 3802 284.2 386.8 586.4

KANNO HJS2-0 1.04 0.78 253.0 594.3 1067.0 1297.0 1080000 3802 284.2 386.8 586.4

DEIERLEIN 10 0.94 0.81 0 457.4 999.0 0 713800 2007 355.6 142.3 165.5

DEIERLEIN 11 1.16 0.90 194.7 916.8 999.0 704.0 1044000 2007 355.6 272.9 329.5

DEIERLEIN 13 1.01 0.81 152.4 457.4 1030.0 568.2 759200 2135 355.6 215.9 246.6

DEIERLEIN 15 1.01 0.80 137.5 457.4 933.0 464.4 622600 1751 355.6 193.4 202.0

DEIERLEIN 17 1.14 0.80 194.7 457.4 910.0 641.2 922900 1665 355.6 213.1 293.6

SHEIKH 4 0.86 0.75 0 431.2 955.5 0 653000 1836 355.6 134.8 151.3

SHEIKH 5 0.89 0.77 0 431.2 955.5 0 653000 1836 355.6 134.8 151.3

SHEIKH 7 0.66 0.78 0 431.2 887.5 0 563400 1584 355.6 128.0 130.5

SHEIKH 8 1.00 0.81 304.8 431.2 874.3 964.2 546600 1537 355.6 245.5 245.4

PARRA 1 0.86 0.94 138.8 680.3 545.6 274.3 592000 2114 280.0 138.4 300.0

PARRA 6 1.21 1.23 169.8 580.8 381.7 277.2 342000 1222 280.0 222.6 228.2

PARRA 9 1.08 0.80 228.0 487.8 377.8 368.4 418900 1496 280.0 226.9 285.9

61

Table 2.5 – Results from Update Guidelines for the joint group failing in vertical bearing. (Units: kN, mm)

NameUpdated

Vmeas/Vpred

ASCE Vmeas/Vpred

bo Vspn Vicn Vohn Mvb Ccn x Vb,PanelShear Vb,Bearing

KANNO OJB1-0 0.89 0.87 151.7 1961 736.9 537.1 515800 1815 284.2 404.8 271.0

KANNO OJB4-0 0.78 0.76 151.7 1961 735.4 536.0 513700 1808 284.2 404.4 270.0

KANNO OJB5-0 0.90 0.87 160.5 1961 716.2 552.4 626800 1714 284.2 404.6 313.8

KANNO OJB6-1 0.82 0.80 151.7 1961 716.2 522.0 487200 1714 284.2 399.9 258.2

SHEIKH 2 0.60 0.60 0.0 500.8 325.6 0.0 151600 568.6 266.7 108.9 69.6

SHEIKH 6 0.63 NaN 0 431.2 921.6 0 607400 1708 355.6 131.4 140.7

Table 2.6 – Summary of values required to compute phi-factor using the beta-reliability index. Failure

Mechanism β - value Rm/Rn V V V VM F P R φ Recommended

φ

Panel Shear 3.0 1.1*(0.96) -1 = 1.15 0.10 0.05 0.138 0.178 0.84 0.85

Vertical Bearing 4.5 1.1*(0.92)-1 = 1.20 0.10 0.05 0.08 (0.138)

0.137 (0.178)

0.85 (0.77) 0.75

62

Steel Beams

Figure 2.1 – Typical construction sequence of cast-in-place composite RCS moment

frames.

Figure 2.2 – RCS precast construction utilizing beam-column modules and column and beam spliced connection.

Bolted Beam Splices

RC Column

Band Plate

Steel Beam Rebars

Grouted Splices

Beam Splice

Precast Beam-Column Module

RC Column

Steel Erection Column

Reinforcing Bar Cage

Formwork

63

Figure 2.3 – Example of precast RCS construction in Japan (Shimizu Corporation).

Figure 2.4 – Example of cast-in-place RCS system that replaces steel erection columns with stiffened reinforcing bar cages. (Shimizu Corporation)

64

Steel Beam

Reinforced Concrete Column

Steel Band Plate

Face BearingPlate

Longitudinal Reinforcement

Stiffener

Joint Ties

Figure 2.5– Connection between steel beam and reinforced concrete column

Figure 2.6 – Schematic diagrams of RCS joint details tested.

65

Figure 2.7– Typical failure modes in RCS beam-column joints (Kanno et al. 2000).

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1-500

-400

-300

-200

-100

0

100

200

300

400

500

Drift Angle (rad)

Bea

m S

hear

(kN

)

Kanno 1993OJB3-0

Figure 2.8 – Typical hysteretic response of a RCS beam-column test failing in joint

bearing failure (Kanno 1993).

concrete crushing

gap

steel web yielding

concrete strut crushing

66

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1-150

-100

-50

0

50

100

150

Drift Angle (rad)

Bea

m S

hear

(kN

)

Kanno 1993OJS2-0

Figure 2.9 – Typical hysteretic response of RCS beam-column test failing in joint shear

(Kanno 1993).

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-250

-200

-150

-100

-50

0

50

100

150

200

250

Drift Angle (rad)

Bea

m S

hear

(kN

)

Kanno 1993OB1-1

Figure 2.10– Typical hysteretic response of RCS beam-column test failing in beam

hinging (Kanno 1993).

67

Reinforcing BarsTransverse Ties

Steel BeamsRC Section

Figure 2.11 – Typical configuration of reinforcement bars in RC columns.

(a) (b) Figure 2.12 – (a) Illustration showing the separation of int./ext. columns for the SCWB criterion and (b) the appropriate load factors with respect to the P-M column curve in

order to obtain the lowest flexural strength.

, ,p col p beamM M≥∑ ∑

EQ Loads

Pbal

Moment

Axial

Figure 2.13– SEOAC Blue Book strong-column weak-beam provisions.

1.2D+0.5L+1.0E

0.9D+1.0E

Mp,col Mp,beam

Min. Flexural Strength

SCWB Interior

SCWB Ext SCWB Ext Min. Flex. Strength

68

ColumnTop Sleeve

High StrengthMortar

Flow In

Flow Out

Flow Out

Flow Out

Rein. Bar

Column

ColumnTop Sleeve

High StrengthMortar

Rein. Bar

Flow In

Flow Out

Flow Out

Flow Out

Column

Figure 2.14 – Details of grouted splice connections for precast RC columns.

Figure 2.15 – Differences between the definitions of effective slab width considering

lateral versus gravity loading.

P/2 P/2

P

(P,M,V)C1

(P,M,V)B1

(P,M,V)B2

(P,M,V)C2

Slab stress concentrated over column width bcol beff

A

A

A

A

Simply supported beam: gravity mid-span condition

Lateral loading: sway condition

M-

M+

M+

69

Flange Plates

Figure 2.16 – Schematic of a typical bolted flange plate beam splice connection

(a)

(b)

(c)

Figure 2.17 – Assumed beam moment diagram from the lateral and gravity loads with respect to beam splice location.

Shear Tab

1.1RyMp+

Gravity + lateral moment diagram

1.1RyMp-

1.1RyMp-

Lb, clear - db

1.1RyMp+

Lateral load moment diagram RC Column

xsplice

hcol

db/2

Theoretical center of hinge

db/2

Gravity load moment diagram

70

xsplice

xsplice-db/2

db

db

Figure 2.18 – Assumed region of severe hinging and location of beam splice.

Figure 2.19 – Cross-section of the beam splice plates and the concrete slab depicting the

force couple between the lower plates and slab.

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 11

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Location of PNA from Bottom (%db)

Mp,

Com

p/Mp,

Ste

el

W21-W44 BeamsSteel Deck (3 in)Slab Depth (3 in)Slab Width (60 in)1.1*R

y*F

y (60.5 ksi)

0.85f'c (3.4 ksi)

Figure 2.20 – Plot of the location of the plastic neutral axis versus the ratio of composite to steel beam strength, 76mm deck and slab. (1in = 25.4mm)

neglected

dslab

ddeck

Cslab = Fplates

Fplates = AplatesFy

71

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

0.2

0.4

0.6

0.8

1

1.2

Distortion (rad)

Nor

mal

ized

Joi

nt L

oad

(0.0015, 0.3)

(0.008, 0.7)

(0.023, 0.95)(0.045, 1)

Total Joint DistortionVertical Bearing DistortionPanel Shear Distortion

Figure 2.21 – Normalized load versus joint distortion response

(Parra-Montesinos et al., 2001)

Figure 2.22 – Joint detail showing the band plate, cover plate, and the transverse beam.

Steel Beam

Reinforced Concrete Column

Steel Band Plate

Face Bearing Plate

Transverse Beam

Cover Plate

72

(a) Steel column

(b) E-FBP

(c) Steel band plate

Figure 2.23 – Definition of outer strut width

hc

bo/2

y

x = hc

bc

bo/2

3 1

bc

dscol

y = bscol bf

bo/2

3 1 bo/2

x

bo/2 6tbp

bc

bo/2 6tbp

73

750 mm

750

mm

W 250 X 49 16-35 mm bars

250 mm

202

mm

266

mm

Figure 2.24 – Joint design example.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Vb

c/Vb

e

KA

NN

O O

JS1-

1

KA

NN

O 0

JS2-

0

KA

NN

O O

JS3-

0

KA

NN

O O

JS4-

1

KA

NN

O O

JS5-

0

KA

NN

O O

JS6-

0

KA

NN

O 0

JS7-

0

KA

NN

O H

JS1-

0

KA

NN

O H

JS2-

0

DE

IER

LEIN

10

DE

IER

LEIN

11

DE

IER

LEIN

13

DE

IER

LEIN

15

DE

IER

LEIN

17

SH

EIK

H 4

SH

EIK

H 5

SH

EIK

H 7

SH

EIK

H 8

PA

RR

A 1

PA

RR

A 6

PA

RR

A 9

Joint Panel Shear Failure

Mean = 0.96COV = 0.138

ASCEUpdated

Figure 2.25 – Predicted versus measured joint shear strength for both ASCE and Updated model

74

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Vb

c/Vb

e

KA

NN

O O

JB1-

0

KA

NN

O O

JB4-

0

KA

NN

O O

JB5-

0

KA

NN

O O

JB6-

1

SH

EIK

H 2

SH

EIK

H 6

Joint Bearing Failure

Mean = 0.92COV = 0.08

ASCEUpdated

Figure 2.26 – Predicted versus measured joint bearing strength for both ASCE and

Updated model

20 25 30 35 40 451

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Depth of Beam (in)

Pla

stic

Str

engt

h of

Com

posi

te B

eam

(%

Mp

,ste

el) W21-W44 Beams

Steel Deck (3 in)Slab Depth (2.5 in)

Column Width (30 in)1.1*R

y*F

y (60.5 ksi)

1.3f'c (5.2 ksi)

Figure 2.27 – Ratio of the composite to the bare steel beam strength for typical W-section beams (1in = 25.4mm, 1ksi = 6.89MPa).

75

Chapter 3: Full-Scale Composite RCS Test Frame

This chapter reviews the background, preparation and design, and execution and results

of a full-scale pseudo-dynamic and quasi-static test of a 3-story composite RCS frame.

This testing program is a collaborative project between researchers at the National Center

for Research on Earthquake Engineering (Dr. Keh-Chyuan Tsai, Chui-Hsin Chen, and

Wen-Chi Lai) and Stanford University (the author and Dr. Greg Deierlein).

Only the relevant information from the testing program that are later used to draw

conclusions in this and in other chapters of this thesis are presented herein. This testing

program is discussed in a more detailed manner in Cordova et al (2006), which reviews

more of the intricacies of the test design, setup, instrumentation, and a more complete

discussion of the results. There are several aspects of the frame test, including the

preliminary analyses, selection of loading events, introduction of loads, etc., which are

discussed in Cordova et al. (2006) but are either condensed or removed in this chapter.

3.1 Background

Near the latter part of the US-Japan Cooperative Earthquake Engineering Research

Program on Composite and Hybrid Structures, it was widely acknowledged that testing

work and design implications studies on full structural systems needed to be undertaken

in order to validate the knowledge that had been gained through the program. This would

also provided the platform to study the 3-dimensional, indeterminate aspects of complete

structure behavior and also allow the investigation of many practical aspects of composite

structures, such as economy and constructability. In the past, there have been a number

of full or near full scale structural tests (Foutch et al 1988, Roeder et al 1988, Lee and Lu,

1990, Atkan and Bertero, 1987, Liang and Ding, 1995) and each of these have uncovered

many nuances and provided a number of insights about the structural system (i.e.

unexpected failures, additional strength capacity, etc.) that could not have been found

through simple subassembly tests.

76

In 2001, researchers from the National Center for Research in Earthquake Engineering

(NCREE) in Taipei, Taiwan and Stanford University began collaboration on developing

the plans for a full-scale composite RCS moment frame to be tested in the NCREE

laboratory. The test specimen is a three-story, three-bay composite RCS moment frame,

consisting of reinforced concrete (RC) columns and composite steel (S) beams.

Measuring 12 meters tall and 21 meters long, the frame is among the largest frame tests

of its type ever conducted.

The three-story prototype structure is designed for a highly seismic location either in

California or Taiwan, following the provisions for composite structures in the

International Building Code 2000. The frame is loaded pseudo-dynamically using input

ground motions from the 1999 Chi-Chi and 1989 Loma Prieta earthquakes, scaled to

represent 50%, 10%, and 2% in 50years seismic hazard levels. Following the pseudo-

dynamic tests, quasi-static loads are applied to push the frame to interstory story drifts up

to 10 percent, which provides valuable data to validate simulation models for large

deformation response.

The test has three primary objectives. First, it provides data to evaluate and validate

design provisions for composite moment frames. Particular topics of investigation

include strong-column weak-beam criterion, composite action of concrete slab and steel

beams, integrity of the pre-cast column and composite beam-column connections, and

overall frame response. Second, the test provides valuable information to validate models

and computer codes for nonlinear simulation and performance assessment. Finally, the

full-scale test provides validation to support the use of innovative composite moment

frames as alternatives to conventional steel and concrete systems for high-seismic

regions. Apart from these direct benefits, the frame provides the impetus to explore

international collaboration and data archiving envisioned for the NEES initiative.

77

3.2 Rationale for Full-Scale RCS Frame Test

As mentioned in Chapter 2, the concept for the RCS moment frame system has been

around in some form for nearly thirty years. A majority of its implementation in the

United States has been limited to high-rise buildings in low seismic regions. Engineers

are quick to take advantage of the many benefits of composite framing in high-rise

applications, which range from optimal material usage to expediting construction time

with innovative staging or precast techniques. Unfortunately, its use in high seismic

zones has been limited in the United States despite the fact this system is widely

implemented in Japan. There has been research (Kanno 1993, Mehanny 2000, Liang et

al. 2004) that has shown RCS systems to be equivalent, if not superior, to the seismic

behavior of all-steel moment frames. As discussed in Chapter 2, the seismic design

provisions are currently available to implement a code-based design of an RCS moment

frame. It is believed that a full-scale test has the potential to be a “proof of concept” for

this structural system. The design, construction, and ultimately the testing and

performance of this frame should be viewed as a complete example of this system from

start to finish. It is hoped that with this testing program, a majority of the issues

concerning this system can be resolved in some way to ensure that the engineering

community will be able to accept this innovative system as a viable alternative to the

conventional steel or concrete moment frames.

Table 3.1 lists some of the issues that that are investigated within this testing program, as

well as those that are neglected. These issues will be further developed and discussed

throughout this remainder of this Chapter (and also in Chapter 4). Obviously this is not

an exhaustive list, and hopefully this will continue to grow as researchers re-examine this

data in the future.

3.3 Design of Full-Scale Test Frame

The loading and design of this test frame is meant to be as realistic as possible to ensure

that the experiment produces meaningful data that can be applied to real world structures.

This achievement of realism must also be balanced with laboratory limitations and

78

constraints, some of which include the available lab space, actuator capacities, and

funding. With this in mind, this section presents the general overview of the design of

the test structure. In addition to this, some of the important design parameters and their

impact of the behavior of the frame are discussed in further detail. Refer to Cordova et

al. (2006) for further information on the design of this test frame.

3.3.1 Plan and Layout of Test Frame

The size of the test frame is restricted by the 15-meter tall strong wall, the 1-meter

spacing of the tie-down holes on the strong floor, and general space limitations due to

other experiments in the NCREE lab. Based on these considerations, the overall plan and

profile is based on a typical rectangular 3-story office building with a 6 by 4 grid of 7-

meter bays and 4-meter story heights. Two of the seven short direction frames are

considered in the lateral resisting system, with the rest acting only as gravity resisting

frames. The plan and location of the RCS moment frames are shown in Fig. 3.1. The

lateral load resisting frames were configured as interior moment frames in order to

provide a symmetric frame (i.e. when the slab is equal on each side of the frame).

The test specimen, shown in Fig. 3.2, is a three-story, three-bay frame meant to represent

one of the two RCS frames within this theoretical plan. In order to capture the composite

slab effect in the behavior, a 2150mm wide slab is integrated with the floor beams on

each level of the frame. To help support this slab as well as provide restraint for the main

beam against lateral torsional buckling, transverse beams are provided at the third points

along the span of the beams. Loading beams are provided at the north end of the frame

and along each edge (east and west) of the slab. The force transfer mechanism between

the actuators and the frame is described in detail in Section 3.4.1.

79

3.3.2 General Design Information

The test frame is designed for a highly seismic region in either California or Taiwan,

following the provisions for composite structures previously outlined in Chapter 2 1 .

Seismic design forces are based on mapped spectral accelerations of Ss = 1.5g and S1 =

0.72g. The soil condition at the building site is assumed to be that of site class D (Fa =

1.0), while the building itself is assigned a Seismic Use Group I and a Seismic Design

Category D according to IBC/ASCE 7-02. The SAP2000 model of the frame calculated

the fundamental period to be 1.0 seconds, while the code-defined period is only 0.47

seconds, with an upper period cap of 0.56 seconds2. Given this information, the design

base shear coefficient defined in equation (2.1), including the additional shear to account

for accidental torsion, is computed to be 0.13V W = , which equates to a required design

base shear of 1160kN. A summary of the design loading, including the dead and live

loads for a typical office building, is presented in Table 3.2.

The frame was intentionally designed to the minimum limits of the building code so as to

represent the minimum expected performance and to interrogate system design

parameters. This approach was also necessary to ensure that the strength of the frame did

not exceed the capabilities of the laboratory. As Taiwan’s seismic design codes adopt

similar requirements to those in the United States, the frame is equally representative of

design standards in both countries. Composite beams were sized based on strength

requirements in negative bending (1.2DL+0.5LL+1.0E), while the reinforced concrete

columns were controlled by the strong-column weak-beam (SCWB) criterion specified in

Equation (2.47). This SCWB criterion was one of the key design parameters in the frame

1 Given that the test specimen was designed during the years of 2001 and 2002, the prevailing building code was the IBC 2000, which referenced the 1997 AISC Seismic Provisions, ACI 318-99, and the AISC-LRFD (1997). It can be verified that the more current design provisions (i.e. IBC 2003, etc.), as discussed in Chapter 2, would result in a nearly identical frame considering that the changes to the codes that apply to this design have been relatively minor. Therefore, unless otherwise noted, the reader is to assume that the applicable design provisions are those specified in Chapter 2. 2 The approximate fundamental period equation changed slightly from IBC 2000 to 2003, but this did not factor into the final design forces since both periods were in the constant acceleration segment of the design spectra.

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and will be discussed further in Section 3.3.3. The drift criterion from the ASCE 7-02,

specified in equation (2.4), is automatically satisfied and did not require any resizing of

the beams or columns. The final member sizes are presented in Table 3.3. It should be

mentioned here that the 1st floor beam was originally sized to be 596x199x10x15mm, but

given its lack of availability during construction, a larger beam was substituted

(600x200x11x17mm), which increased the moment capacity of the beam by

approximately 15.5%. This change will have implications in both the SCWB ratios and

the design of the beam splices.

The 1st and 2nd-floor composite joints were designed based on the 1994 ASCE Joint

Guidelines, with some modifications from the work of Kanno (2000) to account for some

of the details not considered in the older guidelines. The joints were designed to develop

the nominal moment in the adjacent composite beams following the strong-joint weak-

beam criterion of the AISC Seismic Provisions (2005). Joint details include face bearing

plates, a steel band plate above and below the beam, and transverse beams. Since space

frames are more common in Japan and Taiwan, it was decided to incorporate a transverse

beam into the joints to simulate space frame conditions. This detail provides additional

concrete confinement within the joint region and increases the strength and stiffness of

this connection (Kanno 1994). Based on subassembly tests prior to the testing of the full-

scale frame (Cheng 2002, Cordova et al. 2006), it was decided to construct the joint

without complete hoops and simply provide small ties for longitudinal bar support

through the joint, as shown in Fig. 3.3. These ties were considered to be sufficiently

anchored into the concrete that is confined by the beams and face bearing plates. Note

that these ties are not considered effective in resisting joint shear. The design of the 3rd-

floor joints required special details to anchor the longitudinal column bars, as will be

discussed in Section 3.3.7.

3.3.3 Strong-Column Weak-Beam

An important design provision, which often controls the column sizes in special moment

frames, is the strong-column weak-beam (SCWB) criterion. As discussed in Chapter 2,

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the nominal column to beam strength ratio is generally assumed to be approximately 1.2

(ACI 318-02, ASCI Seismic Provisions 2005). Since the intent of the frame test was to

push the limits of current code provisions, we took a liberal interpretation of the SCWB

criterion with respect to whether the calculation is made using properties of the steel or

composite beam for the SCWB check. Differences can be significant, since the

difference in nominal strengths between the steel and composite beam assumption is

about 30%. The calculated strength ratios using the expected steel beam strengths

(1.1RyMp= 1.21Mp) to the nominal strengths of the columns all equal or exceed the

specified ratio of 1.0 (≥1.0 passes SCWB criterion), as shown in Fig. 3.4a. However,

when calculated based on composite beam strengths according to equation (2.47), several

of the joints (shown in dashed boxes) violate the 1.0 limit (Fig. 3.4b). The values shown

in Fig. 3.4b are based on the assumption that beams flexed in positive bending will act

compositely and those in negative bending will act as bare steel beams. Note that the 1st

floor interior joint ratios are approximately 15% below the required SCWB ratio, which

stems from the substitution of the original 596x199x10x15mm to the 600x200x11x17mm

beam during construction, previously discussed in Section 3.3.2. This last minute change

in beam size has the potential to greatly impact the behavior of the frame, but fortunately,

the measured properties of the beam and column helped mitigate this problem. Figure

3.4c summarizes the SCWB checks based on composite beam behavior using measured,

as opposed to nominal, material strengths of the beams (RyFy,nom = Fy,meas) and columns

( and Fy,rebar,meas). Being as the main intent of the SCWB criterion is to avoid story

mechanisms, the fact that one joint in a story violates the criterion is not necessarily

detrimental to the frame behavior. For example, one could interpret the values for the

first and second floors in Fig. 1b as meeting the intent of the SCWB criterion, since the

average ratio for each of these floors exceeds 1.0. However, as will be seen later, the

SCWB ratios alone do not provide an accurate gage of where inelastic deformations will

occur under earthquakes.

',c Measf

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3.3.4 Measured Material Strengths

The material properties of the beam and reinforcement steel were measured prior to the

frame test. The results of these tensile tests are shown in Table 3.4. It was surprising to

learn of the high amount of overstrength in the steel beams, especially in the 2nd floor,

which was found to be 40-50% higher than nominal properties. The 1997 AISC Seismic

Provisions specifies that the expected yield strength of grade A50 steel should be

assumed as RyFy, or 1.1Fy. This expected yield strength was obviously exceeded in all of

the steel beams, which is undesirable considering that we are attempting to control the

failure mechanism of the frame through the SCWB criterion.

The measured strengths of the concrete cylinders were obtained on the first day of testing,

the results of which are shown in Table 3.5. Again, the measured strength properties are

much greater than the nominal concrete properties, with an average increase in strength

of 67% for the columns above the splice at the 1st floor. The 1-meter column stubs below

this splice turned out to have a measured strength approximately 115% higher than the

nominal. Given the low axial load in these RC columns, the strength of these members is

largely controlled by the reinforcement bars. Therefore, these large differences in

nominal to measured concrete strength only resulted in approximately a 10% increase in

the moment capacity.

While some material overstrengths were anticipated in the design (e.g. 10-25% in steel),

the large differences discussed here were not expected. Fortunately, the balance between

the column and beam strengths remained roughly intact and the SCWB ratios were not

severely affected, as reviewed in section 3.3.3.

3.3.5 Beam and Column Splices

Given the popularity of the precast RCS construction in Taiwan and Japan, this method

was chosen for the erection of the test specimen. In discussion with industry engineers

and contractors in the United States, the precast method garnered the most interest based

on the ability to prefabricate these elements and expedite the construction process. This

83

method of construction requires splices in both the steel beams and the RC columns. In

the test specimen, the steel beams are spliced 1500 mm away from the face of the

column. As discussed in Chapter 2, this location is a compromise between competing

desires to minimize the offset for ease of construction (fabrication and shipping of the

precast column-beam assemblies) and maximizing the offset so as to reduce the design

moment for the splice. In Chapter 2, it is recommended that the beam splice be designed

to develop the expected plastic moment of the steel section (1.1 y pR M ); however, the

method implemented in the test frame was slightly different. The beam splice was

originally designed based on requirements interpreted from the FEMA 350 design of

bolted flange plate moment connections. FEMA 350 requires that the flange plate is able

to develop the expected yield moment of the beam at the column face

( ), which means that yielding is expected in the flange plates

and is part of the preferred mechanism. The reason for the difference in the design

philosophy from Chapter 2 is really due to the fact that the appropriate design

methodology of the beam splices was still being considered at the time and the frame test

provided a means to test out an alternative design option.

SFSFRM yyyyf )1.1(==

In accordance with U.S. construction practice and the AISC Seismic Provisions, the

connection is proportioned based on bearing strength of the bolts, as opposed to slip

critical values. As will be discussed later in this Chapter, this design practice resulted in

slipping of the bolts during all of the pseudo-dynamic tests. The main consequence of the

slipping was loud bolt banging during the test; otherwise, the bolt slippage did not have

any appreciable effect on the overall frame behavior. Figure 3.5 shows a typical detail of

one of these bolted beam splices. Unfortunately, the last minute resizing of the 1st floor

beams was not accounted for in the design of the beam splice, and as a result this

imposed particularly high demands on the splice plates. As discussed later, this led to

rupture of the 1st floor connection splice plates during the final pushover test of the frame.

Precast column splices are located 1-meter above the foundation footing and directly

above the connection band plates (at the top of slab) at floors one and two. The influence

of the splice location on performance at the column base was examined through

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subassembly tests, conducted prior to the frame study (Cheng 2002, Chen 2002, Cordova

et al. 2006). Two splice locations were investigated in these tests – the first was flush

against the column-footing interface (Fig. 3.6a) and the second was 1-meter up the height

of the column (Fig. 3.6b). Both tests showed that the precast connection could develop

and maintain the full column strength through large inelastic deformations (Fig. 3.7a),

although the specimen with the splice adjacent to the footing experienced more strength

degradation at high drifts (Fig. 3.7b). In the end, due to the critical nature of the 1st floor

column hinges, it was decided to place the splice at the 1-meter location. The splice

location for 2nd and 3rd floor columns is less critical because analysis studies have shown

that severe column hinging is not likely to occur above the floor beam – except in

instances where the SCWB criterion is not met and a severe story mechanism could

occur. Since it is common practice in Japan to splice the column right above the floor,

and since the intent of the frame test was to investigate the limits of performance relative

to standard practice, it was decided to locate the grouted splices directly above the beam-

column joints.

3.3.6 Shear Studs in Hinge Region

The AISC Seismic provisions and FEMA 350 does not permit the placement of shear

studs within the expected plastic beam hinge region, which is assumed to extend from the

column face to one-half beam depth away from the column. The concern is that the shear

studs will lead to strain localization and premature beam flange fracture during plastic

hinging. During construction of the test frame, the contractor inadvertently placed shear

studs within the hinge region of the 2nd and 3rd-floor beams. This construction mistake

was noted at the time, but it was decided against trying to remove the studs due to

concerns about further damaging the beam flange. As it turned out, the studs in these

regions did not lead to any detrimental behavior of the hinge, which is largely due to the

fact that the upper flange was protected against large inelastic action due to the presence

of the composite slab (i.e. shift of the neutral axis resulted in less strains in the upper

flange).

85

3.3.7 Roof Joints

The 1994 ASCE Joint Recommendations do not provide explicit guidance for designing

the roof joint connection (i.e. where the column does not extend above the joint).

Therefore, it was necessary to develop and evaluate a unique detail for this condition to

ensure adequate force transfer from the beam to the column. Three alternative joint

details were proposed and investigated through subassembly tests conducted prior to the

frame test (Tsai et al., 2002). The design that was selected, shown in Fig. 3.8, employs a

steel cap plate on top of the column to provide anchorage for the longitudinal reinforcing

bars and bearing force for the steel beam. To make the assembly of this joint easier, the

contractor preferred to extend the cap plate to cover the entire top face of the column.

The longitudinal reinforcement bars are plug welded to this bearing plate, as shown in

Figs. 3.9 through 3.11. This joint is assumed to be able to provide the full amount of

bearing resistance similar to that of a typical interior joint. As described later, like all the

joints in the frame, these top details worked very well and were able to develop beam

hinging adjacent to the column with only minimal damage in the joint region.

3.4 Description of Test

3.4.1 Test Setup

Three 1000kN-capacity actuators with a stroke limit of ±500mm are provided at each

floor and are connected to the transverse loading beam as shown in Fig. 3.2. The purpose

of the transverse loading beam is to distribute the load from the actuators equally to both

the longitudinal loading beams. The longitudinal loading beams are cast integrally with

the slab and connected via shear studs interwoven with spiral hoop reinforcement. These

studs and reinforcement help transfer the load from the loading beam into the slab. The

assumption here is that the load transfer from the loading beams to the slab occurs at a

relatively uniform distribution along the entire length of the frame. This was ultimately

proved a valid assumption based on strain measurements in the loading beams during the

test (Cordova et al. 2006). Figure 3.12 depicts the probable load path between the

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loading beams and the moment frame. When a load is applied to the loading beams the

force enters the slab and is distributed to the frame through two main load paths. The

first path requires development of a compression strut between the columns and the

loading beams. This path is mobilized through direct bearing of the column face,

compression of the slab and reinforcement, and the shear force transferred by the loading

beam studs. The second path develops a compression field through the slab between the

main beam shear studs and the loading beam shear studs. Both of these loading paths are

shown in Fig. 3.12.

An interesting result of the load transfer from the slab into the frame is the fact that it

alleviates the axial stresses induced in the slab due to positive and negative composite

bending moments. When the beams are in positive bending (i.e. in composite action) the

load transfer stresses tend to pull the slab away from the column while the opposite is

true when the beam is in negative bending. This mechanism is thought to represent the

conditions present in real world structures given that we are simulating a realistic load

path by imposing loads directly into the slab. The implications of this behavior will be

discussed later with the results of the frame test.

3.4.2 Loading Protocol

Extensive nonlinear static and dynamic time-history analyses were performed using the

analysis program OpenSees (McKenna et al. 1999) prior to testing. These analyses were

used to select suitable records from a suite of ground motions and predict the ultimate

lateral strength and the inelastic demands imposed on the frame specimen under the

simulated earthquake effects. The main focus of these studies was to predict the possible

peak responses of the frame during the test while verifying that both the force and stroke

limitations of the actuators were not exceeded. These analyses are similar to the post-

testing analyses presented in Chapter 4 and will not be presented here. For further

information on these analyses and the procedure to select the records, please refer to

Cordova (2006).

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Ultimately, two earthquake records, TCU082-EW and LP89G04-NS, were chosen from

bins of the 1999 Chi-Chi and 1989 Loma Prieta earthquake records, respectively. The

analytical model predicted that the peak responses from these events would be within the

limitation of the actuators and suggested that the hinging was fairly well distributed in the

frame.

Using the pseudo-dynamic loading methodology described in Cordova (2006), these

records are inputted as a series of four earthquake loading events, which are defined as

follows:

1. 50% chance of exceeding in 50 years (50/50) using the 1999 Chi-Chi (TCU082)

record ( ( )1aS T =0.408g): “Immediate occupancy or service event”

2. 10/50 1989 Loma Prieta (LP89G04) event ( ( )1aS T =0.68g): “Design level event”

3. 2/50 TCU082 event ( ( )1aS T =0.92g): “Maximum considered event”

4. Repeat of the 10/50 LP89G04. ( ( )1aS T =0.68g)

The scaled response spectrums for these events are shown in Fig. 3.13. Following the

four earthquakes, a final static pushover using a triangular loading pattern is applied to a

maximum roof drift ratio of 8%.

For the pseudo-dynamic loadings, the records are scaled based on the spectral

acceleration at the first mode period of the building to represent the range of different

hazard levels. The natural period of the frame is determined by assuming cracked

stiffnesses of RC columns and composite beams and realistic joint size and stiffness.

This period was later validated in the test frame by using the actuators to determine the

stiffness matrix via the flexibility method. One important distinction to make here is that

these hazard levels reflect a highly seismic Taiwanese site. The 10/50 event

(Sa(T1)=0.68g) matches that of the US site, but the 2/50 Taiwan event (Sa(T1)=0.92g) is

slightly less intense and corresponds to approximately a 4/50 hazard level for the US site.

This is apparent from the differences between the 2/50 IBC2000 hazard curve and the

2/50 TCU082 response spectrum curve in Fig. 3.13 at a period of 1 second. The seismic

mass used in the pseudo-dynamic algorithm is consistent with that used in the design, as

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are the gravity loads (1.0DL+0.25LL, approximately 3500kN at each floor) included into

the geometric stiffness (P-Δ) effects.

3.5 Construction of Test Frame

In addition to gaining insight into the performance of these composite RCS frames, the

frame test provided the opportunity to investigate the constructability issues regarding

these innovative systems. As mentioned before, the test frame was detailed and built in

the precast method of construction in conformance with standard industry practice. The

strength and durability of these precast spliced connections are issues that have not been

widely investigated for RCS systems prior to this testing program.

At the precast fabrication plant, single story precast column assemblies were integrally

cast with steel beam stubs to create a beam-column module that can be seen in Fig. 3.14a.

This process was optimized and repeated to generate the beam-column modules for the

entire frame. The beam stubs are pre-drilled and fabricated to accommodate the bolted

splice connections to connect to the central beam spans. The lower region of the precast

column is outfitted with standard mechanical couplers for the grouted splice connections.

The upper region contains the embedded steel beam as well as the face bearing plates,

band plates, and gravity beam as shown in Fig. 2.22. Longitudinal reinforcing bars

protrude beyond the top of the column to allow for the grouted connection of the upper

column. The foundation-column stub assemblies were prefabricated in the same manner.

To begin the construction process, the foundation-column assemblies were first placed

and tied down to the strong floor. This then allowed the workers to begin to build up the

test specimen floor by floor. The beam-column modules were shipped to NCREE and

assembled in the following process:

1. Beam-column modules are fitted into the lower columns (or footings) and

propped up with lateral bracing.

2. The center spans of the steel beams are placed between the beam-column trees,

and the beam splices are bolted into place.

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3. The longitudinal loading beams are erected along the length of the frame and

attached to the embedded transverse beams protruding from the concrete columns.

The transverse loading beam is also attached to the northern end of frame between

the actuators and the east and west loading beams.

4. Transverse steel beams are then placed at the third points between the main span

beam and the bottom of the loading beam.

5. The story is plumbed to construction tolerances and steel bolts are tightened and

RC columns splices are grouted into place.

6. The steel deck is laid out and tack welded to the beams.

This process was repeated until all three floors were completed, with each floor requiring

about 2 days worth of work. Figure 3.14b is a photo of the finished first floor. Once the

3-story, 3-bay bare frame was constructed, workers attached the shear studs to the floor

beams, laid out the wire mesh reinforcement, and then poured the slab. The entire

specimen was constructed in the NCREE lab within two weeks from the positioning of

the precast footings to pouring of concrete slabs. A more complete photo documentation

of the construction process can be found in Cordova et al. (2006).

3.6 Test Results

The NCREE RCS frame test was conducted in October of 2002 and was witnessed by

about thirty researchers from the US, Taiwan, and Japan. Testing was broadcasted live

via the Internet (http://rcs.ncree.gov.tw), including real-time data plots and live video.

The response of the frame was monitored and documented with over 300 data channels,

visual inspections, and photographic images. Instrumentation was set up to measure the

hinge rotations in the RC columns and composite beams, composite joint rotations, slab

rebar strain, slip and lift off between slab and steel beam, elastic strains in beams, footing

slip, interstory drifts, and axial strain in the loading beams. A detailed description of the

instrumentation plan is withheld here and the reader is referred to Cordova et al. (2006)

for information regarding this matter of the test frame. The following subsections

summarize some of the key observations and data that have emerged from this testing

program that have direct applications to the performance assessment and seismic design

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of composite RCS frames.

3.6.1 Global Results

The roof displacement histories for each of the pseudo-dynamic events are shown in Figs.

3.15 through 3.18. Maximum and minimum interstory drift ratios and story shears are

plotted for each earthquake in Figs. 3.19 and 3.20, respectively. During the 50/50

TCU082 event the roof experienced a maximum displacement of about 200mm, with

fairly uniform interstory drift values that ranged from 1.5 to 2.0%. A maximum base

shear of about 3000kN occurred during this event, which is about 2.6 times that of the

design value (1160kN). Residual drifts after this event were negligible. System

identification of the recorded time history show that the fundamental vibration period

elongated from its initial value of 1 second to 1.3 seconds after the 50/50 event,

indicating that the effective stiffness reduced to 60% of its initial value. This period shift

can be easily seen by comparing the elapsed time between displacement peaks in the

beginning and the end of the record in Fig. 3.15.

As can be seen in Fig. 3.16, the first design level event (10/50 LP89G04-1) had to be

stopped at about 7 seconds into the record and then restarted from the beginning. The

first segment of this event produced much larger excursions than the 50/50 event, and

began to cause hinging at the 1st-floor column bases. The frame initially has very little

stiffness in the transverse direction and the development of these hinges resulted in

further reduction of this stiffness. The external steel braced frame is designed to support

the RCS frame in the transverse direction, but a problem occurred during the setup of this

frame that did not permit a fully fixed connection to the strong floor. Therefore, when the

RCS frame required the support of the external frame during this event, the external

frame rocked sideways (in the transverse direction), causing out-of-plane moments at the

base of the RCS columns. This led to out-of-plane hinging and damage of these columns.

Ultimately, the frame rocked out to 1.5% roof drift in the transverse direction before the

external frame provided adequate restraint. Given that the frame had already experienced

the major excursions of the 10/50 event, it was decided to rerun the same event scaled to

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80% of the original intensity. We felt that together, these two events would adequately

represent the intensity and damage of the original 10/50 (design level) event, had it been

run through without incident. Given this assumption, the maximum roof displacement

that occurred during this design level event was about 300mm, with maximum interstory

drifts ranging from 1.5% to 3.0%. The base shear was approximately 3800kN, which is

about 3.3 times larger than the design level event. The residual roof drift after this event

was approximately 0.3%. System identification on the response shows that the period

further elongated to approximately 1.5 seconds during the 10/50 event, indicating that the

frame was now at approximately 45% of its initial stiffness.

Under the maximum considered earthquake (2/50) the frame experienced a maximum

roof displacement of 500mm at about 28 seconds into the record. This displacement

exhausted the maximum stroke of the actuators at the roof, so that loading could not be

continued beyond this point. Examination of the pseudo-velocities and accelerations of

the frame at this time step suggested that the frame had reached its maximum drift and

was beginning to reverse direction. Analytical simulations showed that this was the

maximum excursion of the event and that subsequent cycles were smaller. Given these

observations, it was decided that this event did indeed represent a maximum considered

event (2/50) even though it was subjected to only 28 of the full 45 seconds of the event.

Deformations began to concentrate in the first two stories in this event, with a maximum

IDR of 5.5% occurring in the first floor. The maximum base shear remained about

3800kN, equivalent to the peak value attained in the design level (10/50) event. The

residual roof drift after this event was about 2.7%, with a largest contribution from the

first floor (3.4%). System identification on the response shows that the period elongated

to approximately 1.7 seconds after the 2/50 event, indicating that the frame was now at an

effective stiffness of 35% the initial value.

Given the large amount of residual drift after the 2/50 event, there was concern that the

frame would again hit the maximum actuator stroke during the final 10/50 event.

Therefore the decision was made to straighten the building as much as possible before

continuing with the next loading event. This realignment was accomplished using the

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actuators and reduced the residual roof drift to approximately 0.3%. The final pseudo-

dynamic event was then executed, which involved re-running the 10/50 design level

event. Here the decision was made to repeat the scaled (80%) version of the 10/50 event,

so as to repeat the record used for loading the second segment of Fig. 3.16. Thus, this

event had two purposes. One was to help gage the amount of damage caused by the 2/50

(maximum considered) earthquake. The second was to simulate the possible effects of an

aftershock to the 2/50 event. The maximum roof drift during this record was about

300mm, with interstory drifts remaining within 3%. If the residual deformations are

removed from both the first and second scaled version of the 10/50 event, the transient

response can be directly compared, as is shown for the roof displacement in Fig. 3.21 and

the maximum interstory drifts in Fig. 3.22. Comparison of the roof displacement of the

two events show that the frame responds much differently in the second event given that

the stiffness of the frame has drastically changed from the damage incurred during the

previous events. Despite these differences throughout the time history, the maximum

interstory drift during each of the events was measured as 2.7%, although this occurs in

the 2nd floor in the first event and the 3rd floor in the second. The measured base shear

was considerably lower in this final event than in the previous three, with values peaking

at approximately 2200kN (58% of maximum seen in 2/50 event), presumably due to

softening under the multiple earthquakes. The residual roof drift was about 1.1%.

The final pushover of the frame resulted in a maximum base shear of 3200kN (Fig. 3.23),

which is about 2.8 times that of the design base shear. This reveals that even after

sustaining significant damage through four major earthquakes, the frame still maintained

a very large overstrength value. It was necessary to complete the pushover in two stages

so that the actuators could be readjusted to accommodate the large drifts. This is

apparent in the unloading-reloading sequence that occurs at about 4% drift. During this

test, deformations continued to concentrate in the first and second floors, creating a fairly

pronounced two-story mechanism, characterized by column hinging at the base and

beneath the second floor beams and flexural yielding of the first floor beams. Recall that

the second floor beams were found to have measured yield strengths 40% larger than the

specified minimum strength (484 MPa versus the minimum specified yield strength of

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345 MPa), which led to limited yielding in the second floor beams and hinging in the

columns.

Figure 3.23 also shows the final pushover curve if the P-Δ effects from the gravity loads

(1.0DL+0.25LL) from the tributary area of the moment frame and the interior gravity

resisting columns had been considered. This reduces the maximum base shear by

approximately 30% and also introduces a negative slope to the response curve at about

3.5% drift. Note that this response does not consider the resistance of the interior gravity

resisting frames and other sources of resistance, which would tend to strengthen and

stiffen the realistic response of the building.

3.6.2 Description of Damage

This section will outline some of the typical damage that was observed in the test frame

during each loading event. For the sake of brevity, photos and hysteretic response plots

will only be shown for selective components of the frame. The moment versus rotation

response plots shown in this section are interpreted from tiltmeters located within the

hinging zones of the beam and column components. The rotation in the 1st floor base

column hinges also includes the rotation due to bond slip between the column and the

footing. Joint outer rotation is obtained from pi-gauges on the outer panel, while total

joint rotation is inferred from adjacent tiltmeters in the columns and beams. Given the

indeterminacy of the frame, component forces were inferred from strain gauges in elastic

regions of the beams coupled with assumptions of the inflection point location from the

analytical models. For more complete information on details of the frame response,

derivation of component forces, and instrumentation results please refer to Cordova et al.

(2006).

The hysteretic response plots for selected columns, beams, and joints are shown for the

first four pseudo-dynamic events (50/50, 10/50-1a, 10/50-1b, 2/50) in Figs. 3.24 through

3.41 and will be referred to throughout this section. Corresponding photos of damage

incurred by these components are presented in Figs. 3.43 through 3.60. Photos depicting

94

the damage of components after the final quasi-static pushover are shown in Figs. 3.61-

3.69.

3.6.2.1 EQ#1 – 50% in 50 year

The 50/50 event, which represents the frequent or immediate occupancy event, caused

relatively little damage to the components of the frame. There were very minor hairline

flexural cracks observed in all of the reinforced concrete columns. These cracks were

most noticeable at the 1st floor where they were spaced at 150-200mm over the bottom

1m of the column. Figures 3.24 and 3.42 show a photo and the hysteretic response,

respectively, of an interior 1st floor column hinge (1C3) after this 50/50 event. The ‘+’

mark on Fig. 3.24 represents the estimated plastic moment of the RC section, indicating

the moment at which the base hinges are expected to have reached the yield moment of

the section. These base hinges reach rotations of up to 0.014 radians and begin to show

some small amounts of energy dissipation through hysteretic loops. The rest of the

columns in the frame remain relatively elastic during this event, which is to be expected.

The steel beams in all floors showed very minor yielding in the flanges, with the beams

framing into the exterior joints showing slightly more developed yielding than those into

the interior joints. Figures 3.28 and 3.46 show the photo and hysteretic response,

respectively, of a 1st floor beam framing into an exterior joint (1B1S). All of the

instrumented composite beams responding in a relatively elastic manner to this event,

with hinge rotations reaching a maximum of 0.007 radians in the 1st floor. The composite

slab showed relatively no observable damage after this event.

The interior joints of the first two floors experience the most deformation, with outer

joint distortions reaching approximately 0.4% and total distortion reaching a peak just

shy of 1%. While the estimated shears for these joints are just below their predicted

maximum strengths, there was very little observable damage to the composite joints after

this event, which suggests that these shear values may be overestimated. The hysteretic

response of a 1st floor interior joint (1J3) is shown in Fig. 3.34 with a corresponding

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photo in Fig. 3.54. The remaining joints in the frame experience very little distortion and

remain relatively elastic during this event. Note that the total joint rotation may be

slightly overestimated in all the loading events given that the tiltmeter measurements are

taken from the surrounding beams (on FBP adjacent to joint) and columns (100mm above

and below the joints) and are likely to include some additional rotation from these

elements.

During this loading event, and throughout all subsequent loading events, there was loud

bolt banging associated with slippage of bolts in the beam splices. Aside from the loud

sound, the bolt slippage and banging did not detrimentally affect the frame.

Upon thorough inspection, researchers and engineers witnessing the test agreed that the

frame met the performance target for “immediate occupancy”, where the structural

stability was not compromised and the frame required little, if any, repair.

3.6.2.2 EQ#2 – 10% in 50 year

The 10/50 event, which is considered the design level event, caused moderate damage

throughout the frame. Crack widths near the base of the 1st floor columns opened to

about 2mm and were accompanied by some minor spalling of the cover concrete. Some

of the damage within these columns was caused by the 1.5% out of plane rotation due to

problems with the lateral restraint system. Figure 3.43 shows a photo of a damaged

interior column base (1C3) after segment 1b of the design level event. The hysteretic

response plots for this hinge during events 1a and 1b are shown in Figs. 3.25 and 3.26,

respectively, with hinge rotations reaching as high as 0.037 radians.

Minor cracks appeared in the upper portion of the 2nd floor columns, with crack spacing

between 100-300mm (see Fig. 3.58). In addition to these cracks, there was some minor

spalling below the steel band plates of the 2nd floor joints. Figures 3.39 and 3.40 show

the hysteretic response of a typical 2nd floor interior upper column hinge for both of the

segments of the 10/50 event. This shows that while the deformation demands are not

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nearly as large as the 1st floor column base hinges, there are definite signs of yielding and

dissipation of hysteretic energy.

The steel beams in all floors yielded, although the second floor beams experienced much

less yielding than the other stories. Local buckles appeared in the first and third story

beams in the lower flanges and slightly into the web. The largest buckling distortions at

the flange tips measured up to 15 to 25 mm, which occurred at the first and third floor

beams framing into the exterior joints (i.e. exterior beam hinges). These hinges also

developed much more yielding than the interior framing hinges. The damage in both the

exterior beam hinges (1B1S and 1B3N) in the 1st floor can be seen in Figs. 3.47 and 3.50.

Beam hinge 1B1S reached rotation values of approximately 0.01 radians, with definite

signs of yielding and energy dissipation, as seen in Figs. 3.29 and 3.30. There was also

some slight yielding in the lower flange beam splice plates of the first floor beams (Fig.

3.53).

The design level event continues to push the interior joints in the first two floors to higher

distortions levels, reaching maximum distortions in joint 1J3 (Figs. 3.35 and 3.36) of

0.75% and 1.4% for the outer panel and total joint, respectively. The interior joints

experienced very minor cracking as shown in Figs. 3.57. The third floor joints, as well as

all of the exterior joints, are not pushed quite as far as these two interior joints of the first

two floors. This makes sense in the third floor considering that nearly all of the

deformation was concentrated in the plastification and local buckling of the steel beam

hinges. Similarly, the beams framing into the exterior joints were more susceptible to

local buckles and therefore the deformation was concentrated within this region.

The first and second floor slabs experienced some minor cracking along the length of the

frame, but in general the slab was still very much intact. At this stage, the building was

considered to meet the “life safety” performance target, where the level of damage

required repairs but had not significantly affected the safety of the structure. Repairs to

the structure would likely involve epoxy injection of cracks, patching of spalled concrete,

heat straightening of local flange buckles, and re-plumbing to reduce the residual

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interstory drift.

3.6.2.3 EQ#3 – 2% in 50 year

The 2/50 event, considered the maximum credible event, produced the most significant

damage of all the pseudo-dynamic events. The base of the 1st floor columns experienced

the most severe hinging, with distributed cracks up to 4mm in width and significant

spalling of the cover concrete. In addition, large cracks measuring about 10mm opened

up between the bottom of the column and the footing - presumably due to yield

penetration of the longitudinal bars in the column footing. Figure 3.44 depicts the

damage on the interior 1st floor base column (1C3). The hysteretic response of this hinge

is shown in Fig. 3.27, with maximum rotations reaching 0.06 radians. Measurements

show that the majority of plastic deformation occurs within the first 650mm of the

column height, which is equal to the column depth. The assumption that the plastic hinge

length is equal to the column depth is a common one, and is validated through this data.

During this event, the second floor columns visibly began to experience more

deformation than in the previous events, particularly in the upper hinge zone. The

flexural cracks within these hinges grew to widths of 4mm and were accompanied by

minor spalling just below the beam-column joint, as shown in Fig. 3.59. Plots of the

interior 2nd floor upper hinge (2C3) in Fig. 3.41 are able to pick up this nonlinearity and

show that maximum rotations reached up to 0.02 radians.

First floor beams (1B1S) reached rotations of slightly past 0.06 radians in negative

bending, as shown in Fig. 3.31. This measurement is not completely accurate

considering that there were extreme local buckles occurring at this location (Fig. 3.48),

which may have influenced the tiltmeter readings. These local buckles were more severe

within the exterior beam hinges, concentrating in the bottom flanges and the lower half of

the web, with flange tip distortions up to 70 mm. The first and third floor beams

experienced extensive yielding, with flange yield penetrations reaching as far as 1.25

times the depth of the beam. Again, the second floor beams remained relatively elastic,

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which can most probably be attributed to the large material overstrength in the steel of

this beam.

Measurements show that there was much more nonlinearity occurring in the beams

framing into exterior joints than those into interior joints (a portion of which is likely due

to measurement error given the more severe local buckling in the exterior beam hinge).

For example, compare the response of the exterior hinge in Fig. 3.31 to that of the interior

hinge in Fig. 3.35. This phenomenon was also apparent to the researchers present and is

shown Figs. 3.48 and 3.51 by the large difference in visible damage. This behavior can

be attributed to the difference between the continuity provided at the interior joints (i.e.

continuous slab and beam) versus the truncation of the beam and slab at the end of the

exterior joints. In the interior joint, the beam hinges on each face of the joint work

together to help restrain the rotation of the joint, which reduces the amount of rotation

demand in the beam and mitigates the amount of local buckling that occurs in the hinge

in negative bending. This behavior does not exist in the exterior joints, which allows for

larger local buckling in these beam hinges.

As shown in Fig. 3.37, the interior joints reach outer panel distortions reaching 1% and

total joint distortions measured up to 2.7%. This level of total distortion is too high given

the limited amount of damaged observed in this joint (Fig. 3.56) and may be a result of

problems within the tiltmeters (total joint rotation was inferred from the surrounding

beam and column tiltmeters and may include some rotation from these members as well).

There were some visible cracks within these joints, but nothing to suggest that the

structural integrity these connections had been compromised in any way. While the large

difference between the inner and outer joint panel may be partially due to measurement

errors, this also suggests that the outer panel zone may not be completely mobilized by

the joints details. This is likely a result of the presence of the transverse beams in the

joint that tends to divide the outer joint into two sections thereby reducing the

effectiveness of the outer panel strut. There was very little observable damage in the

remaining joints with measured joint distortions remaining well within 1%.

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The first and second floor slabs experienced some local crushing on the interface of the

slab and the column, as well as cracking, which occurred on all three floors. With

significant local damage and a residual interstory drift of 3.4% (140 mm) in the first story,

the consensus of participants who witnessed the test was that the frame had reached its

“collapse prevention” performance level, implying that the structure would need

significant repairs to restore its strength and stiffness.

3.6.2.4 EQ#4 – 10% in 50 year

The post event inspection for the final design level event revealed little additional

damage beyond that observed after the maximum considered (2/50) event. The column

base hinges at the 1st floor were subjected to several large cycles that resulted in further

deterioration of the concrete, as is apparent in Fig. 3.45. There was a modest level of

shear and flexural cracks up the height of these 1st floor columns with some local spalling

beneath the joint’s steel band plates. The damage patterns within the upper hinges of the

2nd floor columns remained relatively the same as that after the 2/50 event, as depicted in

Fig. 3.60. The spread of plasticity in the steel beams remained within the limits of the

2/50 event, while local buckling continued in the 1st and 3rd floor beams (Fig. 3.49).

These buckles were concentrated in the lower flange and web, and tended to straighten

out once beam was pushed into a positive bending cycle, which can be easily seen by

comparing photos of the beam hinge 1B1S after the 10/50-2 event (Fig. 3.49) to the final

pushover (Fig. 3.68). Figure 3.52 shows the damage in an interior beam hinge (1B1N),

which consists of distributed yielding in the lower flange and up two-thirds the height of

the web. This particular hinge did experience some local buckling, but this had been

straightened out by the end of the event. The composite joints exhibited some cracking,

although this was more severe in the interior connections (Fig. 3.57).

3.6.2.5 Final Pushover

During the final static push the deformations concentrated in the lower two stories of the

frame, with a peak interstory drift ratio of 10% reached in the first story. By the

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conclusion of the test, there was severe hinging at the column bases, with extensive

cracking, spalling, and crushing of the concrete. The concrete was fully deteriorated in

this region and the rebars were primarily acting in dowel action to carry the large amount

of shear transmitted through these columns. Figs. 3.62 and 3.63 show an exterior and

interior base column, respectively.

There was significant yielding and local buckling in the 1st -floor beams (Figs. 3.68 and

3.69) with beam lower flange distortions in the exterior joint reaching approximately 90

mm. The 1st floor slab experienced localized crushing and slight bulging around the

columns (Fig. 3.66). The upper hinges at the second floor columns experienced flexural

cracks up to 8 mm wide and developed a 10mm gap below the joint’s steel band plate.

Figures 3.64 and 3.65 show the damage in an exterior and interior 2nd floor column,

respectively. Yielding and local buckling of the steel beams dominated the behavior in

the 3rd floor, with very little damage occurring in the columns or the composite joints.

The final two-story mechanism is apparent in Fig. 3.61, which shows the frame near its

maximum drift state. The sudden strength drop apparent in Fig. 3.23 at a roof drift ratio

of 6% (corresponding to about 9% interstory drift in the first story) was caused by a net

section rupture in one of the lower beam flange splice plates for one of the 1st floor beam

splices (Fig. 3.67). This first rupture precipitated subsequent ruptures in neighboring

splices, which are evident in the strength drops under continued loading (see Fig. 3.23).

This failure can be traced back to the last minute change in the beam size that was not

accounted for in the beam splice design, which increased the moment capacity of the

beam by 15.5%. Nevertheless, the splice fracture is not considered a serious concern,

given that it only occurred after 10% story drift with significant distortions in the first-

floor framing.

3.6.3 General Observations

The concrete slab performed surprisingly well throughout the entire loading protocol. It

was expected that there would be much more concrete crushing and more severe cracking

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that would compromise the integrity of the slab. Instrumentation confirmed that the slab

did not slip or pull off of the beam, and subsequent dismantling of the slab showed no

evidence of shear stud fracture. This is in stark contrast to many subassembly tests that

have described premature fracturing and shearing of the studs which ultimately leads to

rapid deterioration of composite beam action (Cheng 2002, Civjan 2001, Leon 1998,

Bugeja 2000).

Throughout the test, local buckling of the steel beam was concentrated in the lower beam

flanges and the lower portion of the beam webs. It was evident that the slab provided

considerable restraint to prevent distortions from developing in the upper flanges. The

yielding in the steel beams was most significant in the lower flange where yield

penetration extended out as far as 1.1 and 1.25 times the depth of the beam in the 1st and

3rd floor beams, respectively. Web yielding extended as far as 0.7 to 0.75 times the depth

of the beam near the bottom of the beam and then linearly tapered off up to the upper

flange. The damage in the upper flange was much less than the rest of the section and

showed signs of yielding out to 0.4 times the depth of the beam. The limited damage (i.e.

yielding and local buckling) in the upper flange is largely due to the shift in the neutral

axis due to the contribution of the concrete slab.

It was apparent that the most severe local buckling took place at the beam hinges framing

into the exterior joints. It seems that the continuity of the beam and the slab in the

interior joints provided additional restraint which did not allow the amount of buckling

that was evident at the exterior joints. In addition to this, it was common to see large

buckles form in the beam hinging zones during a negative (steel only) bending excursion,

only to be straightened out later when the earthquake produced an equal positive

(composite) bending excursion. These are particularly interesting issues because they do

not arise within most subassembly tests with steel beams, which points to the

shortcoming associated with proper modeling of boundary conditions in typical isolated

beam-column tests.

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The composite joints behaved very well throughout all phases of the loading protocol.

Even through the final pushover, the composite joints, with standard details, experienced

only minor to moderate cracking and forced hinging to occur in the steel beams.

The RC column base hinges were subjected to significant plastic rotations throughout the

loading history of the test frame. As a result, the concrete within these hinges was

significantly deteriorated to the point that during the final pushover test the rebars were

carrying nearly all the moment and shear. This type of behavior seemed to be a result of a

combination of extensive plastic hinging and progressive shear failure. If the beam

splices had not failed, it is reasonable to state that the test would have been stopped

shortly thereafter due to the severity of damage within the column base hinges.

3.7 Conclusions

3.7.1 General Seismic Performance of RCS Frame

Even when designed to the minimum requirements of current building codes, the RCS

test frame showed excellent seismic behavior under various seismic hazards. Until the

final stages of the static pushover, the behavior and the distribution of damage in the RCS

frame was rather predictable with ductile hinging concentrating in the composite beams

(yielding, local buckling, and slab crushing) and the 1st-floor RC column bases

(distributed cracking, crushing, and spalling). The connections in the test frame has

shown superior ductility through drifts levels that far exceed the requirements of

conforming steel connections as specified by SAC Building Committee (2000).

Although there is not a general consensus on the link between the seismic hazard and

structural performance, there are quite a few documents (IBC 2003, FEMA 273/356) that

specify some broad requirements suggesting that the structure should exceed near-

collapse performance for 2% in 50 year hazard and protect life safety for 10% in 50 year

hazard. More specifically, documents such as FEMA 356 generally describe the

expected damage within particular elements (RC columns, steel beams) after the range of

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seismic hazards investigated in this test program. The overall damage incurred by the

frame after each event, as described in Section 3.6.2, correlates well with FEMA 356

definitions of immediate occupancy (50/50), life safety (10/50), and collapse prevention

(2/50).

3.7.2 Frame Transient Drift

Current building codes, such as IBC 2003 and ASCE 7-02, require that the design story

drift shall not exceed 2.0% of the story height for typical moment frames with standard

interior walls and partitions. As stated in Section 3.3.2, the design of this frame adhered

to this drift criterion, but nevertheless, the drifts attained by the test specimen exceeded

those predicted by the code design procedure. As reported in Table 3.6, the test frame

reached a peak drift of 2% in the 2nd floor during the immediate occupancy event (50/50)

and 3% in the 1st floor during the design level event (10/50).

An argument can be made that the frame became more flexible after enduring the cycles

of the 50/50 event, which then had an impact on the drifts in the subsequent design level

event. As was reported in Section 3.6.1, it was determined that the fundamental vibration

period elongated from its initial value of 1 second to 1.3 seconds after the 50/50 event.

The Loma Prieta event was scaled to the 10/50 hazard level (Sa = 0.68g) based on the

initial period of 1 second. The spectral shape of this event is such that the spectral value

at 1 second is at a local minimum of the spectrum, beyond which at higher periods the

values increase. This is clearly evident in Fig. 3.70, which shows spectral acceleration

versus spectral displacement for the Loma Prieta event scaled to the 10/50 hazard level.

When the period lengthened to 1.3 seconds the spectral acceleration and the spectral

displacement increased by 26% and 114%, respectively, thus making the event much

more intense than a design level earthquake. With this increase in intensity and the

additional flexibility of the frame, it seems that it should have been expected that the

frame would exceed the drift limitation of 2% during this design event.

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When the record was scaled down by 80% to represent the second segment of the design

event, the spectral values were also scaled by the same factor, and are represented on Fig.

3.70 by the white circles along the natural period lines. This scaled design level event

seems to represent the same spectral acceleration level (Sa = 0.68g) as the design level

hazard, but the spectral displacement is still approximately 70% larger. This provides

some insight to explain the high drift levels during this design level event, but given that

the frame had already reached 2% drift during the immediate occupancy event, it seems

highly probable that it would still exceed the design level drift (2%) during the 10/50

event even if it had not gone through the first event.

Therefore the question remains as to why the design methodology with an imposed drift

limit failed to minimize the amount of drift to 2% during the design level event? This

brings up an important issue of how accurate the current design methods are in ultimately

predicting the behavior of the system. These codes are empirical in nature and therefore

it is difficult to rely on their estimates of performance, especially since we are using static

elastic analyses to estimate the dynamic nonlinear behavior of systems. This is the

reason that current research is pushing for a performance-based engineering approach to

design and assessment rather than the current status quo. Therefore, part of the answer to

the initial question may be that the current codes are simply not robust enough to

accurately predict the behavior of systems designed given the current procedure.

After the first design level event, the period had softened to approximately 1.5 seconds.

Figure 3.71 shows the relationship between spectral acceleration versus spectral

displacement for the Chi-Chi record scaled to the 2/50 hazard level at the initial period of

1 second. The shift to 1.5 seconds, as shown in Fig. 3.71, decreases the original spectral

acceleration by 30% and increases the spectral displacement by 54%. The shape of the

response spectrum of the Chi-Chi event is relatively close to that of the IBC 2000 curve

between 1 and 2.5 seconds, which is evident in Fig. 3.72. So it can be argued that even

though the frame had significantly softened from its original MCE point, the final result

was still close to representing a true 2% in 50 year event and the peak drift of 5.4% is

representative of the expected drift in such an event.

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This trend occurs again in the final Loma Prieta event, where the period of the frame at

the beginning of the record is around 1.7 seconds (shown in Fig. 3.72). This raises the

issue as to whether the pseudo-dynamic events should have been scaled differently by

perhaps accounting for this expected softening of the natural period. Figure 3.72 shows

the spectral acceleration graphs of the scaled earthquake records with the IBC 2000 10/50

and 2/50 design spectra. This figure reveals that the first design level event (10/50) is

actually slightly more intense that the IBC 2000 2/50 hazard when considered at 1.3

seconds (light square on Fig. 3.72). This also shows what was discussed earlier that the

imposed maximum credible event is approximately equal to the 2/50 hazard at 1.5

seconds (light diamond on Fig. 3.72).

3.7.3 Frame Residual Drifts

FEMA 351 (2000) and FEMA 356 (2000) both make some references to the amount of

residual drift expected for each structural performance levels (i.e. immediate occupancy,

life safety and collapse prevention). For the 50/50 event (immediate occupancy), the

expected value of residual drift is defined as negligible (FEMA 356) to less than 1%

(FEMA 351). This performance is clearly met by the performance of the test frame. The

10/50 (life safety) event yielded a residual drift in the test frame of approximately 0.3%,

which easily satisfies the 1% limit required by the FEMA 356 document. For the 2/50

event, a residual drift of 3.4% in first floor and 2.7% in total roof drift was recorded in

the test frame. This falls within the requirements of both documents, where FEMA 356

expects between 4-5% residual drift while FEMA 351 simply states that one should

expect a large permanent offset in the building.

One important issue to note here is the interior gravity resisting frames were not

accounted for in the pseudo-dynamic algorithm. Recent studies have shown that the

contribution of interior gravity frames in the seismic response of steel moment resisting

frames can lead to smaller deformation demands, even if the columns and beams in these

frames are considered as pinned connections (Lee and Foutch, 2002). Additional strength

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and stiffness is provided by the interior columns and the simple shear tab connections

acting with a concrete slab. This additional capacity would definitely apply to composite

RCS moment frames and could help reduce both the residual drift and the maximum

transient drift.

Despite being permitted by current standards (e.g. FEMA 356, etc.), it should be

recognized that large residual deformations are extremely difficult to repair and may even

result in the demolition of the building after a seismic event. As performance based

earthquake engineering is becoming more of a reality, ductile systems such as moment

resisting frames and buckling-restrained braces need to be able to control the amount of

residual drifts in the building in order to mitigate the cost of repair. This is an issue that

has not been fully resolved and is an area that requires some further study. One such

approach to reduce the amount of residual drift may be to incorporate these composite

frames into a dual system with either a braced or reinforced concrete wall core, as is

shown by Uang et al (2003).

3.7.4 Frame Repair

Damage patterns after each loading event were discussed in detail in section 3.6.2.

Numerous researchers were on hand to witness this test and were able to make comments

on the damage and the likely repairs. It was largely concluded that the damage incurred

by the frame during the 50% in 50 year event, was minimal and required little, if any,

repair. This hazard level is often correlated with an immediate occupancy damage state,

which implies minimal damage and no interruption to the function of the building. Given

the limited amount of damage to the frame following this event, it is reasonable to state

that the frame met the general conditions for immediate occupancy.

After the first design level event, the frame had some noticeable damage, none of which

affected the immediate safety of the structure but, nevertheless, still required some form

of repair. The 1st-floor RC columns would likely require epoxy injection of some of the

cracks and some minor patching of the spalled cover concrete. Some local buckles that

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occurred in the 1st and 3rd-floor may require heat straightening to recover some of the

initial stiffness of the element. Perhaps the most difficult repair would be straightening

or plumbing of the frame to reduce the residual interstory drift, which amounted to

approximately 0.3% roof drift.

The maximum credible earthquake resulted in severe cracking and spalling of the RC

columns and a large amount of yielding and local buckling in the steel beams. In

addition to the local member damage, there was a large amount of permanent drift in the

frame that would undoubtedly need to be straightened to resume operation of the

building. Researchers present agreed that although the frame could be repaired using

similar techniques described for the design level event, it would most likely be

economically unfeasible to fund the level of repairs required.

For each of the hazard levels examined in this testing program, the resulting damage

within the frame seems to correlate well with the structural performance expected by

current building codes, such as FEMA 356. A majority of the damage seen in this

composite frame would also occur in the more traditional all concrete or all steel moment

frames. The advantage within this system is that some of the more serious problems of

these traditional systems, including early steel beam fracture, have been avoided.

This test is considering only the performance of the bare lateral resisting frame, but in the

context of performance based engineering, one should also account for the level of

damage expected in nonstructural elements (i.e. partitions, cladding, building contents,

etc.) and the gravity resisting elements. In fact, these components will ultimately

comprise a majority of the cost of the building damage (Aslani 2005). While it is

acknowledged that this is an important aspect of the performance assessment of

buildings, it is not in the scope of this study, where the focus is primarily on the structural

performance of these composite RCS frames.

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3.7.5 Precast System Performance

As discussed in Section 3.3.5, the prefabrication of the column-footing and beam-column

modules and the ultimate construction of the test frame were handled by the Ruentex

Construction and Development Company of Taiwan. Ultimately, this was a very

successful exercise in both the precast fabrication and construction of composite RCS

frames. Discussions on the constructability of these frames with Pankow Builders

(www.pankow.com) have shown that this precast option is likely the most attractive

alternative to make these systems competitive in the United States market. It is

recognized that the economy of a system plays perhaps even a more critical role than

performance in the acceptance and application of new building systems in today’s

marketplace.

3.7.5.1 Beam Splices

As described in section 3.3.5, the design philosophy for the beam splices was taken from

FEMA 350 for prequalified bolted fully restrained moment connections. This

methodology allows some yielding in the flange plates by setting the design force equal

to the expected yield moment of the beam at the column face ( ). As was

indicated in section

yyye MRM =

3.6.2, the lower flange splice plates did experience some minor

yielding during the earthquake events (10/50 and 2/50). The yielding became much more

extensive in the 1st-floor as the frame was pushed out to extremely large drifts during the

latter part of the final pushover, and as described earlier, ultimately resulted in net section

rupture near 10% story drift.

Although they performed adequately during the test, in retrospect, it seems that these

beam splices should be designed to experience only minimal yielding during the hinging

of the beam at the column face. Rather than adopting the FEMA 350 philosophy and

reducing the design moment to the expected yield moment at the column face, perhaps

one should design these splices for the expected plastic moment ( prM = 1.1 y e yR Z F =

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(1.1)(1.1) pM ). This design approach would ensure the relatively elastic behavior of these

splices and minimize the potential for unexpected failure within these components. It is

for this reason that design for 1.1 y pR M is recommended in Chapter 2.

Another design consideration that has arisen from the test behavior is whether or not the

bolts in these connections should be designed as bearing or slip critical. As discussed in

Section 3.3.5, these bolts were designed as a typical bearing strength connection that

would allow slip to occur. This decision led to a significant amount of “bolt banging”

during each of the simulated earthquake events, including the “operational” or immediate

occupancy 50/50 event. While the bolt slippage did not cause any detrimental effects on

the performance of the building, it was clear to those witnessing the test that these loud,

sharp noises generated during each of the hundreds of slips could terrify the building

occupants. This brings about the question as to whether these connections should be

designed as slip-critical or at least not to slip during the more frequent events. The

occurrence of “bolt banging” throughout the test ultimately led to the design debate

presented in Section 2.3.2.2.3.1. This is not a new issue and has been observed in both

field and laboratory studies of steel framing systems with bolted connections (Schwein

1999, Tide 1999, Mann et al. 1984, Committee on Design of Steel Building Structures of

the Committee on Metals 1992).

3.7.5.2 Column Splices

The precast column splices were standard grouted splices designed by the Ruentex

Construction and Development Company of Taiwan. These splices, which are sized to

fully develop the expected plastic strength of the reinforcement bars, performed

exceptionally well throughout all phases of the test program. The behavior of these

splices during this frame test and the RC column-footing subassembly tests (Cordova

2006) have proven their strength and durability and should be considered as an extremely

robust connection between precast RC columns.

110

3.7.6 Frame Overstrength

The overstrength of the frame is defined as the ratio of the maximum base shear and the

design base shear. The AISC Seismic provisions (1997) specify the upper bound of the

overstrength factor for moment-frame systems to be 3. During the final pushover, the

RCS test frame reached a maximum base shear of approximately 2.8 times the original

design value (2.0 including PΔ loads), indicating that the frame possessed a large amount

of overstrength even after enduring significant damage throughout the four pseudo-

dynamic events. The peak base shear attained during the pseudo-dynamic events

corresponds to an overstrength value of approximately 3.2. Although this peak value

does not necessarily equate to the maximum strength of the frame, it does show that the

damage in the frame caused the overstrength to reduce by at about 13% (from 3.2 to 2.8).

The final pushover also revealed that the stiffness of the test frame had been reduced to

approximately 50% of the original undamaged stiffness. Although the pseudo-dynamic

events had caused a significant amount of damage and drastically reduced the stiffness of

the frame, there was still a large amount of overstrength present in the test specimen,

which emphasizes the robust nature of the RCS moment frame.

3.7.7 Behavior of Composite Beams

As described in section 3.6.3, the composite beams performed exceptionally well

throughout all phases of the loading protocol, with the performance and durability of both

the slab and the shear studs far exceeding the initial expectations. The 1st and 3rd-floor

beams successfully endured repeated cycles of large plastic rotations without

experiencing any kind of premature fracturing, even when subjected to the large drifts

imposed by the final pushover. There were no instances of shear stud fracture and

instrumentation verified that no differential slip or lift off occurred between the steel

beam and the slab.

The concrete slab greatly enhanced the ductility of the beam section by providing

adequate restraint to the upper flange of the steel beam, thereby preventing the

111

occurrence of local buckling within the upper quarter of the beam depth. In addition to

this, the presence of the slab shifted the neutral axis into the upper half of the beam depth,

which significantly minimized the amount of yielding that occurred in the upper flange.

This is likely the reason that the shear studs that were accidentally placed within the

hinge zones of the 2nd and 3rd floor beams did not lead to any fracture-related incidents in

the upper beam flange.

As discussed in section 3.6.2, local buckling of the web and lower beam flanges began to

occur during the design level (10/50) event and became even more severe during the

maximum credible (2/50) event. In the FEMA 350 (2000) document, the structural

performance levels for steel girders are defined for the both the immediate occupancy

(50/50) and the collapse prevention event (2/50). For the 50/50 event, some of the steel

beams are expected to undergo minor local yielding and buckling, which is consistent

with what occurred in the test frame. In the 2/50 event, the extensive local yielding and

buckling present in the test frame is a damage state that is anticipated by FEMA 350 for

steel beams given this hazard level. It is also anticipated that some girders may

experience partial fractures for this event, which did not happen in any of the beams in

the test frame.

As mentioned in section 3.6.3, the most severe buckling took place at the beam hinges

framing into the exterior joints. The continuity of the beam and the slab in the interior

joints seems to provide additional restraint which (1) limits the amount of buckling that

occurs in these hinges and (2) helps straighten out buckles when the hinge is in positive

moment (i.e. tension in the bottom flange and compression in the slab). In subassembly

tests, this trend does not happen but rather the local buckles build up throughout each

cycle while the length of the beam physically shortens (Civjan 2001). This is drastically

different than what happened in the frame test and points to the difficulty and unresolved

error in modeling the boundary conditions in typical beam-column subassembly tests.

The behavior of the slab and shear studs indicate that composite action was maintained

throughout the loading protocol. This is much different than the behavior that is typically

112

found in subassembly tests (Cheng 2002, Civjan 2001, Leon 1998, Bugeja 2000), where

fractures of shear studs and the loss of composite action occurs relatively early and

abruptly. This difference in behavior points to the disparity between subassembly tests

and real moment frames and will be further discussed in section 3.7.11.

3.7.7.1 Shear Stud Design

The shear studs were originally designed based on the AISC-LRFD recommendations

(defined in Section 2.3.2.2.2) to develop a fully composite section, which required

approximately 42 studs over the entire beam span. The AISC Seismic Provisions reduces

the allowable strength of shear studs to 75% of that defined by AISC-LRFD to account

for the cyclic behavior of shear studs, which would therefore require 56 studs. As

discussed in Chapter 2, more recent work by Civjan (2003) has proposed that the AISC-

LRFD predicted strength of shear studs should be further reduced to 60%, indicating that

the amount of studs required should be 64. While the number of studs was originally

selected based on the requirements of the AISC Seismic Provisions, the final number of

studs called out in the construction drawings (64 studs per beam) coincidentally met the

requirements specified by Civjan (2003). As previously discussed, behavior of the studs

surpassed all expectations from the subassembly tests, but it is difficult to attribute this to

placing 8 extra studs to meet the requirements of Civjan (2003) or rather the overall

boundary conditions and continuity of the full scale test. Considering these points, it is

recommended to follow the AISC Seismic Provisions and provide studs to develop full

composite action, based on stud strengths equal to 75% of the (monotonic) values

specified in AISC-LRFD.

3.7.8 Behavior of RC Columns

The hinges in the RC columns performed as expected throughout all of the pseudo-

dynamic loading events, with the most severe damage occurring in the base hinges where

estimated plastic rotations reached as high as 0.055 radians during the 2/50 event. As

described in Cordova et al. (2006), the tiltmeter data revealed that the hinge length was

113

approximately equal to the depth of the column, which supports the common assumption

for design and assessment purposes.

Bond slip was found to be a significant contributor to the total rotation of the RC column

base hinges. In retrospect, the instrumentation of these columns should have been

planned such that this portion of the column rotation could be monitored and separated

from the total hinge rotation.

The final static pushover provided some insight into what may have been the governing

failure mechanism for these columns. After being subjected to numerous large plastic

excursions and experiencing a large amount of cracking and spalling during the

earthquake events, the column base hinges were considered to be well within the “near

collapse” damage state. The pushover imposed a maximum drift of 10% in the first floor,

which resulted in further deterioration of the column base hinges. The final failure

mechanism seemed to be a combination of extensive plastic hinging followed by

localized shear failure in the hinge region. Since the concrete was severely damaged in

this region, the high shear seemed to be carried only through dowel action of the

longitudinal bars. Figure 3.73 depicts an interior column after the loose concrete has been

chipped away. It is evident in the photos that there is significant kinking of the main

longitudinal bars, which raises the question as to whether or not this sort of behavior is

acceptable. It is possible to provide additional support for these columns, perhaps in the

form of a steel jacket or fiber reinforced polymer composite wrap, but ultimately, it

seems that the demands imposed on these hinges may be too extreme to make any

conclusions on their behavior during the final pushover.

3.7.9 Strong-Column Weak-Beam Criterion

During the design stages of the testing program, one of the most important questions had

to do with whether one should consider the strength of the composite action of the

concrete slab with the steel beams in the strong column-weak beam (SCWB) checks.

The AISC Seismic Provisions (2002 and 2005) do not explicitly address this issue and it

114

is seemingly left up to the engineer’s interpretation. As described in Section 3.3.3, the

strength differences between a steel or a composite section has a significant impact on the

final SCWB ratios and can ultimately effect the final design of the RC columns and if not

considered can shift the failure mechanism from beam to column hinging. Based on the

overall performance of the slab and shear studs during the test (Section 3.7.7) and

reinforced by recommendations of other researchers (Leon and Hajjar 1998), it is critical

to consider the composite strength of the beam during the SCWB design check.

The intention of the SCWB criterion is to ensure that the columns in any floor are strong

enough to force hinging to occur within the beams, thus reducing the probability of the

formation of a story mechanism. It is clear that the SCWB criterion that is implemented

in current building codes (AISC 2002, ACI-318 2002) was not able to prevent the two-

story mechanism from occurring during the final pushover event (Section 3.6.2.5),

particularly if one were to consider the strength of the steel beams only (Fig. 3.4a). This

mechanism is particular interesting because the SCWB ratios at the 2nd floor are amongst

the highest in the entire frame (interior joints: 1.18col beamM M =∑ ∑ ) and satisfies the

spirit of the SCWB criterion with an average column-to-beam strength ratio of 1.04 over

the entire floor considering the composite beam strengths (refer to Section 3.3.3 and Fig,

3.4c). Another issue that should also be discussed is why a first floor story mechanism

did not develop given that the average SCWB ratio over this floor is also approximately

1.08. This lack of correlation between the SCWB design criteria and the performance of

the test frame brings about some concern with these current provisions.

As discussed in Chapter 2 (Section 2.3.2.1.1.1), the SEAOC has proposed an alternate

provision for the SCWB criterion, which recommends that the sum of the strengths of the

columns below a floor should be greater than the sum of the strengths of the beams at the

floor. Considering a building where the beams on two consecutive floors are identical,

this SCWB provision has the effect of increasing the conventional column-to-beam

strength ratio to 2.0 at each joint. Using this updated design criterion, this illustrates that

both the first and second floors fall below the permissible design value of unity with 0.67

and 0.63, respectively. The test data tend to support this new provision, since the second

115

floor columns (where hinging occurred) do not meet the proposed requirement, but again

it does not explain why the first floor columns did not form a story mechanism.

Perhaps the answer to why a first floor story mechanism did not occur has to do with the

location of the inflection point in these columns. A typical assumption that is used to

estimate the force distribution in moment frames is that the inflection points (i.e. points of

zero moment) are located at mid-height for the columns and mid-length for the beams.

Computer analyses often show that while this assumption is true for the floors above the

first floor, it often does not hold for the first floor itself, where the inflection point tends

to be above mid-height and closer to 2/3 to 3/4 the height of the column. This would

suggest that it is more difficult to develop the full moment capacity of the upper hinge in

the first floor columns than it would be in any higher story. This implies that the SCWB

criterion may need to be adjusted to account for this difference. If we assume that the

location of the inflection point is closer to two-thirds up the height of the column, then

the permissible design value for the SEAOC SCWB check should be 0.67 rather than 1.0

for the first floor columns only, which would suggest that the first level in the test frame

passes the SEAOC SCWB check. Given this adjustment, it seems that the test data tends

to support this new provision, since the second floor columns (where hinging occurred)

does not meet the proposed requirement, whereas all the other floors do. Note that this

modification for the first floor columns may not apply when the column base is not fully

fixed, and some flexibility in the footing exists.

3.7.10 Behavior of Composite Joints

With standard details, the composite joints retained their strength and stiffness throughout

all phases of the loading protocol, including the final pushover. The most significant

damage consisted of relatively minor shear cracking and some spalling below the band

plates in the 1st-floor joints, which indicates that the joints had not yet reached their

maximum strength. Following the behavior of past subassembly tests (Liang 2003,

Kanno 1994, etc.), these composite joints continued to prove their inherent strength and

116

durability whether subjected to either monotonic or cyclic loading, making them

extremely attractive for use in high seismic zones.

The roof joints proved to be a unique challenge in the design of the test frame, since

details for top floor connections have not been studied extensively. The solution that we

developed employed a reinforcing bar plate detail, described in section 3.3.7, which

mobilized both the bearing resistance for the beam and developed the longitudinal

reinforcement bars. The proposed reinforcing bar plate detail for the top beam-column

joint of a composite RCS frame has been shown in both subassembly tests and the full-

scale testing program to possess adequate strength and stiffness to force hinging to occur

in the surrounding beams. This joint performed well in both tests and is recommended as

a practical detail for use in top (roof) joints.

3.7.11 Differences between Subassembly and Frame Tests

Beyond the performance and design issues brought up by this frame test, there are several

issues regarding the differences in boundary conditions between an isolated beam-column

subassembly and a complete moment resisting frame. The continuity of the slab and

beam in the test frame provides a significant amount of restraint which prevents beam

shortening, a common phenomenon in steel subassembly tests that allows physical

shortening of the beam as local buckling builds up in the hinge zone. This continuity in

the frame restricts local buckling in steel beam hinges, particularly in those hinges

adjacent to interior joints where the continuity effect has a greater impact. Conversely,

the beams framing into the exterior joints did not have the complete benefit of the

continuity of the slab and beam, and as a result experienced noticeably more local

buckling than those framing into the interior joints. This issue was discussed in detail in

section 3.7.7 and demonstrated that the boundary conditions in typical subassembly tests

tend to overestimate the amount of damage in the beam hinge due to the problems

associated with the lack of continuity.

117

Another important difference between this test frame and subassembly tests was the

introduction of the earthquake loads into the system. In the test frame, story shears were

applied through the east and west loading beams, which in turn transferred the loads

through the slab and into the frame through bearing on the columns and shear studs on

the main girder. This introduction of loads attempts to follow the load path in a real

structure under earthquake excitation. The strain gauges on the loading beam proved that

this system performed as expected and the earthquake loading was distributed relatively

uniformly along the frame length. As described in Section 3.4.1, this loading mechanism

seemed to improve the durability of the slab by counteracting the natural tendencies of

the composite beams in positive and negative bending. As illustrated in Fig. 3.12, when

the beam is in negative bending, the slab is put into tension by the natural curvature of the

beam, but the loading mechanism is offsetting this tension by pushing the slab into the

column imposing compressive bearing stresses (location A in Fig. 3.12). The opposite is

true on the other side of the beam, where positive bending is causing compression in the

slab but the loading beam is pulling the slab away from the column (location B in Fig.

3.12).

The traditional method used to impose loads into a beam-column subassembly is by

directly applying shear to the beams, as shown in Fig. 3.74. This method has the

tendency to try to pry the slab away from the beam and does not capture the beneficial

effects that occur when the loads are imposed through the slab. This seems to provide

one explanation as to why the slab and shear studs in subassembly tests seem to degrade

at much quicker rate than what was seen in the full-scale test frame. Note that this effect

has less of an impact in the lower stories of taller buildings where the shear imposed in

the slab is generally considerably smaller than the shear accumulated in the frame from

the upper floors.

This testing program has underlined some of the problems that beam-column

subassembly tests face with their inability to enforce certain boundary conditions that

seemingly have a positive effect on the behavior of the components. These deficiencies

in the boundary conditions are very difficult to implement without greatly complicating

118

the traditional test setup. Nevertheless, it needs to be recognized that these subassembly

tests are likely overestimating the severity of the damage that one could expect to see in a

complete moment frame system.

119

Table 3.1 – Rationale for large-scale test Issues Explored Issues Neglected

Investigate the often-overlooked connection details: location of the beam and column splices for precast system, top floor beam/column joint detail, and foundation/column splice location. Given the state of current analyses and drift requirements of performance based codes, an attempt will be put forth to push the test frame to large drifts. Avoid the problems of b/c cruciform tests, such as unrealistic restraints that may lead to erroneous results (i.e. beam shortening). Comparison of subassembly tests and actual frame. Test and validate the importance of current design criteria (e.g. SCWB and drift requirements). Will test our assumptions about composite beam behavior; beff for strength/stiffness, effects of continuity of slab, the extent of damage that we can we count on the composite action, and with the restrictions on shear studs within the plastic hinge zone (FEMA 351) and the length of the beam splice, how much composite action is really occurring? Verify our assumptions on the effective EI of the RC columns. Determine and work through all construction issues for this system.

Evaluate the response of a damaged frame. Track the change in structural period during each earthquake and its effect on the response. Investigate the performance-based design issues of the test. This may prove to be a benchmark testing-program, with hopes to encourage widespread collaboration through open discussions and an accessible database record of the results. Once damaged, determine how difficult it is to repair the structure. Extrapolate the cost to a realistic structure and compare to all-steel or all-concrete frames. Validation problem for current analytical tools and damage indices.

3-dimensional framing effects Effect of high axial loads on RC columns The effect of non-structural elements on the stiffness and damping on the frame. Additional damping techniques such as visco-elastic dampers. Shaking table versus psuedo-dynamic test procedure High P-delta forces Structural Irregularities – bay width, story height, stiffness and mass irregularities Utilize advance measurement techniques beyond the standard tools. Investigate the response of a repaired structure.

120

Table 3.2 – Design loads summary

Dead Load Floor: 4.4 kPa (92 psf) Roof: 4.3 kPa (89 psf)

Live Load 2.4 kPa (50 psf)

Effective Seismic Weight, W 17250 kN (3878 kips)

Base Shear, V (+ Acc. Torsion)

1078 (+ 81) kN (242.4 (+ 18.2) kips)

Shear Distribution, Fx F1: 193 kN (43.44 kips) F2: 395 kN (88.88 kips) F3: 570 kN (128.23 kips)

Table 3.3 – Test frame member properties. RC Columns

Floor

Steel Beams (d, bf, tw, tf)

Fy,nom = 345 MPa (Fy,meas)

Section f’c,meas=40

MPa ( f’c,meas)

Rein. Bars Fy,nom = 415 MPa Fy,meas = 527 MPa

1st H600x200x11x17mm (426 MPa)

650x650mm (89 MPa)

Exterior Interior

8-#11bars 12-#11bars

2nd H500x200x10x16mm (501 MPa)

650x650mm (68 MPa)

Exterior Interior

4-#11bars 12-#11bars

3rd H396x199x7x11mm (419 MPa)

650x650mm (68 MPa)

Exterior Int. Lower Int. Upper

4-#11bars 12-#11bars 8#11bars

121

Table 3.4 – Measured strengths of steel tension coupons.

Steel Fy (MPa)

Percent Difference

(meas. and min. spec.) Flange 409 19% 1st Floor Web 442 28%

Flange 484 40% 2nd Floor Web 517 50%

Flange 407 18% 3rd Floor Web 431 25%

#3 bars 390 -6%

#4 bars 411 -1%

#10 bars 586 42%

#11 bars 527 27%

Table 3.5 – Measured crushing strength of concrete cylinders.

Concrete 'f c (MPa) Percent

Difference (meas. and min. spec.)

1st Floor Columns 89.0 (lower) 70.8 (upper)

115% 71%

2nd Floor Columns 68.2 65%

3rd Floor Columns 68.4 65%

Slab 31.0 13%

Table 3.6 – Summary of maximum and minimum drifts during each pseudo-dynamic event (both absolute drift and with the residual removed).

50/50 10/50-1a 10/50-1b 2/50 10/50-2 Max Drift

(residual removed) 1.76

(1.76) 2.99

(3.10) 2.65

(2.26) 3.40

(3.07) 1.36

(1.62) Min Drift

(residual removed) -1.91

(-1.91) -2.20

(-2.15) -2.28

(-2.67) -5.32

(-5.78) -2.85

(-2.75)

122

Figure 3.1 – Plan View of Building

Figure 3.2 – Plan and elevation views of full-scale composite test frame

Mo es ment Fram

6 @ 7m = 42m

4 @ 7m = 28m

123

Ties Face Bearing Plate

Figure 3.3 – Joint detail showing the transverse beam and placement of ties.

(a)

(b)

Figure 3.4 – ΣMc/ΣMg ratios at each joint assuming a) steel beams (nominal) and b) composite beams (nominal).

0.76 0.86 0.86 0.76

0.68 0.97 0.97 0.68

0.58 0.72 0.72 0.58

0.99 0.97 0.97 0.99

1.03 1.23 1.23 1.03

1.06 1.06 1.11 1.11

124

(c)

Figure 3.4 cont. – ΣMc/ΣMg ratios at each joint assuming c) composite beams and RC columns with measured material properties.

Figure 3.5 – Schematic of a typical bolted flange plate beam splice connection

Shear Tab

Flange Plates

0.70 0.86 0.86 1.22

0.72 1.18 1.18 1.07

0.91 1.03 1.03 1.36

125

(a) (b)

Figure 3.6 – RC column cantilever tests with the grouted splice located (a) 1-meter up the column height and (b) flush at the column-footing interface.

Splice

Splice

126

-8 -6 -4 -2 0 2 4 6 8-800

-600

-400

-200

0

200

400

600

800

Drift (%)

For

ce (

kN)

FFH08

(a)

-8 -6 -4 -2 0 2 4 6 8-800

-600

-400

-200

0

200

400

600

800

Drift (%)

For

ce (

kN)

FFL08

(b)

Figure 3.7 – Response of RC column subassembly test with precast splice at (a) 1-meter above the footing and (b) flush at the column-footing interface. (Tsai 2002)

127

Figure 3.8 – Top joint option #1. Section AA in Fig. 3.9.

Figure 3.9 – Section A-A from Fig. 3.8.

Figure 3.10 – Reinforcement cap plate

A A

12#32 bars

396x199x7x11

650x650mm

see Fig. 3.10

Band Plate

#10 bars

Rein. Cap Plates

Band Plate & FBP (20mm)

Band Plate 130x20mm

top of concrete

stiffener

Rein. Bar Plate

FBP 374x20mm

#32 bars

beam flange (11mm)

PP

see fig. 3.11

beam web

128

Figure 3.11 – Plate to reinforcing bar detail.

Figure 3.12 – Schematic of load path between actuators, loading beams, and test frame.

#10 bar These reinforcing bars must be weldable, ACI 318 defines these as type A706

compressive strut against column

compression field against shear studs

Deflected Shape

Mpos slab in compression

Mneg slab in tension

Beam Moment Diagram

Mneg slab in tension

Loc. A Loc. B

CL

129

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Sa (

g)

Period (sec)

50/50 TCU0822/50 TCU08210/50 LP89G0410/50 IBC20002/50 IBC200050/50 Taiwan Hazard10/50 Taiwan Hazard2/50 Taiwan Hazard

Figure 3.13 – Final records scaled at T1 = 1sec to appropriate Taiwanese hazard levels.

(a) (b)

Figure 3.14 – Construction photos of (a) a typical pre-cast beam-column module and (b) the completion of the first floor.

130

0 5 10 15 20 25 30 35 40 45-200

-150

-100

-50

0

50

100

150

200

Time (sec)

Roo

f D

ispl

acem

ent

(mm

)

EQ1: 50/50 TCU082

Figure 3.15 – Roof displacement versus time for the 50/50 event.

0 5 10 15 20 25 30 35 40 45 50-300

-200

-100

0

100

200

300

400

Time (sec)

Roo

f D

ispl

acem

ent

(mm

)

EQ2: 10/50 LP89G04 - 1

Figure 3.16 – Roof displacement versus time for the 10/50-1 event.

131

0 5 10 15 20 25 30-500

-400

-300

-200

-100

0

100

200

300

400

Time (sec)

Roo

f D

ispl

acem

ent

(mm

)

EQ3: 2/50 TCU082

Figure 3.17 – Roof displacement versus time for the 2/50 event.

0 5 10 15 20 25 30 35 40-350

-300

-250

-200

-150

-100

-50

0

50

100

150

Time (sec)

Roo

f D

ispl

acem

ent

(mm

)

EQ4: 10/50 LP89G04 - 2

Figure 3.18 – Roof displacement versus time for the final 10/50 event.

132

-0.06 -0.04 -0.02 0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR

Flo

or

EQ 1: 50/50EQ 2: 10/50-1aEQ 2: 10/50-1bEQ 3: 2/50EQ 4: 10/50-2

Figure 3.19 – Maximum interstory drift ratios for each floor during each pseudo-dynamic loading event.

-4000 -3000 -2000 -1000 0 1000 2000 3000 40000

0.5

1

1.5

2

2.5

3

Story Force (kN)

Flo

or

EQ 1: 50/50EQ 2: 10/50-1aEQ 2: 10/50-1bEQ 3: 2/50EQ 4: 10/50-2

Figure 3.20 – Maximum story shear for each floor during each pseudo-dynamic loading event.

133

0 5 10 15 20 25 30 35 40-300

-200

-100

0

100

200

300

Roo

f D

ispl

acem

ent

(mm

)

Time (sec)

Test Frame Results80%-LP89G04 10/50

1st Event2nd Event


-0.06 -0.04 -0.02 0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

Interstory Drift Ratio (%)

Flo

or

Test Frame Results80%-LP89G04 10/50

1st Event2nd Event


134

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-2000

-1000

0

1000

2000

3000

4000

Maximum Drifts1st Floor: 10.12nd Floor: 7.93rd Floor: 3.1

Roof Drift Ratio

Bas

e S

hear

(kN

)

Measured ResponsePΔMeasured+P Δ

Figure 3.23 – Base shear versus roof drift ratio for the final static pushover (p-delta loads are superimposed in dotted line).

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

Rotation (rad/1000)

Mom

ent

(100

0kN

-m)

1C3 Base Hinge

Figure 3.24 – Hysteretic response of a 1st floor interior column base for the 50/50 event.

135

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

Rotation (rad/1000)

Mom

ent

(100

0kN

-m)

1C3 Base Hinge

Figure 3.25 – Hysteretic response of a 1st floor interior column base for the 10/50-1a event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

Rotation (rad/1000)

Mom

ent

(100

0kN

-m)

1C3 Base Hinge

Figure 3.26 – Hysteretic response of a 1st floor interior column base for the 10/50-1b event.

136

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

Rotation (rad/1000)

Mom

ent

(100

0kN

-m)

1C3 Base Hinge

Figure 3.27 – Hysteretic response of a 1st floor interior column base for the 2/50 event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

Figure 3.28 – Hysteretic response of a 1st floor exterior beam hinge for the 50/50 event.

137

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1SM

omen

t (1

03 kN

-m)

Rotation (rad/1000)

Figure 3.29 – Hysteretic response of a 1st floor exterior beam hinge for the 10/50-1a event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

Figure 3.30 – Hysteretic response of a 1st floor exterior beam hinge for the 10/50-1b event.

138

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1SM

omen

t (1

03 kN

-m)

Rotation (rad/1000)

Figure 3.31 – Hysteretic response of a 1st floor exterior beam hinge for the 2/50 event. (Large rotations are due to measurement errors caused by severe local buckling).

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

Figure 3.32 – Hysteretic response of a 1st floor beam for the 10/50-2 event.

139

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1NM

omen

t (1

03 kN

-m)

Rotation (rad/1000)

Figure 3.33 – Hysteretic response of a 1st floor interior beam hinge for the 2/50 event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000)-30 -20 -10 0 10 20 30

-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)

Outer Panel Rot. (rad/1000)

Figure 3.34 – Total and outer panel hysteretic response of a 1st floor interior joint for the 50/50 event.

140

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

66

4

1J3Jo

int

She

ar (

103 kN

)

Total Rot. (rad/1000)

1J3

Join

t S

hear

(10

3 kN)


Figure 3.35 – Total and outer panel hysteretic response of a 1st floor interior joint for the 10/50-1a event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000)-30 -20 -10 0 10 20 30

-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


Figure 3.36 – Total and outer panel hysteretic response of a 1st floor interior joint for the 10/50-1b event.

141

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

66

4

1J3Jo

int

She

ar (

103 kN

)


1J3

Join

t S

hear

(10

3 kN)


Figure 3.37 – Total and outer panel hysteretic response of a 1st floor interior joint for the 2/50 event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000)-30 -20 -10 0 10 20 30

-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


Figure 3.38 – Total and outer panel hysteretic response of a 1st floor interior joint for the 10/50-2 event.

142

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2C3 Upper HingeM

omen

t (1

03 kN

-m)

Rotation (rad/1000)

Figure 3.39 – Hysteretic response of the 2nd floor upper interior column hinge after the 10/50-1a event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2C3 Upper Hinge

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

Figure 3.40 – Hysteretic response of the 2nd floor upper interior column hinge after the 10/50-1b event.

143

-80 -60 -40 -20 0

144

20 40 60 80-3

-2

-1

0

1

2

3

2C3 Upper Hingeen

t (1

03 kN

-m)

00)

Mom

Rotation (rad/10

Figure 3.41 – Hysteretic response of the 2nd floor upper interior column hinge after the 2/50 event.

Figure 3.42 – Damage in 1st floor interior column base after the

50/50 event. Figure 3.43 – Damage in 1st floor interior column base after the

10/50-1b event.

145

Figure 3.44 – Damage in 1st floor interior column base after the

2/50 event. Figure 3.45 – Damage in 1st floor interior column base after the

10/50-2 event.

146

Figure 3.46 - Yielding in 1st floor beam after the 50/50 event

Figure 3.47 - Yielding and local buckling in 1st floor beam (1B1S) after the 10/50-1b

event

147

Figure 3.48 - Yielding and local buckling in 1st floor beam (1B1S, exterior beam hinge)

after the 2/50 event

Figure 3.49 - Yielding and local buckling in 1st floor beam (1B1S, exterior beam hinge)

after the 10/50-2 event

148

Figure 3.50 - Yielding and local buckling in 1st floor beam (1B3N) after the 10/50-1b

event

Figure 3.51 - Yielding in 1st floor beam (1B1N, interior beam hinge) after the 2/50 event

149

Figure 3.52 - Yielding in 1st floor beam (1B1N, interior beam hinge) after the 10/50-2

event

Figure 3.53 – 1st floor splice plate after the 10/50-1b event.

150

Figure 3.54 – Joint 1J3 after the 50/50 Chi-Chi event.

Figure 3.55 – Joint 1J3 after the 10/50-1b Loma Prieta event.

151

Figure 3.56 – Joint 1J3 after the 2/50 Chi-Chi event.

Figure 3.57 – Joint 1J3 after the10/50-2 Loma Prieta event.

152

Figure 3.58 – Damage in upper hinge of 2nd floor interior

column hinge after the 10/50-1b event. Figure 3.59 – Damage in upper hinge of 2nd floor interior column

hinge after the 2/50 event.

153

Figure 3.60 – Damage in upper hinge of 2nd floor interior

column hinge after the 10/50-2 event. Figure 3.61 – Frame at its maximum drift state during static push.

IDR in 1st floor:10%, 2nd: 8%, and 3rd: 3%.

154

Figure 3.62 – Damage in 1st floor exterior column base after the

final pushover event. Figure 3.63 – Damage in 1st floor interior column base after the

final pushover event.

155

Figure 3.64 – Damage in upper hinge of 2nd floor exterior column

hinge after the final pushover event. Figure 3.65 – Damage in upper hinge of 2nd floor exterior

column hinge after the final pushover event.

156

Figure 3.66 – Slab above exterior beam hinge, 1B1S, after the final static push.

Figure 3.67 – Net section rupture of lower flange plates in 1st floor beam splice.

157

Figure 3.68 - Yielding and local buckling in 1st floor beam (1B1S, exterior beam hinge) after the final pushover event.

Figure 3.69 - Yielding and local buckling in 1st floor beam (1B3N, exterior beam hinge) after the final pushover event

158

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

Sd (cm)

Sa (

g)

Sa=0.68g, S

d=16.8cm

Sa=0.86g, S

d=36.0cm

Sa=0.42g, S

d=30.0cm

IBC 10/50Scaled Loma Prieta Record (LP89G04)

Figure 3.70 – Spectral acceleration versus displacement for the Loma Prieta event.

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

Sd (cm)

Sa (

g)

Sa=0.92g, S

d=22.8cm

Sa=0.63g, S

d=35.0cm

IBC 2/50Scaled Chi-Chi Record (TCU082)

Figure 3.71 – Spectral acceleration versus displacement for the Chi-Chi event.

159

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Sa (

g)

Period (sec)

1.0sec→ 1.3sec→ ←1.5sec

50/50 TCU0822/50 TCU08210/50 LP89G0410/50 IBC20002/50 IBC200050/50 Taiwan Hazard10/50 Taiwan Hazard2/50 Taiwan HazardLP89G04 at 1.3s80% LP89G04 at 1.3sTCU082 at 1.5s

Figure 3.72 – Spectral acceleration graphs of final records with highlighted spectral values at the elongated periods.

Figure 3.73 – RC column base hinges after loose concrete had been chipped away.

160

Figure 3.74 – Boundary condition in subassembly tests causes slab to pull away from beam.

Pulling beam away from slab

Actuator Forc

161

Chapter 4: Analytical Modeling and Validation

4.1 Introduction

This chapter investigates techniques to analytically model composite RCS frames. First,

the modeling issues at the material and element level are addressed, using calibration

studies on subassembly component tests, including reinforced concrete columns,

composite steel beams, and composite beam-column connections. While the focus of this

chapter is on composite RCS frame, the results and guidelines can be applied to any

systems that utilize these structural members (e.g. conventional all-steel or concrete

moment frames). Emphasis is placed on two specific types of element models: (1) a

flexibility derived beam-column element that is able to capture distributed plasticity by

employing a fiber cross-section at integration points along the member and (2) a beam-

column joint model that captures finite size kinematics and inelastic behavior of the joint.

These models are then used to analyze the 3 story test frame described in Chapter 3, and

validated against the measured pseudo-dynamic test data. Attempts are also made to

relate the analytical response to the physical damage observed in the test specimen.

4.2 OpenSees Component Models

Open System for Earthquake Engineering Simulation (OpenSees) is a software

framework for simulating the seismic response of structural and geotechnical systems

(McKenna et al., 1999). OpenSees is an open source program that is continually

evolving as researchers improve existing models and add new models and features. This

section will specifically discuss the uniaxial materials and elements in OpenSees that can

be used to represent the behavior of composite RCS frames.

4.2.1 Material Models

The uniaxial material models are the most basic components in OpenSees to model a

variety of force versus displacement (or stress versus strain) hysteretic responses.

162

Material models can be used to make up the fiber cross-sections within beam-column

elements (as described in Section 4.2.2) or can be used in a non-linear spring to represent

the response of a designated degree of freedom (i.e. rotational, axial, or shear spring).

There are a number of material models provided in OpenSees. The three used in this

study are the steel, concrete, and tri-linear hysteretic model to represent the composite

steel beams, RC columns, and composite joints in RCS frames.

The steel uniaxial material model (Filippou et al., 1983) incorporates isotropic strain

hardening and allows a smooth transition between the elastic and hardening portions of

the response, which can simulate the Bauschinger effect (Fig. 4.1). The backbone of the

steel material model is defined by the elastic modulus ( sE ), the yield strength ( ), and

the hardening ratio (b). The remaining input parameters to define the transition curve and

isotropic hardening are all typically set to the default values, as defined by Filippou

(1983). This material is referred to as “Steel02” in OpenSees.

yF

The concrete material model is defined by the modified Kent and Park model (Scott et. al.

1982) and represents typical concrete crushing and residual strength behavior. It also

allows for tensile strength with linear softening that helps to represent the interaction of

the concrete and the reinforcement bars in tension (Fig. 4.2). The compression backbone

of this model is defined by the points at which the material reaches the maximum

crushing strength ( 'ccf , ccε ) and the point when the residual strength attained ( '

2cf , 2cε ).

The tensile segment of the backbone is defined by the ultimate tensile strength ( tf ) and

the tensile softening slope ( ). This material model is referred to as “Concrete02” in

OpenSees.

tsE

The hysteretic material model, shown in Fig. 4.3, has a tri-linear backbone and the

capability to introduce both pinching behavior and stiffness degradation. The tri-linear

backbone is defined by sets of three positive and negative force-deformation points,

which provides the capability to define different positive and negative backbone curves.

Pinching is defined by the xη and yη factors, which define the intermediate force-

163

deformation point that the model will shoot for before returning to the previous

maximum point. Damage can be introduced to the model either through a deformation

( ) or an energy-based factor (dΔ Ed ), which causes the current excursion to shoot for a

force-deformation point that is further out than the last excursion (thus resulting in the

accelerated loss of stiffness). This material model is referred to as “Hysteretic” in

OpenSees.

For a RCS composite frame, there are a minimum of five distinct material models that are

required to represent the concrete and steel fibers in the RC columns and composite beam

sections. Specific modeling recommendations for each of these materials are discussed

in section 4.2.2. For the composite RCS joints, two distinct material models are

employed via rotational springs to represent the two different deformation mechanisms;

these models are discussed in section 4.2.3.

4.2.2 Flexibility-Based Fiber Beam-Column Elements

There are several options in OpenSees to represent the nonlinear behavior of beam-

column elements, one of which is the flexibility or force based element that can capture

distributed plasticity with fiber cross-sections at a number of integration points along the

element. The flexibility-based formulation is based on linear force interpolation

functions that accurately estimate the internal force distribution of members where forces

are applied at each end node (although this does not account for the P-delta moments

along the member length). This derivation does not encounter large discretization errors,

as is generally found in the stiffness-based elements that use approximate displacement

interpolation functions (Neuenhofer and Filippou, 1997). When compared on a one to

one basis, each flexibility-based element is more computationally intensive than a

displacement-based element. However, the benefit of the flexibility derivation lies in the

fact that an accurate answer can be achieved with fewer elements (often a single element

per member for beams and columns in moment frames), whereas displacement-based

elements require more discretization to reach the same answer. This flexibility-based

164

element is referred to as the “nonlinearBeamColumn” or the “forceBeamColumn” in

OpenSees.

The fiber sections at each integration point represent the cross-section of the component

being modeled (i.e. reinforced concrete column or composite steel beam) and are

composed of a mesh of fibers, each of which is assigned a uniaxial material hysteretic

property (i.e. steel, concrete, etc.). In RCS moment frames, these fiber sections are

composed of steel and concrete models to represent materials in the composite steel beam

and the reinforced concrete column. The details of each of these cross-sections and the

material models that compose the fibers are discussed in sections 4.2.2.1 and 4.2.2.2.

4.2.2.1 Reinforced Concrete Columns

The reinforced concrete column fiber section is comprised of confined and unconfined

concrete and steel reinforcement bars. The cover concrete, located outside of the

transverse reinforcement, is considered as unconfined and will quickly begin to spall after

reaching its crushing strength. The core concrete is confined on all sides by the

longitudinal and transverse reinforcement and will behave in a more ductile manner.

Confined and unconfined regions are both modeled with the Concrete02 material in

OpenSees (see Section 4.2.1).

The compression backbone of the Concrete02 model can be defined according to the

modified Kent and Park model (Scott et al. 1982), which adjusts the backbone parameters

( 'ccf , ccε , '

2cf , 2cε ) based on the amount of volumetric confinement provided by the

transverse reinforcement ( sρ ). The maximum stress attained is defined as follows:

''fcc cKf= (4.1)

which is assumed to be reached at a strain of:

0.002cc Kε = (4.2)

The residual strength is defined as:

165

''f 2 0.2c cKf= (4.3)

which begins at a strain defined according to the following equations:

1/ 2' "

'

0.5

3 0.29 0.75 0.002145 1000

m

cs

c h

Zf h K

f sρ

=⎛ ⎞+

+ −⎜ ⎟− ⎝ ⎠

(4.4)

20.8 0.002c

m

KZ

ε = + (4.5)

where:

K = factor defined by '1 s yh cK fρ= + f

sρ = volumetric ratio of transverse steel to core concrete

yhf = yield stress of the transverse reinforcement (MPa)

'cf = concrete compressive strength (MPa)

"h = width of confined concrete measured to the outside of the perimeter

hoop

hs = center to center spacing between hoop reinforcement sets

When calibrated against physical tests, the analytical models consistently overpredicted

the strength of the RC column subassembly tests, and it was reasoned that this was due to

the concrete strength used in the modified Kent and Park model. For this reason, rather

than entering the modified Kent and Park model with the full , a more accurate

solution is obtained when the input strength is set to 0.85 , recognizing that the in-situ

strength of concrete may be less than the measured from concrete cylinder tests. This

difference follows the design provisions for columns and beams in ACI-318 (2002). This

adjustment improves the correlation between the predicted and measured strengths of RC

columns, as will be described later in this section.

'cf

'cf

'cf

The cover concrete is assumed to be unconfined ( 0=sρ ) and as a result will provide

very little ductility. However, it is not recommended to use the modified Kent and Park

166

model to define the backbone for the cover concrete. Using 0=sρ , Kent and Park

model predicts very little ductility in the concrete and does not seem to accurately model

the behavior of cover concrete. Moreover, this definition tends to cause convergence

problems in OpenSees. Therefore, it is recommended that the backbone of the cover

concrete be defined as follows: 'ccf = 0.85 , '

cf ccε = -0.002, '2cf = 0, and 2cε = -0.010.

This definition fits the calibrated subassembly tests and also improves the numerical

convergence. The tension strength of the cover concrete is assumed to be negligible.

The tensile cracking strength, ft, of the core concrete is defined according to the following

equation defined by Carrasquillo et al. (1982):

'0.94 ( ) 11.3 ( )t c c'f f MPa f psi= = (4.6)

where ft and carry the unites shown. The tension stiffening effect is an important

phenomenon that accounts for the interaction between the reinforcement bar and the

surrounding concrete when subjected to tension. This effect provides a smooth transition

in the moment curvature response by allowing the concrete to reach its maximum tensile

stress and then slowly shedding the load until it reaches zero tensile strength. This effect

has been modeled by Stevens et al. (1991) and can be represented linearly between zero

and maximum tensile stress, beyond this point the stress decays as a function of the bar

diameter and the ratio of total steel in the cross-section. Figure 4.4 depicts the typical

tensile response of concrete accounting for this tensile stiffening effect. The concrete

model in OpenSees allows one to model the tension strength decay using either an

exponential decay, as suggested by Stevens (et al., 1991), or a linear decay. The linear

model performed quite well in the calibration studies in Section

'cf

4.2.2.1 and was selected

for its simplicity. The slope of the line is defined as a best fit to the curve computed by

the Stevens et al., (1991) method.

Based on calibration studies presented in Section 4.2.2.1, the unloading stiffness ratio

cu EE=λ = 0.1 is suggested for RC columns.

167

The column reinforcement steel can be modeled in OpenSees using the Steel02 material

model, as described in section 4.2.1. The yield strength of the steel should either be taken

from the measured value or as the expected yield strength, assumed equal to . The

1.25-factor for the expected yield strength is based on the seismic design criteria in ACI-

318-02 (2002). The strain hardening stiffness, , can be taken as the slope of the line

between the measured yield stress and strain to the measured ultimate stress and strain. If

this information is not available, then a hardening slope of 2% of the initial stiffness of

the steel, , is assumed. The parameters that define the transition

between the elastic and hardening branch are set to the default values of

yF25.1

hE

MPaEs 000,200=

5.180 =R ,

, and . 925.01 =c 15.02 =c

The fiber beam column element alone cannot capture the additional rotation in RC

columns as a result of yield penetration and bond slip near the hinge zone. This

deformation occurs due to the relative movement of the longitudinal reinforcing bar with

respect to the concrete at the face of the joint (or footing). This deformation results in the

opening of a gap between the two concrete interfaces e.g. an RC column and footing

interface, as shown in Fig. 4.5. As suggested by Fillipou et al. (1983), the reinforcing bar

bond stress versus slip behavior can be idealized as shown in Fig. 4.6. Bar pullout will

only occur when the anchorage is insufficient to develop the bar strength, which is

unlikely in the seismically detailed members of the RCS frame. However, yielding of the

reinforcement, which is not considered in Fig. 4.6, can lead to significant slip of the bar,

even when pullout does not occur. The rebar slip is calculated as a function of the strain

distribution along the embedded bar and assumed to be zero at the point of zero-bar stress

(i.e. once full bar development is attained, as shown in Fig. 4.5). Models to describe this

type of mechanism are reported by Filippou and Popov (1984) and Mazzoni (1997).

This inelastic bond-slip phenomenon will lead to a reduction in the overall frame stiffness

and less concentrated damage in the column base hinges as compared to a fixed base

model. A simplified approach is taken to capture this effect. Concentrated rotational

elastic springs are inserted between the RC columns and the fixed bases and are assigned

168

an elastic stiffness equal to the rotational stiffness of the column, which essentially

doubles the flexibility of the columns. The spring stiffness is calculated as follows:

3 eff

roti

EIK

L= (4.7)

where:

effEI = Effective stiffness of RC section, defined in Chapter 2, equation 2.5

iL = length to column’s inflection point

This model is based on findings within the literature, which report that bond slip accounts

for up to 50% of flexural deformations in experiments on fixed-fixed reinforced concrete

beam columns (Saatcioglu et al, 1989, 1999). It should be recognized that this approach

is only capturing the additional flexibility of the quasi-elastic loading and unloading of an

RC column, and it does not explicitly account for inelastic effects after column hinging.

This approach is necessary given that base rotation elements are in series with the

nonlinear beam-column, and once either of them begins to plastically deform the inelastic

deformations will concentrate (localize) in one of the two components. For this reason, it

is not advisable to model the inelastic behavior of the bond-slip phenomenon using an

inelastic spring, since there is a potential to localize all the plastic deformations in either

the nonlinear beam-column or the base rotation spring. There are other more

sophisticated methods to handling this bond slip issue, some of which are discussed in

Altoontash (2004), but this simplified technique is adopted as a relatively accurate and

practical way to capture the additional flexibility introduced by bond slip into RC

columns.

Given these material definitions and the bond-slip spring, several code-conforming RC

column subassembly tests were modeled in OpenSees using the flexibility-based fiber

section beam-column element and compared against the experimental results. The test

data includes some extracted from the PEER Structural Performance Database

(http://nisee.berkeley.edu/spd/, Tanaka and Park, 1990) as well as four columns tested in

the NCREE lab (Tsai 2002), which include grouted precast column splices. Selected

details of these column tests are presented in Table 4.1, with further information in the

169

supporting references. Shown in Figs. 4.7 through 4.14 are results of this calibration

study to evaluate how well the analytical models simulate the experimental response.

The tests completed by Tsai (2002) were part of the testing program described in Chapter

3. The specimen names reflect the following attributes: the second letter indicates

whether the column is full (F) or reduced (R) scale, the third letter describes the splice

location either at the column base (L) or 1-meter above the base (H), and the number at

the end indicates the percentage of axial load on the specimen. As shown in Fig. 4.7,

OpenSees adequately captures the response of specimen FFH08. To illustrate the

influence of these elastic bond-slip springs, Fig. 4.8 shows this same FFH08 test

compared to an OpenSees fiber element model with a fixed base connection (i.e. no

springs). While the overall response is similar in Figs. 4.7 and 4.8, it is evident that the

initial and unloading stiffness of the analytical model with the fixed base connection (Fig.

4.8) overestimates that observed in the test. The secant stiffness up to the yield point in

Fig. 4.8 is about twice as large as that in Fig. 4.7. When the elastic base spring is

introduced (Fig. 4.7), the stiffness of the analytical and test model matches up quite well

compared to the element without the spring.

Specimen FFL08 experiences more strength deterioration and pinching than what is

predicted by OpenSees (Fig. 4.9). The deterioration is due to the influence of the grouted

precast spice connectors within the hinge zone and the lack of transverse reinforcement in

this region. These effects are not represented in the OpenSees model. The strength of

specimen FRL08 (Fig. 4.10) is about 20% greater than that predicted by the OpenSees

cyclic model. This strength increase is attributed to an exaggerated influence of the

grouted couplers in this reduced scale column. It is believed that the couplers provided

additional capacity to the hinge region thereby pushing the hinging zone up above the

base of the column. This additional strength provided by the couplers was considered a

in a second OpenSees model, and the monotonic backbone response is also plotted on

Fig. 4.10. This figure reveals that the strength of the specimen is enveloped by these two

different models, but the degradation of the strength is not captured.

170

Specimen FRL60 (Fig. 4.11) contains a very high amount of axial load yet was designed

to fail at roughly the same moment capacity as FRL08. Despite this approach, the

physical specimen reached strengths nearly 60% larger than the predicted value (Fig.

4.11). This overstrength may be attributed to the differences between expected versus

measured material properties, but unfortunately, these details are not available and

therefore the reason for this large difference from the predicted strength is not easily

apparent. Using the expected material properties, the OpenSees model predicts

approximately the same strength as the FRL08 specimen, which was the intention of the

original design. As the column is pushed just beyond its design strength, the concrete

loses its strength very rapidly and the section quickly degrades to residual strength of the

core concrete and the reinforcement bars. This behavior is much different than the

physical test, but given the lack of information regarding material properties, they cannot

be directly compared. This case is specific to columns above the balance point (i.e.

concrete fails prior to yielding of reinforcement bars) and will not be considered in this

calibration study. Further validation of the fiber models to represent RC columns with

high axial loads above the balance point of the section is reserved for future study. Note

that the RC columns in the 20-story building modeled in Chapter 5 does not encounter

the problem discussed here, as all the columns remain below the balance point and

yielding of the rebars precipitates concrete crushing providing a much more ductile

section.

The Tanaka and Park (1990) tests examined the effect of confinement configuration on

the ductility of RC columns, so other than differences in the transverse reinforcement,

each of the columns in tests #2-4 are the same. These tests are configured as a double-

ended setup (as shown in Fig. 4.12) whereas the previously described tests from Tsai

(2002) are the standard cantilever setup. The setups introduce a subtle difference in the

bond-slip characteristics since the rebars in the two opposing columns of the double

ended tests will tend to interact with one another, as is depicted in Fig. 4.12. The

previously described calibration is for cases where the rebars are fully developed (i.e.

rebar stress eventually goes to zero), since this is the condition at the RC column base

hinges where large inelastic rotations are expected. In the double-ended setup, it is likely

171

that the bond-slip spring would be stiffer than the cantilever case given that the rebar are

anchored and stiffened by the opposing forces in the adjacent columns. This effect is

evident in Fig. 4.13, which shows the calibration results of specimen #4 for with (Fig.

4.13a) and without (Fig. 4.13b) the bond-slip spring. These results show that the bond

slip deformations are not as significant for the double ended setup as they are in the

previous cantilever cases. The difference in response is highly dependent upon the test

setup and how large the loading block dimension (d1 in Fig. 4.12) is in the test. Given

this difference, the remaining results from the Tanaka and Park (1990) columns are

shown without the bond-slip spring in Figs. 4.14-4.15.

Overall, the analytical material, bond-slip spring, and fiber beam-column models of the

RC column experiments match the response of the experiments rather well up through

large inelastic rotations. There are some discrepancies (i.e. double-ended bond-slip issue,

high axial loads), but those are limited to cases that are not relevant for the frame

analyses in the present study.

4.2.2.2 Composite Steel Beams

The fiber section for the composite steel beams consists of steel for the beam and slab

reinforcement (when present) and concrete for the composite slab. The beam steel is

represented in OpenSees as the Steel02 material model. The yield strength of the steel

should either be taken from the measured value from a tension coupon or as the expected

yield strength, . The parameter is defined by the AISC Seismic Provisions

(2002) as the ratio of the expected yield strength to the nominal yield strength and is

taken as 1.1 for typical Grade 50 steels. Additional strain hardening factors should not be

used for given that the Steel02 material already has strain hardening built into the

model ( ). The strain hardening factor can be set to b = 0.02 or determined

from measured properties. The isotropic hardening and curve transition parameters are

identical to the definitions for the reinforcing steel (

yy FR yR

yF

sh EEb /=

5.180 =R , , and

).

925.01 =c

15.02 =c

172

Several researchers have studied how to correctly model the slab to achieve a realistic

representation of the ultimate moment capacity of composite beam sections in positive

bending. The primary modeling concern is defining the effective width and the effective

compressive stress of the slab. This information is important because it is used in the

seismic design criteria (i.e. strength check and strong-column weak beam criterion) as

well as in the analytical model. The effective width of the slab that is cited in design

standards is typically intended for the evaluation of the elastic stiffness and strength near

the mid-span of a composite beam. For example, the AISC definition of the effective

slab width ( ) is defined in equation 2.10 and shown graphically in Fig. 4.16. While

the AISC criteria is valid for composite beams under gravity loading, it is unclear

whether or not this effective width can also be applied in cases when lateral loads causes

hinging at the beam ends in a moment frame. For beam hinging in the region adjacent to

the column, the effective width of the slab at the ultimate strength of the section is more

likely related to the slab area which is in direct contact with the column flange (du Plessis

et al 1972). The validity of the effective slab width assumptions described here (and

shown in Fig. 4.16) will be evaluated later in this section.

AISCb

Past research has shown that the concrete compressive strength can reach an effective

stress greater than due to the high confinement of the localized bearing region of the

slab near the column flange. For example, du Plessis et al. (1972), Tagawa (1989), and

Lee (1987) report ultimate effective stresses in the range 1.3 to 1.8 (du Plessis et al.

1972, Tagawa 1989, and Lee 1987). On the other hand, other researchers (Civjan et al.,

2001 and Cheng et al., 2002) who have performed beam-column subassembly tests report

that the ultimate effective stress of the concrete slab was approximately 0.85 over the

column width. However, in these cases the shear studs were not designed to develop

fully composite action (25-35% for Civjan et al. [2001] and 75% for Cheng et al. [2002],

with percentages based on AISC-LRFD definition of composite action) and the beams

often failed by shear stud rupture before the concrete was fully mobilized. Based on

Bugeja et al. (2000) composite beam-column subassembly tests suggest that the effective

'cf

'cf

'cf

173

width is equal to the AISC design specification (Manual 2001) with an effective concrete

stress of 0.85 . However, it can be shown that the strength calculated using the AISC

width and bearing stress of 0.85 is roughly equivalent (within 10%) of that calculated

assuming 1.3 over

'cf

'cf

'cf colslab bb = .

Figure 4.17 shows the test setup and dimensions for the composite beam subassembly

experiments that were considered in this study. Table 4.2 briefly summarizes the key

failure mechanism and general observations for each of these tests. A few of these tests

were simulated in OpenSees using fiber beam-column elements to validate the effective

slab width and stress that is appropriate to use for both design and analysis purposes. In

addition to these two parameters, the strain at which the slab reached its residual strength,

2Cε , (described in section 4.2.1) is another important parameter that affects the ductility

of the slab and influences the element response. The strain corresponding to the

maximum concrete strength ( ccε ) is assumed to be -0.002 and the residual stress of the

concrete after reaching 2Cε is assumed to be 20% of 'ccf . The tensile strength and the

tensile softening properties of the slab are defined in a similar manner to that proposed

for the core concrete (Section 4.2.2.1). The individually calibrated material properties for

each of the investigated subassembly tests are summarized in Table 4.3. Those that were

not simulated in OpenSees are reported as “not analyzed”, although the recommendations

of the researcher are presented in the description column of this table. Note that in the

test by Lee (1987), hinging occurred in the steel columns rather than the composite

beams and therefore the ultimate strength and effective width of the slab cannot be

deduced from this test.

The effective stress, slab width, and the slab ductility parameter ( 2Cε ) were calibrated to

each test and the “best-fit” parameters are listed in Table 4.2 for each of the simulated

tests. For all but the Uang test, the calibration study shows that the effective width of the

slab is best represented by the width of the column ( colslab bb = ) where the concrete

compressive strength is 1.3 . The Uang test is unique given that the test is setup as a 'cf

174

cantilever where the slab not only bears against the column but also against a strong wall

just behind the column. This setup mobilizes a larger effective slab width that is better

represented by approximately 2.5 when the effective stress is assumed to be 1.3 . colb 'cf

The results from the calibration study showed that, as expected, the effective stress of the

concrete is highly correlated with the design and performance of the shear studs. Those

tests where the shear studs were designed to provide a fully composite section (Tagawa

1989, Bursi and Ballerini 1996, Bugeja et al. 2000) performed very well (i.e. higher

moment strength and larger ductility) and attained effective slab stresses of

approximately 1.3 . These well-behaved tests also show that a value of 'cf 2 0.05Cε = is

appropriate to reflect the ability of the slab to achieve high ductilities during larger

excursions.

On the other hand, the tests where the shear studs were designed for a partially composite

section did not perform nearly as well (i.e. less than design strength and low ductility),

with the effective slab stresses reaching only 0.85 for the tests reviewed in this study

(Cheng ICLCS, INUCS and ICLPS 2002, Civjan et al. 2001). Given that the shear studs

are the weak link in these sections, the studs limit the amount of stress that can be

developed in the slab and also control the level of ductility that the section can attain.

Therefore, the stress in the slab is really a function of the shear capacity of the studs, and

the effective stress of 0.85 may deviate if the studs are designed for different levels of

composite action. The ductility of a partially composite section is much less than if it

were designed as fully composite. Accordingly, for these cases, a lower calibrated value

of

'cf

'cf

2Cε as 0.012 is used. This large difference in behavior in both strength and ductility

demonstrates why it is more attractive to ensure a fully composite section rather than

permitting the shear studs to be the critical element in seismically designed beams.

Given the results of this composite beam calibration study, a fully composite beam can be

modeled with an effective slab width equal to the column width ( in Fig. 4.16) and a colb

175

maximum effective concrete stress of 1.3 . These assumptions should be applied when

computing the plastic moment strength of the composite beam section for the strong-

column weak-beam design check as well as for analytical modeling purposes. The results

from the analytical models using these assumptions are compared against the

experimental results and shown in Figs. 4.18 through 4.28. For those tests results in Fig.

4.23-4.28 that were designed as partially composite, the analytical models were treated as

a fully composite section to emphasize the adverse effects of a partially composite

member. Although partially composite beams were briefly investigated in this calibration

study, the focus in this work will remain on fully composite beams. The results from the

simulations demonstrate that OpenSees is able to capture the overall behavior of these

elements.

'cf

The behavior of a composite beam will differ based on whether or not the metal deck is

running parallel or perpendicular to the main girder. Apart from differences in the

effective slab area, when the deck is parallel to the beam, the upper flange of the beam is

continuously braced by the slab, thereby significantly reducing the probability of

buckling in this region during composite bending. When the flutes are running

perpendicular to the beam, the upper flange is only braced when the ribs of the deck are

in direct contact with the flange, which leaves the upper flange more susceptible to

buckling in the unbraced zones. Another factor to consider is the relative effectiveness of

shear studs, depending on the deck orientation. While these aspects of behavior are not

specifically investigated in this study, they are issues that should be considered when

modeling the inelastic behavior of composite beams in moment frames.

4.2.2.3 Convergence issues

A couple of important comments should be mentioned here to improve numerical

convergence of local member and global solution operations in OpenSees. If the fiber

cross-section contains a non-ductile or softening material (i.e. concrete), then it is useful

to finely discretize this region of the section (i.e. increase the number of fibers) so that

this softening effect is smoothly captured and sudden large changes in stress in the

176

section are minimized. However, this should not be overdone, as it increases the

computational time and could potentially lead to numerical instabilities. Using the

analytical model described in section 4.3 as an example, the core of the 650-mm square

RC column section is meshed with approximately twenty 30-mm thick fibers.

The second issue that affects convergence is the number of integration points specified

along the length of the fiber beam-column element. Using the Gauss-Labotto integration

scheme, the information at each of the fiber sections are used to compute the response

parameters at the two end nodes. By increasing the number of integration points, the

nonlinear curvature can be better represented along the length of the element. Increasing

the number of sections to a certain point has a positive effect on element convergence,

although if the number is increased such that multiple consecutive sections are within the

nonlinear hinging region, then convergence problems can arise (particularly when the

section exhibits softening behavior). It should also be recognized that increasing the

number of integration points is roughly proportional to the amount of operations

performed on each element. Based on the experience gained from this study, it is

recommended that the number of integration points be set to 7.

There is also an option in the OpenSees nonlinear beam column element to control the

residual error at the element level by applying iterations within the element flexibility

solution. While this option increases the local element computation, it is highly

recommended since it improves the global convergence of the OpenSees model. If this

iterative approach is not applied at the local level, then the error is filtered into the global

system of equations and dealt with at a global level. Experience in this study is that

reliance on the global system to control the error leads to convergence problems.

Therefore, it is recommended to use the optional error control routine in the flexibility

element and to specify a maximum number of iterations of 10 with a minimum tolerance

of 1x10-18.

177

4.2.3 Composite Joints Elements

The composite joint panels are represented in OpenSees using a 2-dimensional joint

element (Fig. 4.29) that can accurately model the finite joint size effect and the

kinematics of joint deformation. This element has the capability to model large

deformation response of the joint panel, however, this option was found to be

unnecessary in this study given the drift levels examined. The joint hysteretic properties

are defined by an internal rotational spring which can accommodate any number of

moment versus rotation springs.

To accurately model the deformation behavior of composite RCS joints, the internal joint

spring must represent both the panel shear and vertical bearing deformation. Panel shear

deformation possesses characteristics similar to that of the steel model presented in

section 4.2.1 (e.g. Steel02). This mechanism relies on yielding of the steel web panel and

development of diagonal concrete struts, which exhibit fat and stable hysteretic loops, as

shown in Fig. 4.30. Vertical bearing deformations exhibit a pinched hysteretic response

associated with the local crushing of concrete and the opening of gaps above and below

the steel flanges. The hysteretic material model presented in section 4.2.1 can be utilized

to fit the response of vertical bearing deformations, as shown in Fig. 4.31. These two

springs are implemented in series to model the total deformation response of composite

RCS joints.

The two spring models (joint shear and joint bearing) are calibrated against beam-column

cruciform tests from Kanno (1994). These series of tests are also used in the RCS joint

strength model validation studies presented in Chapter 2; and details of these tests are

provided in Section 2.4.9.1. The panel shear (Mps) and vertical bearing strength (Mvb,total)

of each of these tests are determined using the proposed design equations 2.33 and 2.34,

respectively. The test setup and the displacement time history are simulated in OpenSees

and the beam shear versus total joint rotation is compared to the measured test data. Four

of these joints failed in predominately a vertical bearing mode (OJB1, OJB4, OJB5, and

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OJB6-1), with the measured panel shear rotations remaining within the elastic limits.

These tests provide the best opportunity to calibrate the vertical bearing hysteretic spring

of these composite joints. The tri-linear backbone of the hysteretic model, as well as the

cyclic pinching and damage factors described in section 4.2.1, were adjusted in a manner

to best fit all four of the tests investigated. The initial stiffness of the bearing spring

follows the recommendations from Kanno (1993):

2 , 0.01 0.008vb

eb bobo

MK θθ

= = − p (4.8)

where:

Keb = initial stiffness of the vertical bearing spring

θbo = rotation at which the applied moment is equal to Mvb

p = ratio of the applied axial force to the squash load of the column.

The calibrated backbone of this model is presented in Fig. 4.31, with vbM being the

strength of the joint in bearing. The pinching factors, xη and yη , were determined to be

0.2 and 0.5, respectively; and the damage factors, dΔ and Ed , were chosen to be 0.015

and 0.0, respectively. The calibrated results from these joints are shown in Figs. 4.32

through 4.35.

Nine of Kanno’s tests can be classified as failing primarily in a panel shear mechanism,

but unlike the four previously described joints, these joints also have considerable

deformations in the vertical bearing mode. This interaction of the two failure modes

makes the calibration of the panel shear spring slightly more challenging since the panel

shear mode is not completely isolated from the bearing mode. Given that the parameters

of the bearing spring have already been set, these nine shear failure tests will be used to

calibrate the panel shear spring. The specified yield strength of the panel shear (Steel02)

model should be set to the computed joint shear strength ( psM ), as determined from

equation 2.33 in Section 2.4.8. The stiffness of this spring follows the recommendations

from Kanno (1993) per the following equation:

2

, 0.01 0.0067pses so

so

MK θ

θ= = − p (4.9)

179

where:

Kes = initial stiffness of the panel shear spring

θbo = rotation at which the applied moment is equal to Mps

The kinematic hardening slope is taken as 2% of the initial stiffness, Kes. The remaining

parameters in the Steel02 model that define the transition of the curve between the elastic

and the hardening branch are set to the following values: , , and

. The calibrated results for these nine joints are shown in Figs. 4.36 through

4.44. Note that the pinching behavior in these hysteretic plots is primarily coming from

the contribution of the joint bearing spring. In several of the tests (such as OJS7-0, HJS1-

0, and HJS2-0), the pinching is not adequately captured. This phenomenon has less to do

with the calibrated hysteretic models of the joints springs and more to do with the actual

prediction of the relative joints strengths. If the panel shear strength is slightly

underestimated then it is possible that the joint deformations localize in this spring. On

the other hand, if the prediction of the shear strength had been slightly increased, the

relative strengths of the two springs may be such that the deformations become more

distributed between the two springs. This provides some insight into the variability that

is inherent in these nonlinear models. Figure 4.45 shows the contribution of each spring

to the total rotation for the OJS3-0, OJS4-1, and OJS5-0 tests. Here, it is evident that the

two springs in series predicts larger panel shear rotations and underestimates the bearing

deformations in this test. Once the panel shear spring begins to yield it limits the amount

of force transmitted through the bearing spring and therefore dominates the inelastic

deformation response. This type of behavior is a result of the fact that the actual panel

shear strength is slightly underestimated in these cases.

5.180 =R 1 0.96c =

15.02 =c

4.3 Test Frame Validation Study

An analytical model of the 3-story test frame discussed in Chapter 3 is created using the

elements and techniques described in Section 4.2. Every effort is taken to reasonably

account for laboratory conditions such as member dimensions, measured material

strengths, and test loading protocol. The ultimate goal is to compare the analytical to the

experimental response in an attempt to validate the nonlinear frame elements described in

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this chapter. It should be acknowledged that differences will undoubtedly occur between

the analytical and experimental response, but ultimately the point is to verify where and

why these discrepancies occur, how the models could be improved to better capture the

behavior, and what applications are appropriate for the current models given the

limitations present.

A general schematic of the OpenSees model is presented in Fig. 4.46. The reinforced

concrete columns and composite steel beams are represented by the flexibility-based fiber

beam-columns described in section 4.2.2.1 and 4.2.2.2, respectively. Each of the

composite joint panels is represented by the 2-dimensional joint element described in

section 4.2.3. Bond-slip springs, discussed in Section 4.2.2.1, are placed between the 1st

floor RC columns and the fixed base since large inelastic rotations are expected in this

region and bond-slip will tend to play an important role in global deformations. The 3rd

floor columns are discretized into two elements to model the change in longitudinal

reinforcement at approximately one-third the height of the floor. Fictitious leaning

columns are also modeled to simulate the P-delta effect caused by the gravity loads from

one-half of the total building area (which equals approximately 3500kN at each floor).

The leaning columns are not meant to provide any flexural resistance, so each joint must

be free of rotational restraint. This is accomplished by using co-rotational truss members

(2nd floor column and 1st-3rd floor rigid links) mixed with elastic beam-column elements

(1st and 3rd floor columns). All of these elements have a very large axial stiffness to

ensure that there are no unrealistic vertical deformations in the leaning column when the

gravity loads (equal to one half the building weight) are applied.

The dead and live loading and the seismic mass in the analytical model follow the same

assumptions as presented for the test frame in Section 3.3.2. The pseudo-dynamic

loading protocol is simulated in OpenSees using the same input ground motions applied

at the base nodes of the structure (e.g. the actuator forces are not simulated, but rather the

base nodes are excited using the same earthquake acceleration time histories). These

events are applied consecutively to ensure that the cumulative damage effect of the test

frame is represented in the analytical model. Twenty seconds of zero ground acceleration

181

is provided between each ground motion excitation in order to damp out all of the

transient vibrations between each loading event.

4.3.1 Errors within the Pseudo-Dynamic Testing Method

Before proceeding with the comparison of the measured and simulated responses, it is

important to recognize that there are a couple sources of error inherent in the pseudo-

dynamic testing algorithm that could potentially lead to variations from the actual (real

time) dynamic frame response. Two of the most important errors are described below:

1. Since pseudo-dynamic testing is performed quasi-statically, strain rate effects can

have an impact on the inelastic behavior of the test frame. During the “hold”

phase of the pseudo-dynamic algorithm (Fig. 4.47), the data acquisition system

collects the data and the system of equations is solved to obtain the next

displacement increment. During this stage, the actuators are maintaining a

constant displacement (within some tolerance) over a period of time, which can

lead to some relaxation of inelastic hinges, particularly in RC columns where

cracking and other types of softening occur in real time. As a result, the inelastic

strength of a system is underestimated when tested quasi-statically as compared to

a system that is tested dynamically (Mahin et. al., 1985).

2. It is impossible to impose the exact computed displacements to the structure with

actuators, so a tolerance is set at each time integration step. Even with a very

small error (±0.1mm), these errors can build up over the duration of the

earthquake and can cause errors in the algorithm. In multi-degree of freedom

systems, higher modes contributions are highly vulnerable to these errors and can

even make the test system unstable. The pseudo-dynamic algorithm implemented

in the test of the composite RCS frame used the explicit Newmark method as the

numerical integration scheme. This particular method has been found to

minimize the propagation of error that is a result of experimental inaccuracies

(Mahin et. al., 1985). Regardless, this is less of a problem in the 3-story test

frame given that the effect of higher modes is relatively small.

182

Therefore, it is important to recognize when evaluating the analytical models in this

section that the differences between the measured and simulated response may not be

completely due to problems within the modeling assumptions. Potential manifestations

of these errors will be discussed in the following sections.

4.3.2 Comparison to Experimental Global Response

The first-mode period of the analytical model ( 1 1.0secT = ) matches the measured period

of the test specimen exactly, indicating that the assumptions influencing the initial elastic

properties of the frame have been adequately captured. The test frame was subjected to a

couple preliminary pseudo-dynamic events that were well within the elastic region of the

response which were also captured quite well by the analytical model. These results were

not reported in Chapter 3, but they revealed excellent agreement for imposed drift ratios

up to 0.1%. Both of these checks were used to initially validate the analytical model as

well as the test setup and the pseudo-dynamic algorithm.

The analytical model is subjected to the same loading protocol as the test specimen,

including the truncated records and the realignment (re-straightening loading) imposed

after the 2/50 event (see Section 3.4.2 for further description of the loading protocol).

The results from each of these tests are presented in Figs. 4.48 through 4.52, each of

which contains the time histories for the roof displacement and base shear as well as the

maximum and minimum of story shear and interstory drift ratios. The first event, the

50/50 Chi-Chi ground motion, is the least damaging of all events and the measured and

calculated response plots of the frame (roof displacement and base shear time history)

agree well up until approximately 25 seconds, beyond which there seems to be a phase

shift developing between the experimental and analytical histories. This shift is

attributed the change in natural period due to inelastic softening that is occurring in the

test frame but is not accurately captured in the analytical model. This softening behavior

is likely a result of cracking in the slab and columns and perhaps from slippage in the

bolted steel beam splices. In addition to this, inherent features of the pseudo-dynamic

loading algorithm, described in section 4.3.1, may be causing some of the softening

183

response due to relaxation of force in the RC column hinges. This period shift can be

tracked by performing a Fourier analysis on a sliding window of the time history

response. The results of this analysis are shown in Fig. 4.53 and 4.54 for the analytical

and experimental response, respectively. The contours in these figures represent the

peaks of the power spectral density function, which correspond to the principal frequency

(or the inverse of the period) during that time region of the event. These figures show

that while the experimental response clearly softens to 1.3 seconds (60% of original

stiffness), the analytical response hovers just above 1.0 seconds. In spite of this lack of

agreement in the change of stiffness and period shift, the maximum and minimum

interstory displacements and story shears (Figs. 4.48c and 4.48d) are captured fairly well,

with differences in displacements ranging from 2% to 30% and story shears from 3% to

10%.

Analytical versus experimental comparisons of the first design level event (10/50 Loma

Prieta 1a and 1b) are shown in Figs. 4.49 and 4.50. The residual drifts in both the

analytical and experimental models have been removed in these and all subsequent plots

so that only the transient response is compared. During the first truncated event (Fig.

4.49), the analytical model is within 35% of the peak displacements and 21% of the

maximum base shear of the test frame. The roof displacement of the second complete

event (Fig. 4.50) shows that the analytical model, other than the first large excursion,

consistently underestimates the deformations of the frame. Calculated peak

displacements are within 33% of the measured values. The base shear (Fig. 4.50b, 4.50b)

is captured rather well by the analytical model during the larger excursions of the record.

After the first couple of large excursions, the phase shift again becomes apparent in both

the roof displacement and base shear time histories. Predominate frequency versus time

graphs are shown in Figs. 4.55 and 4.56 for the analytical and experimental results,

respectively. These graphs can been further interpreted by extracting the periods at

which the peaks occur at each time step and plotted versus time as shown in Fig. 4.57.

This figure shows that while there are some times where the predominate period of the

analytical response is large; most of the time it remains around 1.0 second. This is in

contrast to the period of the experimental response which lengthens to approximately 1.7

184

seconds. Again, the cause of this shift is perhaps a combination of the stiffness

degradation in the analytical models and the force relaxation effect caused by the pseudo-

dynamic algorithm.

Figure 4.51 summarizes the analytical and experimental comparisons for the maximum

considered earthquake event (2/50 Chi-Chi). It is apparent from the roof displacement

time history (Fig. 4.51a) that the analytical model is responding with a higher frequency

(shorter period) than that of the test frame. This is evident in the predominate period

versus time plot shown in Fig. 4.58, which shows that the test frame is responding at a

period of approximately 1.7 seconds while the analytical response is predicting about 1.3

seconds. It should be noted, that severe local beam flange buckles occur during about 18

seconds into the record, which cannot be modeled by the fiber section element. This

additional flexibility in the test frame is evident in the longer period and much larger

interstory drifts observed during this event, particularly after about 20 seconds into the

record (Fig. 4.51c). The excursion at approximately 24 seconds is not picked up by the

analytical model and results permanently offset between the two responses. Differences

between the model and the test frame’s maximum displacements range from 2% to 73%,

while the agreement in story shears is much better, with a range from 4% to 16% between

the measured and calculated values.

The final pseudo-dynamic loading event repeated the design level event (10/50 Loma

Prieta). The results of the analytical model are compared with that of the test frame in

Fig. 4.52. As shown in Fig. 4.52a, the model drastically underestimates the first large

excursion of the test frame that occurs at about 5 seconds into the event. This is

important because beyond this point the test frame never seems to recover from this

inelastic push and simply oscillates about the -100mm position. This is particularly

evident at the end of the record (40 seconds) where the analytical model is oscillating at a

drift of less than half of that of the test frame. Just as in the 2/50 event, it is evident that

the fundamental period of the test frame has lengthened beyond that of the analytical

model (1.7 to 2.0 seconds versus 1.3 seconds, respectively), as is shown in Fig. 4.59. The

predicted base shear history (Fig. 4.52b) consistently overestimates the true value which

185

is probably a result of two things; (1) the limitation of the fiber elements to model local

buckling and strength reduction of in steel beams and (2) the idealized behavior of the

RC column base hinges and their strength deterioration. As described in Section 3.6.2,

prior to this event, most of the severely hinged elements were thought to be at a “near

collapse” damage state, or past the level at which repair was still an option. The

associated behavior modes, particularly the extensive beam local buckling, are not

captured by the analysis, which explains the inaccuracies in modeling the overall frame

response. The errors in predicting the maximum displacements for this event were in the

range of 2% to 30%. The story shears were predicted with an error that ranges between

3% and 50%.

The final pushover is also simulated in the analytical model and the comparison to the

experimental results is shown in Fig. 4.60. It is quite apparent that in the initial stages the

analytical model is significantly stiffer than the actual test frame (approximately 1.9

times as stiff). This again confirms that the simulated model underestimates the amount

of stiffness degradation that takes place in the test frame. Despite the large difference in

stiffness, the ultimate strength of the analytical model is within 7% of the measured

strength of the test frame. This indicates that the plastic strengths of the composite

beams, RC columns, and composite joints are captured rather well by the analytical

model.

4.3.2.1 Comparison of First and Second Design Level Event

As discussed in Section 3.4.2, the 10/50 1989 Loma Prieta event was applied before and

after the maximum considered event (1999 Chi-Chi record) to examine the response of a

heavily damaged frame. Analytically, this allows the opportunity to validate how well

the models capture stiffness and strength degradation that occurs through these events.

The actual measured roof displacements for both the first and second 10/50 Loma Prieta

events are shown in Fig. 4.61. As shown, there is a quite noticeable difference between

the measured response of the first and second event, with a significant phase shift

occurring in the latter event. The elongation of the period between these events has been

186

discussed in Section 4.3.2. This same plot is shown for the analytical results in Fig. 4.62.

One point to notice between the two simulated events is that they seem to be oscillating

about different permanent displacements at the end of the record, where differences are

first seen at the excursions between 5-6 seconds. Despite these differences, which seem

to stem from only a couple of the major excursions, the two responses look strikingly

similar and show only a very small phase shift (not nearly as large as in the measured

results). This again points to the lack of stiffness degradation in the analytical models,

where even after being subjected to the 2/50 event, the stiffness of the frame did not

experience an appreciable degradation.

4.3.3 Comparison to Experimental Local Response

Over three hundred data channels were recorded during the test, with a large majority of

these dedicated to tracking the local response of the beams, slabs, joints, and columns.

While a select number of the plots were shown in Chapter 3, a more complete set is

presented in Cordova et al. (2005). This section will extract a couple of the measured

beam, column, and joint hysteretic plots for each pseudo-dynamic event and compare

them to the analytical results predicted by OpenSees. These plots are shown in Figs. 4.63

through 4.77. The OpenSees response is represented as a dashed line while the measured

test response is shown as a solid line. The moments for the instrumented response are

estimated from strain gauges in the elastic portions of the beams and behavioral

assumptions informed by the OpenSees results (i.e. column inflection points and shear

distribution). It should be recognized that the hysteretic response plotted from the

measured values are subject to a number of assumptions in the force distributions and

when pushed to larger excursions there are some errors due to disruption of the tiltmeters

(e.g. large local buckling caused out of plane distortions in the tiltmeters).

A couple of the composite beam hysteretic plots are shown for each event in Figs. 4.63

through 4.67. In Fig. 4.63, it is evident that the analytical models are picking up the

initial stiffness of the composite beams and correctly predicts that they remain relatively

elastic during the 50/50 event. The first design level event pushes the beams further into

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the inelastic range (Figs. 4.64 and 4.65), which seems to be accurately captured by the

fiber beam elements. The 2/50 event produce the largest inelastic excursions of all

pseudo-dynamic events, which resulted in the formation of large local buckles in the

lower flanges of the steel beams, a phenomenon that cannot be modeled with a simple

fiber section element. One of the primary assumptions in the fiber models is that plane

sections remain plane, which allows the modeling of steel yielding and concrete crushing

and cracking. This fundamental difference in behavior is apparent in Fig. 4.66, with the

1st-floor beams (1B1S050) reaching measured rotations of approximately -0.07 radians

during the largest excursion, which is underestimated by the analytical model by a factor

of 3.5. This shortcoming is something that must be acknowledged when using fiber

beam-column sections and can only be corrected by either (a) supplementing this model

with semi-empirical degrading material fibers, or (b) by using a different type of element

altogether (e.g. nonlinear hinge). The composite beam behavior in the final 10/50 event

is generally modeled well, as shown in Fig. 4.67.

Selected hysteretic response plots for the RC columns are shown in Figs. 4.68 through

4.72. As shown in Fig. 4.68, the analytical model correctly predicts the stiffness and a

moderate amount of yielding in the 1st floor column base hinges. For the first design

level event (10/50-1a and 1b in Figs. 4.69 and 4.70), the fiber models seem to capture the

strength of the columns rather well, yet fail to pick up some of the pinching that is taking

place in these hinges. This is similar to the 2/50 event (Fig. 4.71), where the strength is

captured fairly well, but the amount of pinching that occurs in the test is not modeled as

well as one would like. This difference in behavior again has to do with the fundamental

assumption in fiber models that plane sections remain plane. In the case of the RC

column hinges, there is likely slip occurring between the reinforcing bars and the

surrounding concrete within the hinge zone, which would tend to soften the response

when unloading and reloading and therefore lead to more of a pinched response before

attaining its full plastic moment. The final 10/50 event also exhibits similar trends, where

the analytical model represents the strength well but underestimates the hysteretic

pinching response. It is also apparent that while the stiffness of the RC columns has

degraded throughout each of the loading events, the analytical models roughly maintain

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their original stiffness. This is most apparent in the comparison of response in the 2/50

event (Fig. 4.71) and the final 10/50 event (Fig. 4.72).

Samples of the joint shear versus joint rotation plots for all events are shown in Figs. 4.73

through 4.77. Results from the 50/50 event (Fig. 4.73) show that the initial stiffness of

the analytical model matches that of the measured response rather well, yet there is some

very minor inelastic action that is not being picked up by the OpenSees model. The

moments of the 1st floor joint (1J3 in Fig. 4.73) for the 10/50-1a event seems incorrectly

estimated as the stiffness of the joint is much lower than anticipated. This is thought to

be the result of errors in predicting the internal forces in the test frame based on the

estimation procedure described in Cordova et al. (2005). Unfortunately, these errors

cannot be resolved since there were no direct measurements of the forces in the

indeterminate test frame. Joint 2J3 in the first design event (10/50-1a and 1b in Figs.

4.74 and 4.75) attain roughly the same amount of joint rotation as the 50/50 event, which

seems to be sufficiently replicated in the analytical model. On the other hand, joint 1J3

seems to show slightly more joint rotation than the analytical model, which can perhaps

be attributed to the fact that these measurements were inferred from surrounding beam

and column tiltmeters and may include additional rotation from these members as well.

During the 2/50 event, joint 1J3 (Fig. 4.76) shows a considerable amount of inelastic

cycles, which is considerably underestimated by the analytical joint model. Again, given

the level of damage observed in these joints, these large measured joint rotations seem

unrealistic and are likely a result of problems with the tiltmeters. Fig. 4.77 shows that the

joint 2J3 is remaining relatively elastic during the final 10/50 event, which is adequately

simulated by the analytical joint model. The analytical model slightly underestimates the

amount of inelasticity and energy dissipation that occurs in joint 1J3. The fact that the

level of inelasticity is not well represented by the analytical model for the last two events

may have less to do with the validity of the joint model and more to do with the

interaction of these joints with the surrounding elements and the distribution and

redistribution of forces during the event. In other words, some small errors in modeling

the surrounding elements may lead to an incorrect force distribution that does not push

the joint models to large moments which can produce inelastic joint response.

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4.3.4 Residual Drifts

The importance of residual displacements in a structure after a major earthquake and their

role in performance based earthquake engineering has recently become a topic of much

interest (Ruiz-Garcia 2005). The evaluation of these permanent displacements is

important for both the repairability of the building and its capacity to withstand

aftershock excitations. The results from this test frame provides an opportunity to verify

how well the residual deformations in a moment resisting frame can be captured by an

structural analysis program such as OpenSees. Each of the pseudo-dynamic events

produced a finite amount of residual drift in the test specimen. For all of the events

through the 2/50 loading event, the residual drifts were allowed to accumulate in the test

frame, where each subsequent event was imposed to the frame relative to its permanently

deformed state. After the 2/50 event, the decision was made to straighten the frame as

much as possible to avoid exceeding the stroke limit of the actuators during the final

10/50 loading event. This straightening procedure is simulated in the analytical model so

as to provide a realistic simulation of the full loading history.

The measured and analytical residual drifts after each pseudo-dynamic loading event are

compared in Fig. 4.78, where the thicker of the two lines is the measured value and the

thinner line is from the OpenSees simulation. The prediction error is also reported on the

figure. For the first 50/50 event, the measured residual drifts are relatively small (0.1%

residual interstory drift), which makes the comparison to the analytical predictions not

very interesting, particularly in the 1st floor where the analytical prediction is off by less

than 3 millimeters yet the error percentage is close to 200%. Measured residual

deformations increase to 0.5% in the 1st floor during the second event (10/50-1a), with

the predictions by the analytical model fairing rather decently with a general

representation of the deformed shape and maximum error of 33%. For the last three

events (10/50-1b, 2/50, and 10/50-2), the analytical prediction of the residual

displacements are not very accurate, with prediction errors ranging from 45% up to

134%. These large errors in the prediction of residual displacements should be expected

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given the great number of factors during an inelastic time history analysis that can

influence the final deformed state of the building. At the element level, some of these

include the variability of the strength and stiffness of the models, the degradation of

stiffness, and the unloading and reloading stiffness. These in turn influence the softening

of the structural model which therefore affects how the model responds to the excitation.

It is easy to see that if any one of these parameters is altered either in the input or as a

result of the excitation, the remainder of the event will be affected and the permanent

deformations will be changed as a result. It is difficult to foresee a model that would be

able to consistently and accurately capture the residual deformations on such a large scale

given all of the variables that influence the results. This suggests that a probabilistic

approach is required to evaluate the residual drift demand on a structure where the

variability of several of the key modeling parameters is considered over a suite of ground

motion records. This sort of approach has been recently investigated by researchers such

as Ruiz-Garcia (2005).

4.3.5 Time Evolution versus Predetermined Analysis

There is an important distinction to make on how analytical models are typically

calibrated versus how they ultimately perform in a nonlinear time history analysis. The

typical method to validate models is to compare their response to a series of subassembly

tests, as was done in Sections 4.2.2 and 4.2.3. The way this is typically accomplished is

by subjecting the analytical model to the displacement history that was imposed on the

subassembly test and then compare the force versus displacement hysteretic response.

Given that the displacements were predetermined in this process and the analytical model

is guaranteed to reach the same drift levels, the comparison between the model and the

test comes in the form of the maximum strengths, the initial, unloading, and reloading

stiffness, and the strength and stiffness deterioration. This is not an exhaustive list, but it

does cover some of the key parameters typically scrutinized in calibration studies. In the

end, the goodness of fit of the model is based on how well the simulated response

represents the measured response. This process is then repeated for multiple

subassembly tests and compromises are made in each of the tests in order to generate

191

final recommendations that can be generally applied to a range of component behaviors.

A typical result of this process is shown in Fig. 4.79, where the hysteretic model has been

fit to a number of composite joints tests in order to produce the results seen in the figure.

While the calibration shown in Fig. 4.79 is considered to be a good fit for the composite

joint model, there are several subtle differences that are pointed out in the figure that can

potentially lead to large differences in response during a time evolution analysis. These

subtle differences are typically always present in these types of calibration studies. In a

time evolution analysis, both the force and displacement are unknown prior to the test,

and all of these subtle differences play a more critical role in the evolution of the

response of the structure than compared to the displacement controlled simulations of

subassembly tests.

4.3.6 Comments on Analytical Models

It is evident that there are some limitations to the use of the fiber beam-column elements,

one of which stems from their fundamental assumption that plane sections remain plane

(PSRP) and normal to the longitudinal axis. This assumption ensures that all nonlinear

behavior in the section is a result of material nonlinearities (i.e. steel yielding, concrete

crushing, etc.) and all strains and stresses act parallel to the longitudinal axis of the

member. In the behavior witnessed in the test frame, this assumption is violated in three

important ways:

1. During large inelastic excursions, the steel beams experienced local buckling in

lower flange and lower half of the web. This behavior resulted in strength and

stiffness degradation in the hinge region, contributing to an overall increase in

frame flexibility that ultimately led to much larger floor displacements than what

was predicted in the analytical model. Such behavior is not represented by the

fiber models.

2. It is evident that there are cases where the pinched response of the RC column

hinges are not adequately captured by the fiber section model and it is likely that

bond deterioration and slip within the hinging zone is a large contributor to this

behavior. The rebars and the surrounding concrete do not have perfect bond and

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slip occurs along the interface of the two materials delaying the mobilization of

the force in the rebar. This phenomenon softens the response of the hinge which

leads to the pinched behavior in the measured response.

3. The RC column base hinges were subjected to significant plastic rotations

throughout the loading history of the test frame. As a result, the concrete within

these hinges was significantly deteriorated to the point that during the final

pushover test the rebars were carrying nearly all the moment and shear. This type

of failure seemed to be a result of a combination of extensive plastic hinging

followed by progressive shear failure. The fiber element model does not capture

this sort of failure mechanism.

The impact of the first two behavioral effects can be significant, and tends to increase the

flexibility of the hinges and the entire system. Both of these effects violate the basic

PSRP assumption of the standard fiber section model and, therefore, are difficult to

incorporate into these models without introducing adhoc techniques such as manipulating

material properties. A logical alternative would be to provide an additional spring in

series with the fiber elements to account for either the bond slip or local buckling

behavior. While this conceptually makes sense, these springs would end up dominating

the response of the hinge once they began to soften therefore limiting the amount of

plastic rotations that would occur in the fiber section. This sort of approach would be

better suited to simply model all nonlinearities in a rotational spring using more of a

lumped plasticity approach. The third point is important as well, although it became

important only after significant deterioration of the column hinge during the final

pushover of the frame. It seems unreasonable to expect the fiber beam-column element

to represent the behavior of this column after such a significant amount of damage. This

type of behavior may be better suited to be represented by a P-M yield surface model

(Kaul 2004) where the hysteretic properties can be controlled up through significant

strength and stiffness loss.

In addition to the bond slip effect on the column stiffness, there was also an overall

degradation of stiffness over the series of loading events that was not adequately captured

by the analytical model. This resulted in a phase shift between the predicted and

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measured response, which indicated that the period of the test frame was elongating more

than that of the analytical response. In general, once the first-mode period of two models

begins to deviate, this leads to a divergence in the response and it becomes quite difficult

recover and converge to a similar answer. In addition to bond slip and local buckling,

there are several likely sources that contribute to this degradation of stiffness:

1. The measured response of the RC columns shows a general degradation in

stiffness that may be a result of the deterioration of the concrete in the hinge zone.

Another contributing factor is the degradation of the unloading and loading

stiffness which seems to stem from the previously described bond slip issue.

2. Inelastic shear deformations in the RC columns may also contribute to the

flexibility of the test frame and the elongation of the natural period.

These issues can be significant in terms of the final behavior of the moment frames. The

issue with modeling bond slip has already been discussed, but the new issue of

deterioration of concrete can be handled within the material model level by incorporating

a stiffness degradation parameter such as one that might be a function of cumulative

plastic strains or other damage indices. Shear deformations can be incorporated into the

analytical model using inelastic shear springs in series with the fiber element models.

While first thought to be relatively insignificant, under the large interstory drifts some

shear cracking was observed in the 1st floor columns.

An important engineering demand parameter that directly translates to the cost of repair

is the amount of residual drift in a building following a large earthquake. In this study it

was found that the permanent deformations are perhaps the most difficult index to

capture in a frame subjected to dynamic loading. The residual displacements are

dependent on a number of different factors, all of which can significantly affect the final

results. This potential for variability suggests the need for a probabilistic evaluation of

the residual drift demands on a structure.

It is evident from the response of the test frame and the comparative studies of the

analytical models that the composite action between the steel beams and concrete slab

was maintained throughout the entire loading protocol. Recall that this was also

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validated in the test specimen by examining the condition of the slab and the shear studs

after the completion of the test (see Section 3.6.3). The behavior of the composite beams

reinforces the recommended calibration parameters presented in section 4.2.2.2.

4.4 Damage Indices

In this section, the OpenSees results are interpreted using local damage indices and

related to the physical damage and performance limit states in the frame. These limit

states are referred to as specific damage designations used in FEMA 356 (2000) and

similar standards, such as immediate occupancy, life safety, and collapse prevention.

Immediate occupancy corresponds to the onset of structural damage while collapse

prevention is the point in which the structural system is becoming unstable. Life safety is

an intermediate level that accepts a certain level of damage to structural and non-

structural elements, but ensures the general safety of the occupants. While system

damage descriptions of this sort are helpful to describe acceptance criteria and

performance targets, it is recognized that more explicit and detailed models are currently

under development by PEER and other organizations.

4.4.1 Damage Model

The local damage index presented herein is based on the work of Mehanny and Deierlein

(2001). Chief characteristics of this index are to (1) account for cumulative damage, (2)

reflect the temporal effects of loading sequence, and (3) readily accommodate the

response of structural components with unsymmetrical behavior, e.g., composite beams.

The index is described by the following expression,

( )

( )( )current PHC FHC,

1

FHC,1

| |

|

n

p pi

n

pu p ii

D

βα

θ βα

θ θ

θ θ

+

+

+ +

=+

+ +

=

⎛ ⎞+ ⎜ ⎟

⎝=⎛ ⎞

+ ⎜ ⎟⎝ ⎠

∑

∑

i⎠ (4.10)

where inelastic component deformations (expressed symbolically as θ) are distinguished

between primary and follower cycles and accumulated over the loading history. A

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Primary Half Cycle (PHC) is a half cycle with an amplitude that exceeds that in all

previous cycles, and the Follower Half Cycles (FHC) are all the preceding and

subsequent cycles of smaller amplitude, including the previously eclipsed PHCs. The

denominator term ( )puθ+

is the plastic rotation capacity of the element under monotonic

loading in the positive deformation direction, and α, and β are calibration parameters. A

similar damage component is defined for negative deformations. The positive and

negative indices are then combined into a single damage index as follows,

−θD

( ) ( ) γ γθ

γθθ

−+ += DDD , where γ is a third calibration parameter. Component failure is

defined when ≥ 1.0. The following default parameters are recommended for RC

columns and composite beams: α = 1.0 β = 1.5 and γ = 6.0 parameters. For composite

joints, the recommended values are α = 0.75, β = 3.0, and γ = 5.0.

θD

The maximum rotation capacity, ( )puθ+

, θ of seismically detailed RC columns is

assumed to be a function of the ultimate compressive strain in the confined core concrete.

The ultimate compressive strain, calculated following Paulay and Preistley (1992), is

limited by the tensile rupture of the confining transverse reinforcement. The plastic

rotation capacity for steel beams is a function of the relative influence of lateral torsional

buckling versus local flange and web buckling based on an effective lateral slenderness

ratio (Kemp and Dekker, 1991). The ultimate plastic rotation for composite joints is

determined from an empirical relationship based on tests performed by Kanno (1993),

who defined this capacity as the point where the connection resistance drops to below 0.8

times its maximum strength. Further details on how to compute the plastic rotation

capacities of these components can be found in Mehanny and Deierlein (2001). Table 4.4

summarizes the plastic rotation capacities found using these methods for each of the

components of the test frame.

Note that the predicted plastic rotation capacities for the RC columns are rather large,

particularly in the exterior columns. Given the low axial load and the fact that these

columns are under-reinforced, the RC column section must experience a large amount of

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hardening prior to the concrete reaching compressive strains that would fracture the

hoops. Therefore, while the calculated rotation capacities in Table 4.4 are consistent with

the model recommended by Paulay and Preistley (1992), this model does not consider all

possible failure modes in the column (e.g., reinforcing bar buckling or fracture).

Fardis et al. (Fardis et al. 2003; Panagiotakos et al. 2001) assembled a comprehensive

database of experimental results of RC element tests. The segment of this database

includes a total of 230 monotonic tests of rectangular columns having code-conforming

detailing and failing in a flexural mode. From this data set, they define the "ultimate"

chord rotation as a reduction in load resistance by 20% or more under either monotonic

or cyclic loading. Using this definition, approximately 30% of the columns in their

database have a rotation capacity greater than 0.1 radians (10% drift ratio) with two-

thirds of these falling within 0.1-0.2 radians (10% to 20% drift ratio). This implies that

the computed plastic rotations for the interior columns (Table 4.4) are within the range

expected in monotonic tests. However, the predicted rotation capacities of the exterior

columns (0.3-0.4 radians) are too large, and in retrospect, should be reevaluated

considering other sources of failures (i.e. bar buckling, strength deterioration, etc.). One

alternative approach may be to utilize the empirical equations to predict chord rotations

developed by Fardis and Panagiotakos, which are based on the comprehensive data set of

RC element tests previously discussed.

This damage index can be roughly distinguished into four divisions that correlate to the

damage state of the element. These divisions are typically broken up into the following

damage levels: insignificant, moderate, significant, and complete loss of resistance.

Table 4.5 shows the original ranges of damage index value and the corresponding

damage level state description, as suggested by Mehanny and Deierlein (2001). The

additional column in this table shows proposed adjustments to these damage index ranges

as validated through the observed damage in the test frame. These index values and the

corresponding damage levels are investigated in the following section.

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4.4.2 Plastic Rotations

The simulated plastic rotations are directly obtained from an element recorder in

OpenSees. This is an internal command that computes the elastic stiffness of the element

to find the total elastic rotation at each end given the forces on each node. These are then

subtracted from the total rotations to obtain the plastic rotations in the member.

The measured plastic rotations are obtained by making an assumption on the elastic

stiffness of the component’s hinge, which coupled with the estimated force demand

(derived in Chapter 3) could then estimate the elastic rotation of the hinge. This is then

subtracted from the total rotation measured by the tiltmeters to obtain the plastic hinge

rotation.

4.4.3 Overview of Damage after Each Event

Using the plastic rotation output from the OpenSees model, component damage indices

for all members and joints in the frame are calculated for all of the pseudo-dynamic

loading events. The results of this process for all of the frame elements (columns, beams,

and joints) are summarized in Fig. 4.80 through 4.84 for each of these events. The

damage indices are reported as percentages (100% = 1.0); and for clarity, values below

Dθ = 0.3 (30%) are not shown in these figures. Recall that the observed damage state of

the frame after the 50/50 earthquake is limited to minor concrete cracking and steel beam

yielding, requiring little if any repair (see Section 3.6.2 for further details). The Dθ-

values for a majority of the elements after the 50/50 event are less than 30 – 40% (Fig.

4.80), which is consistent with the observed damage. However, there are several

members that reach higher Dθ-values, such as the 3rd floor beams, which indicate that the

analytical model and the damage index are overestimating the amount of damage in these

elements. In particular, several of these 3rd floor beam hinges have Dθ-values close to

70%, suggesting that there is some significant hinging and local buckling taking place,

neither of which physically occurred in the members. In the test frame there was no local

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buckling of any of the steel beams during the 50/50 event and only very slight yielding,

which was only noticed due to minor flaking of the paint in the hinge zones.

Figure 4.81 and 4.82 depicts the values of the damage indices after the first 10/50 event

(segment 1a and 1b, respectively). The RC column base hinges are now reaching values

up to 78% and 60% for the interior and exterior columns, respectively, predicting that

there is some moderate to significant hinging occurring in these regions, which is a

reasonable prediction, although perhaps slightly conservative considering the level of

damage witnessed in the test (Section 3.6.2). The 1st floor beams have Dθ-values

between 73 to 84%, implying that there is a significant amount of hinging in these beams,

while the observed damage would imply more moderate level of damage. The analytical

model predicts a significant amount of damage (67-82%) in the 2nd floor beams, whereas

the test specimen had only limited hinging occurring in these hinges. The 3rd floor beams

now reach predicted damage levels on the brink of loss of capacity (79-94%) which again

overestimates the actual damage observed in these beams.

After the 2/50 event, researchers present at the frame test concluded that that the frame

had reached the collapse prevention limit state, characterized by significant local damage

(concrete crushing, large crack openings, local beam flange and web buckling) and

residual drift that were on the verge of being technically infeasible to repair. The

analytical results in Fig. 4.83 reflect that there is severe damage to the frame after this

event, with all of the beams reaching Dθ-values between 81% and 101% and the base

columns within the 77-92% range. This seems to be an accurate representation, because

at this point, the base columns experienced extensive hinging, with distributed cracks and

spalling of the cover concrete and the beams in the first and third floors had been

subjected to extensive yielding and significant local buckles of the bottom flange.

However, the OpenSees model overestimates the amount of inelasticity occurring in the

second floor beam. Whereas the calculated damage indices are between 82% and 93%,

this beam only experienced slight yielding with no local buckles. The OpenSees model

correctly picks up damage (concrete cracking and spalling) that concentrates in the upper

region of the second floor columns, with damage indices reaching up to 76%. Several of

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the interior joints in the model are showing a Dθ-value of up to 73%, which overestimates

the observed damage of limited to moderate cracking.

The final design level event continues the same trend as the previous events (Fig. 4.84),

since by this point all of the largest excursions have already occurred in the previous 2/50

event. This event pushes all of the RC column base hinges and the beam hinges at each

floor to the near collapse or the loss of capacity level (85-104%). Recall that the test

frame was subsequently pushed out to extremely high drift demands and showed quite a

bit of residual strength as a system after this final design level event, so it is apparent that

there was a significant amount of strength left within the system. Except for the 2nd floor

beams, it can be argued that the observed damage of these hinges reflect the conditions

expected for near collapse or loss of capacity damage levels. Furthermore, it may be

unconservative to rely on the strength of these elements after attaining the type of damage

that was observed at this point in the test. Therefore, it is reasonable to assume that the

analytical model is roughly capturing the point at which the frame is reaching its near

collapse limit state.

4.4.4 Evolution of Damage Indices and Maximum Plastic Rotations

In this section, the focus will shift towards tracking the evolution of calculated indices

and physical damage of a few important column and beam hinges over the duration of the

pseudo-dynamic loading events. For comparisons sake, the maximum plastic rotations

are also reported.

4.4.4.1 Columns

Figure 4.85a-d presents photos tracking the damage of a 1st-floor interior column base

hinge after each of the four main pseudo-dynamic loading events. Figure 4.85e depicts

the computed damage evolution (Dθ) from OpenSees of this same column (1C3). In this

figure, the evolutions of the Dθ-index for the lower (solid line) and upper hinge (dashed

line) are plotted over the four earthquake time histories. Also included is the damage

200

evolution during two time intervals, marked I and II, which stand for (I) the first 7

seconds of the LP89G04 event (1a) that had to be stopped and (II) the frame straightening

imposed after the 2/50 event. In addition to the Mehanny et al. (2001) damage index, the

ratios of the maximum plastic excursion (DImaxExc) to the ultimate capacity for the lower

(solid) and upper (dashed) hinge are in Fig. 4.85f.

Figure 4.85g depicts the damage evolution of column 1C3 using the measured tiltmeter

response from the hinges in the test frame. The tiltmeter data is processed to obtain

effective plastic hinge rotations using assumptions of elastic stiffness and the force in the

hinge. These plastic rotations are then processed through the damage index equation

presented in equation (4.10). Comparison of the analytical and measured response data is

provided to help determine whether discrepancies between the damage index, Dθ, and the

observed physical damage are inherent to the damage index or are a by-product of

differences in the input response data (i.e., calculated versus measured plastic rotations)

used to calculate the index. Note that the tiltmeter data was not recorded during the

realignment push (event II), which explains the missing data in Fig. 4.85f during this

event. Table 4.6 summarizes the simulated and measured maximum plastic rotations for

this column during each of the pseudo-dynamic loading events as well as the percent

difference between the two ( [ ]100 Measured Calculated Measured× − ).

Now that all of the information in Fig. 4.85 has been described, this information can be

used to evaluate how well OpenSees can track progression of the physical damage in the

test frame. During the 50/50 event, Figs. 4.85e and 4.85g indicate that the progression of

damage in the lower hinge as measured by the Dθ-index is relatively the same for the

simulated and measured response and the final value of 0.44 matches quite well. This

Dθ-value corresponds to a negligible amount of damage (Table 4.6) and seems to match

the physical behavior of this hinge quite well, as seen in Fig. 4.85a. During segment I,

both the simulated and measured Dθ-values both experience a sudden increase near 50-

second mark, where the frame was subjected to its first major inelastic excursion, as is

evident in Fig. 4.85a. During the subsequent 10/50-1b event, both the predicted and

measured Dθ-values increase at relatively the same rate and end at final predicted values

201

of 0.78 and 0.88, respectively. While these values suggest that the hinge is at a near

collapse damage state, Fig. 4.85b shows that this is not the case as observed damage is

limited to minor cracking and spalling. During the 2/50 event, the predicted Dθ-index

gradually increases to 0.92, which indicates that significant amount of damage is

predicted in this hinge. This is consistent with the observed damage state shown in Fig.

4.85c. After the final 10/50 event, loss of capacity is predicted in this hinge for both the

analytical and measured Dθ-value, which for all relevant purposes can be argued as the

approximate observed damage state (Fig. 4.85d). The more basic damage index

(DImaxExc) in Fig. 4.85f only reaches a peak value of just over 0.2, which shows how

much of an impact the cyclic damage term in equation (4.10) can have in earthquake

excitations. The maximum plastic rotations in the lower hinge are captured rather well

throughout all events except for the 2/50 event, where the error is reported as 56% in

Table 4.6.

Figures 4.85e, f, and g also show the evolution of damage for the upper hinge with the

dashed line. The damage in this hinge is largely underestimated by the analytical model,

which predicts an ultimate Dθ-value of 37% while the test data suggests almost 90%. This

is surprising considering that the physical damage in this hinge was relatively small

(photos are not shown here) compared to the lower hinge, suggesting that the damage

index is perhaps overcompensating for the cyclic damage or rather the assumptions made

in obtaining plastic rotations lead to an overestimation of nonlinearities. Maximum

measured plastic rotations for this hinge are reported as high as 1.47% for the 2/50 event,

while the predicted values are only 0.16% (Table 4.6).

Figures 4.86 through 4.90 are organized in the same way as Fig. 4.85, except that the Dθ

and DImaxExc-index prediction from OpenSees is now combined into one plot. Figure 4.86

reveals that the damage progression in the lower hinge of an exterior column in the 1st

floor (1C4) is roughly the same for both the predicted and measured values, despite

having some differences in the rate of damage. At the conclusion of each of the pseudo-

dynamic events, the analytical model correctly predicts the amount of damage witnessed

in the test: negligible damage for the 50/50 event (Fig. 4.86a), moderate damage for the

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10/50 event (Fig. 4.86b), and significant damage for both the 2/50 event (Fig. 4.86c) and

the final 10/50 event (Fig. 4.86d). The simulated maximum plastic rotations compare

well to the measured values (Table 4.7), with the highest error coming in the 2/50 event

at approximately 50%.

The overall damage in the upper hinge is much less severe than the lower hinge, with the

analytical model predicting negligible damage (~0.1) while the measured values predicts

the hinge to be at the onset of noticeable damage (0.45). The latter prediction is a bit

more representative of the observed physical damage in this element. While the errors

between the simulated and measured maximum plastic rotations are rather high in this

hinge (Table 4.7), the absolute magnitudes of these rotations are fairly low.

The evolution of damage for the interior and exterior 2nd floor columns are shown in Figs.

4.87 and 4.88, respectively. Both of these figures show that the amount of damage

predicted by the analytical model for the lower hinges greatly exceed the predictions

from the measured response. This is also reflected in the comparison of the maximum

plastic rotations in Table 4.8. The damage in this lower hinge was observed as relatively

minor supporting the measured results in Fig. 4.87f. On the other hand, the damage in

the upper hinge was much more significant, and seems to be captured generally well by

the analytical model and the damage index. After the 50/50 event, the analytical model

correctly predicts an insignificant amount of damage in both the interior and exterior

upper hinge (Dθ≈20%), which is validated in the photos in Figs. 4.87a and 4.88a. The

10/50 event produces a moderate level of damage, as seen in Figs. 4.87b and 4.88b, and

is captured relatively well by the simulated Dθ-value, but are overestimated by the

simulated maximum plastic rotations. With a Dθ-value of 76% for the interior upper

hinge at the end of the 2/50 event, the predicted results indicate a significant amount of

damage in this hinge, while the measured Dθ-value indicates that the damage remains

relatively moderate (Fig. 4.87c). Meanwhile, the exterior hinge correctly captures the

moderate level of damage (Fig. 4.88c) with a Dθ-value of 54% at the end of this event.

After the final 10/50 event, the damage states of the interior (Fig. 4.87d) and exterior

203

hinges (Fig. 4.87d) correlates well with the predicted Dθ-values of 84% (significant

damage) and 64% (moderate damage), respectively.

4.4.4.2 Beams

The evolution of damage for 1st floor beam hinges are shown in Fig. 4.89, with the

exterior hinge shown with a solid line and the interior hinge shown with a dashed line.

Photos of the exterior (south) hinge are shown in Figs. 4.89a-d since this is the location of

most severe beam damage. During the first 50/50 event the beam hinge experienced

relatively minor yielding (Fig. 4.89a), which is reflected by the measured Dθ-value of just

below 20%. The predicted Dθ-value increases at a much quicker rate and estimates the

hinge to be at brink of moderate damage (44%). This difference between the measured

and simulated Dθ-value is surprising considering that the total hinge rotation versus

moment response plot in Fig 4.63 (1B1S050) was captured so well. What this reveals is

that the way OpenSees is extracting the plastic rotations from the fiber beam-column

element seems to be overestimating the actual values. OpenSees estimates a peak plastic

rotation of 0.76 radians while the measured counterpart is only 0.25 radians. The reason

there is an overestimation of plastic rotations is likely due the fact that the initial stiffness

of the beam used to derive the plastic rotations includes the effect of the uncracked slab

for both the positive and negative stiffness. This would overestimate the elastic stiffness

of the beam in negative bending and lead to higher plastic rotations. This effect will be

considered again after examining the rest of the results.

After the 10/50 event, the analytical model predicts significant amount of damage (76%)

while the beam hinge experienced only moderate yielding and very minor flange

buckling. The Dθ-value of 45% and 60% from the measured results seems to be a better

indicator of the true damage in these hinges, as seen in Fig. 4.89b. The simulated and

measured peak plastic rotations are better correlated during this event with values of

0.014 and 0.012 radians, respectively. During the final excursion of the 2/50 record, the

Dθ-value from the measured results of the left hinge (solid line) encounters a large spike

in the response which is a result of the large local buckling that occurred during this push.

204

The tiltmeter reading at this point in the record may not be completely accurate given that

the web began to buckle and caused out of plane distortions in the tiltmeter gauge. As

discussed before, the local buckling behavior is not captured by the fiber models and at

this point the measured Dθ-value surpasses the analytical Dθ-value. This large increase in

the Dθ-value is not present in the right beam hinge (dashed line) given that this section

was experience positive (composite) bending and therefore no occurrence of local flange

or web buckling.

At the end of the final event, the left hinge is correctly predicted by OpenSees to be

within the significant/loss of capacity damage region, but in general the progression of

damage was not captured as effectively as it should have been. The damage in the

northern hinge (dashed line) is overestimated by the analytical model (Fig. 4.89e) and is

better captured by the measured results (Fig. 4.89f).

Figure 4.90 shows the results for a 2nd-floor beam, which experienced only moderate

yielding throughout all of the pseudo-dynamic events as a result of the large material

overstrength in the steel (discussed in Chapter 3). This progression of damage is picked

up rather well by the measured Dθ-value in Fig. 4.90f, and the final value of 0.48 (south

hinge) and 0.58 (north hinge) reflects the moderate level of damage seen in Figs. 4.90a-d.

Conversely, both the progression of damage and the final Dθ-values from OpenSees

predictions overestimate that of the true damage in these beam hinges.

It seems that predicted plastic rotations for the composite beams consistently

overestimate that of the measured results, as is reflected in Tables 4.10 and 4.11 as well

as the evolution of damage index plots presented in this section. The only exception to

this is the point at which large local buckling occurs in the test frame which is not

captured by the fiber model. This suggests that the proposed theory that the negative

stiffness of the composite beam is overestimated by including the uncracked stiffness of

the slab is likely correct. The composite stiffness can be up to two to three times as stiff

as a bare steel beam, which, as shown in this section, could prove to have a large impact

in the calculation of plastic rotations.

205

4.4.4.3 General Comments

The purpose of these damage indices is to provide a link between the analytical models in

OpenSees and the physical damage observed in the test frame. This test program

provides a unique opportunity to both validate these damage indices using measured

output from the test and predicted results from the analytical models. In general,

comparisons between the processed Dθ-values from the measured data show good

correlation to the observed damage levels in the components of the test frame when based

on the proposed levels in Table 4.5. There are cases where the measured results tend to

overestimate the level of damage (upper hinge of 1C3, Fig. 4.85), but perhaps this could

be attributed to errors in determining the plastic rotations from the tiltmeters. These

results reinforce the validity of the Mehanny (2001) damage index and shows that it is

able to accurately correlate the plastic rotations with the actual damage in an element,

which has further implications associated with repair types and cost.

The plastic rotations from OpenSees coupled with the damage indices have shown to

accurately capture the damage in those hinges that experienced heavy damage during the

frame test. There are cases where the simulated Dθ-values tend to overestimate the

damage condition in hinges that were less damaged in the in the frame test, but these are

largely a result of over predicting the levels of plastic rotation in these hinges rather than

problems with the index itself. There is a legitimate issue regarding the estimation of

plastic rotations in composite beams given that OpenSees is accounting for the uncracked

slab in the elastic stiffness. This assumption tends to overestimate the plastic rotations in

the beams when subjected to negative bending. While this can be corrected in the post-

processing of the plastic rotations, this should really be corrected within OpenSees.

Despite this issue, these damage indices show promise in their ability to connect the

analytical response from OpenSees to a range of physical damage states seen in

experiments.

The problems with the damage indices stemming from the determination of plastic

rotations can be largely avoided with the use energy-based damage indices. Energy-

206

based indices (i.e., Kratzig et al. 1989, Mehanny 1999) are less sensitive to such subtle

issues that have been discussed within this study. These energy-based indices also avoid

the problems associated with interpreting the plastic rotations of a highly pinched

response. In this case, the deformation-based damage index would tend to overestimate

the amount of damage given the difficulty of determining the plastic deformations of a

pinched response, whereas the energy-based index would be able to more easily interpret

the energy of each cycle.

4.5 Summary of Recommendations

A brief recap of the modeling recommendations specified in this chapter for composite

RCS moment frames are presented within this section.

4.5.1 RC Column Summary

It is recommended that reinforced concrete columns are modeled using the flexibility-

based fiber elements described in Section 4.2.2. The RC fiber section can be defined

using three different materials to represent the core and cover concrete and the

reinforcement steel. The Concrete02 material model is used to represent both the core

and cover concrete. The backbone of the core concrete can be defined using the modified

Kent and Park model (Scott et al. 1982), which adjusts both the strength and ductility of

the concrete according to the amount of confinement provided. Based on the calibration

study presented in Section 4.2.2.1, it is recommended to specify the nominal compressive

strength in the modified Kent and Park model as 0.85 rather than the full , since

this was found to provide a better estimate of the strength of the subassembly tests

considered in the calibration study. The tension strength of the concrete can be defined

by equation

'cf '

cf

(4.6) according to the research by Carrasquillo (et al., 1982). Concrete

tension stiffening effect can also be accounted for using the work from Stevens (et al.,

1991). In this research, the linear decay model in Concrete02 was used for simplicity and

fit to the curve derived by Stevens (et al., 1991). Modeling recommendations for the core

concrete are summarized in Table 4.12.

207

The backbone of the cover concrete is defined according to the following backbone

parameters: 'ccf = 0.85 , '

cf ccε = -0.002, '2cf = 0, and 2cε = -0.010. This definition stems

from both the calibration studies and the practical aspects of numerical convergence. The

complete definition of the cover concrete material is summarized in Table 4.12.

It is recommended that the longitudinal reinforcement steel be modeled using the Steel02

material model in OpenSees. The yield strength should be assigned either as the

measured strength or the expected yield strength of . Strain hardening can be

determined experimentally or assumed as 2% of the elastic modulus of steel. The

hysteretic parameters that define the cyclic properties of the material should be defined as

, , and

yF25.1

5.180 =R 925.01 =c 15.02 =c . The parameters necessary to create the

longitudinal reinforcement bar material are summarized in Table 4.13.

Elastic bond slip springs with a stiffness defined by equation (4.7) have been shown to

accurately capture the additional flexibility of bond slip and yield penetration in RC

columns. This model assumes that the reinforcement bars are sufficiently developed and

will not experience pull out. The elastic springs are represented by the rotSpring2D

function, which can be downloaded from the OpenSees website

(http://opensees.berkeley.edu/).

4.5.2 Composite Beam Summary

The Steel02 material model can be used to define the steel beams, with the yield strength

and hardening ratio either determined experimentally or assumed as and 2% of the

initial stiffness, respectively. The concrete slab can be modeled with the Concrete02

material with a peak stress (

yy FR

'ccf ) of 1.3 and an effective slab width equal to the width

of the column that the beam frames into. The strain corresponding to the maximum

concrete stress (

'cf

ccε ) should be taken as -0.002 and the strain marking the beginning of

208

the residual strength ( 2cε ) as -0.05. The post-peak residual stress of the slab ( '2cf ) should

be taken as 20% of the peak stress, 'ccf . These modeling assumptions assume that the

shear studs have been designed to provide a fully composite section according the

requirements in the AISC Seismic Provisions (2002). The remaining concrete

parameters, including the tensile strength and softening, can be defined similar to that of

the core concrete described in Section 4.5.1. These parameters needed to define the steel

beam and concrete slab are summarized in Tables 4.12 and 4.13, respectively.

In addition to the specific recommendations provided for the RC columns and the

composite beams, general recommendations were also provided to help in the overall

convergence of flexibility-based beam-column elements. These issues include: (1)

providing a finer discretization of the fiber section in regions where the material is non-

ductile (e.g. concrete cover) in order to capture the softening response, (2) providing

seven gauss integration points along the length of the member, and (3) enforcing the

mitigation of error at the element level by setting the maximum number of iterations to

10 and the minimum tolerance to 1x10-18.

4.5.3 Composite Joint Summary

The Joint2D model is recommended to represent the composite joint panels in OpenSees.

Joint dimensions should correspond to the depth of the steel beam and the width of the

concrete column. The two different deformation mechanisms, panel shear and vertical

bearing, can be represented by two nonlinear springs in series. The panel shear spring

can be best represented by the Steel02 model with a strength and stiffness defined by

equations (2.33) and (4.9), respectively. The remaining Steel02 parameters determined in

the calibration study are recommended as follows: 5.180 =R , , and 1 0.96c = 15.02 =c .

The vertical bearing spring can be defined using the Hysteretic material model with the

backbone defined in Fig. 4.31. The strength and stiffness of this spring can be defined by

equation 2.34 and (4.8), respectively. The recommended values for the pinching factors,

xη and yη , are 0.2 and 0.5, respectively, and the damage factors, d and Δ Ed , are 0.015

209

and 0.0, respectively. Again, the values needed to model the vertical bearing spring are

summarized in Fig

4.6 Conclusions

Calibration studies have the shown that the analytical models used in this study are able

to consistently and accurately capture the behavior of subassembly tests. The intention of

this study is not to overly tune the analytical models to the point where they perfectly fit

the specific tests that were used in this calibration study, but rather the approach is to

provide simple recommendations that are grounded in mechanics that could be used to

accurately model a variety of different types of structures.

The pseudo-dynamic test of a 3-story composite RCS moment frame described in

Chapter 3 has provided a unique opportunity to extend the validation of the analytical

models from the typical subassembly tests to a full-scale building subjected to realistic

excitations. Using the recommendations derived from the subassembly tests, the

analytical model of the test frame is able to capture the experimental response quite well

during the 50/50 and 10/50 events. Interstory drifts and story shear forces, both critical

engineering demand parameters necessary for design and assessment, are captured

relatively well throughout the entire time history. While there are some occurrences of

minor local buckling in the steel beams during the 10/50 event, the frame behavior is still

largely dominated by flexural hinging of the RC columns and composite beams.

Therefore, the fiber models are able to accurately capture the deformation mechanisms

that occur in the test frame during these events.

Comparison of the maximum considered event (2/50) highlighted some of the limitations

of the fiber beam-column elements. During the first 18-seconds of the event, the

analytical model represents the behavior of the test frame fairly well, but beyond this

point, large local buckling in the steel beam hinges began to dominate the response of the

test frame. It is acknowledged that the fiber beam-column models are not able to capture

this phenomenon and only model the flexural yielding behavior of these hinges. This is

210

also compounded by the fact that this event is now the third major earthquake that the test

frame was subjected to and the damage in the RC column base hinges and the composite

beam hinges continue to accrue over the repeated cycles. Based on the results within this

study, it is suggested that the reliability of the fiber beam-column models to accurately

model the realistic inelastic behavior be questioned once interstory drift ratios exceed 3-

4%.

There is a noticeable elongation of the natural period that occurs in the test frame that is

not accurately captured by the analytical model. This difference stems from two primary

issues: (1) the rate of deterioration of the component’s stiffness in the test frame is not

accurately simulated by the fiber beam-column elements and joint models and (2) strain

rate effects and the force relaxation that occurs due to the pseudo-dynamic algorithm

soften the global response of the frame. The latter issue is inherent to the testing method

and could only be corrected if the test were conducted in real time or using a shake table.

As far as the analytical models, this difference in stiffness degradation is partly due to the

local buckling that is not being captured in the simulation, but also a result of stiffness

degradation of the RC columns and bond slip deterioration that occurred at the base of

the 1st floor. These differences are readily apparent when comparing the stiffness of the

frame during the final pushover.

4.6.1 Future Work

An improved hysteretic model has recently been implemented into OpenSees that gives

the user more control over the strength degradation of the backbone (Ibarra 2004). The

“Hysteretic” model used in this study does not directly allow the degradation of the

strength, so therefore this was accomplished by imposing a cap on the strength at 5%

rotation, beyond which there is a negative stiffness which brings it down to a residual

strength of 65% of Mvb. For future studies, it would be better suited to recalibrate the

joint bearing model using the recently developed model proposed by Ibarra (2004).

Despite this recommendation, the model used in this study will prove to be sufficient

211

given that the joints in RCS frames are inherently strong and do not experience large

deformations that would push the negative backbone of the current model.

The large differences in the residual drifts between the simulated and measured response

highlight the sensitivity of this important engineering demand parameter to the precise

details of the inelastic hysteretic model. These details include parameters such as yield

strength, hardening stiffness, unloading and reloading stiffness, pinching, and the strength

and stiffness degradation. Each of these parameters can be assigned a mean and

coefficient of variation based on the calibration study of the component. This suggests

that a probabilistic approach could be adopted when defining these hysteretic models, and

the residual drifts could be evaluated considering the distribution of each of the

parameters.

Local buckling of the steel beams proved to be an important behavior effect that

ultimately had a large impact on the response of the frame when subjected to larger

excursions. The next step in modeling these composite RCS frames is to calibrate hinge

models, such as that proposed by Ibarra (2004), to capture this loss of strength and

stiffness in these composite beam hinges (which primarily occurs when subjected to

negative bending). These updated composite beam models will provide the capability to

model these composite frames out to very large drifts and perform more detailed analysis

that are able to capture the onset of structural collapse.

The deformation-based damage model used in this study has been shown to work well

with correlating the analytical response to the physical damage, but there are some

problems stemming from the assumptions used to compute the plastic deformation in the

fiber beam-column elements. In addition, the definition of plastic rotation becomes less

clear when dealing with a highly pinched component and would likely lead to

overestimations of damage. Switching to an energy-based damage model could avoid

some of the problems observed in this study. On the other hand, these energy models

require the force as well as the hinge rotation, which may also introduce another problem

in the evaluation of measured hinge response from the test frame given that the forces are

212

interpreted from strain gauges and are not exact. Nevertheless, these energy-based

models provide another path to investigate the data from this study and could prove to be

an important validation exercise for these models.

213

Table 4.1 – Summary of RC column specimens used in calibration study. 'Test

Specimen Test

Config Section Rebar Details

cf (MPa)

Fy,rebar (MPa)

Fy,trans (MPa) H (mm) B (mm) L (mm) '

c gP f A sρ

Tsai 2002 FFH08 650 650 3000 0.086 0.017 FFL08

12-36mm 650 650 3000 0.086 0.017

FRL08 340 340 1200 0.084 0.025 FRL60

Cant-ilever 12-

19mm

41.3 414 414

340 340 1200 0.586 0.025 Tanaka & Park 1990

#2, 3, 4 Double Ended

8 bars, dbar=

20mm 25.6 474 333 400 400 1600 0.2 0.026

214

Table 4.2 - Composite beam validation study Experiment Best Fit Parameters Description of Test and Failure

Tagawa (1989) 1.3 'cf

05.02 ≥Cε

colslab bb =

Fully composite beam with two steel columns part of a 1-story, 1.5-bay substructure. Local buckling occurred in the lower beam flange (pt. B) at the 4th cycle. They assume colslab bb = and '

,maxcf =1.8 ' . Details of the test are shown in Fig. XXX. cf

Bursi and Ballerini (1996)

1.3 ' cf07.005.02 −=Cε

colslab bb =

Fully composite beam with rigid column and panel zone. Inelastic behavior is governed by steel beam yielding and concrete crushing. Web and flange buckling occurred at the first negative cycle (δ/δy=4). Final failure mechanism is governed by crushing and uplifting of composite slab. Details of the test are shown in Fig. XXX.

Uang (1985) – CG3 1.3 ' cf

07.02 ≥Cε 2.5slab colb b=

Small scale cantilever composite beam that is fixed to a rigid steel column which is attached to a strong wall. The entire width of the concrete slab also runs into the strong wall, which may help provide a larger effective width for the plastic moment. Severe local buckling occurred at every cycle of the loading protocol. Details of the test are shown in Fig. XXX.

Lee (1987) – EJ-WC Failure in columns

Fully composite beam with a majority of the inelasticity occurring in the beam, although it was predicted that the steel columns were 40% weaker than the beam. Early local buckling occurred in the steel beam at cycle 19- and continued to grow as the test progressed. Final failure was due to fracture in the lower beam flange near the middle of the local buckle. Lee (1987) generated analytical models to simulate this test with AISCslab bb = and an effective concrete stress of 1.3 ' . Details of the test are shown in Fig. XXX.

cf

Cheng (2002) – ICLCS 0.85 ' cf

012.02 =Cε

colslab bb =

Cheng (2002) – INUCS 0.85 ' cf

012.02 =Cε

colslab bb =

Partially composite beams with 75% of the AISC-LRFD required number of shear studs. There were very little shear studs placed within the region of higher moment. The composite beams and to a lesser extent the composite joints governed the inelastic action of the specimen. Shear studs fractured at about 3% drift and local buckling and slab separation occurred at 4% drift. Fracture of the bottom beam flange occurred at the 6% drift cycle. Details of the test are shown in Fig. XXX.

215

Table 4.2 (cont.) - Composite beam validation study

Cheng (2002) – ICLPS 0.85 ' cf

012.02 =Cε

colslab bb =

The only difference from the first two specimens is that the imposed displacements followed near fault earthquake response (Krawinkler 2000). Local buckling occurred during the large 8% drift excursions. Details of the test are shown in Fig. XXX.

Civjan et al (2001) Not analyzed

Partially composite beam (25-35%) with shear studs designed to develop 1.3 ' over cf

colslab bb = . Failure of the shear studs at their welds often occurred. Overall deterioration due to local and lateral buckling of the steel beams. Attained strengths for the composite beams showed that the effective concrete stress was less than or equal to 0.85 ' . The slab compressive zone was found to be wider than the column face, initiating at the far column flange. Slip of composite slab was witnessed as well as shortening of the beams.

cf

Leon, Hajjar et.al (1998) Not analyzed

Partially composite beam (55% and 35%) assuming composite strength based on AISC-LRFD specifications (0.85 ' , cf effslab bb = ). The maximum composite strengths

attained were 0.73-0.80 (specimen 2) and 0.90-0.92 (specimen 3). In specimen 2, the bottom flange of the beam fractured during the second cycle of 1.5% drift. Specimen 3 experienced local buckling at 2% drift and ultimately failed in low cycle fatigue type ruptures of the bottom girder flange.

+calcpM ,

+calcpM ,

Bugeja et al (2000) Not analyzed

Fully composite beam with shear studs designed to meet the requirements of AISC design specifications (1994). They found that the attained strength of the composite beams suggest that AISCslab bb = with an effective concrete stress of 0.85 ' . If the plastic moment is computed using 1.3 ' and

cf

cf colslab bb = , the ultimate moment is only 9% lower than by assuming 0.85 ' and cf AISCslab bb = .

216

Table 4.3 – Material properties for composite beam test specimens.

Composite Beam Test '

cf (MPa)

,y webF (MPa)

,y flangeF (MPa)

,y rebarF (MPa)

Column Properties

Tagawa et al.1989 24.5 283.8 329.8 355.7

,y webF =377MPa

,y flangeF =286MPaBursi and Ballerini

1996 39.0 299.7 299.7 481.6

,y webF =300MPa

,y flangeF =300MPa

Uang 1985 (CG3) 29.4 285.9 254.9 544.3 -

Lee 1987 (EJ-WC) 35.1 260.4 252.5 413.4

,y webF =270MPa

,y flangeF =251MPa

Cheng 2002 (ICLCS) 22.5 478.5 444.2 -

'cf =50MPa

Fyr=443MPa Fyh=431MPa ρs=0.0175

Cheng 2002 (ICLPS) 21.0 478.5 444.2 -

'cf =54MPa


Cheng 2002 (INUCS) 24.3 478.5 444.2 -

'cf =50MPa


217

Table 4.4 – Plastic rotation capacity of test frame components. puθ (rad)

Floor RC Columns Steel Beams Comp. Joints

Inner 0.15 1st Outer 0.31 0.072 0.087

Inner 0.16 2nd Outer 0.41 0.093 0.093

Inner 0.16 3rd Outer 0.42 0.098 0.10

Table 4.5 – Correlation between the Mehanny damage index and the expected damage in

the component. Original

Dθ Range Proposed Dθ Range Anticipated Damage State

0.00-0.30 0.00-0.50 Little to no damage in element and corresponds to immediate occupancy damage level

0.30-0.60 0.50-0.70

Structural element experiences noticeable damage, such as spalling of cover concrete and minor shear cracking in RC columns, and hinging and some local buckles in steel beams. In terms of the component damage and necessary repairs, this region of the damage index roughly corresponds to a life safety limit state.

0.60-0.95 0.70-0.95 Structural element is assumed to be at a near collapse state, with extensive cracking and hinge formation in RC columns and significant hinging and local buckles for the steel beams.

>0.95 >0.95 The damage is so extensive that the capacity of the element is assumed to be exhausted.

Table 4.6 – Comparison of the simulated to measured maximum plastic rotation in 1st

floor interior column. 1st Floor Int. Column Hinge (1C3) – Max. Plastic Rotation (rad)

OpenSees Measured Error Event Lower Hinge

Upper Hinge

Lower Hinge

Upper Hinge

Lower Hinge

Upper Hinge

50/50 0.007 0.001 0.008 0.005 14% 88% 10/50-1a 0.022 0.002 0.026 0.008 13% 81% 10/50-1b 0.020 0.002 0.016 0.006 -22% 74%

2/50 0.025 0.002 0.057 0.015 56% 89% 10/50-2 0.017 0.001 0.017 0.010 3% 88%

218

Table 4.7 – Comparison of the simulated to measured maximum plastic rotation in 1st

floor exterior column 1st Floor Ext. Column Hinge (1C4) – Max. Plastic Rotation (rad)


Upper Hinge

Lower Hinge

Upper Hinge

Lower Hinge

Upper Hinge

50/50 0.008 0.001 0.008 0.004 -9% 67% 10/50-1a 0.024 0.002 0.021 0.004 -13% 64% 10/50-1b 0.021 0.001 0.015 0.004 -36% 70%

2/50 0.027 0.002 0.055 0.016 51% 90% 10/50-2 0.018 0.001 0.016 0.010 -9% 87%

Table 4.8 – Comparison of the simulated to measured maximum plastic rotation in 2nd

floor interior column 2nd Floor Ext. Column Hinge (2C3) – Max. Plastic Rotation (rad)


Upper Hinge

Lower Hinge

Upper Hinge

Lower Hinge

Upper Hinge

50/50 0.003 0.002 0.001 0.004 -142% 43% 10/50-1a 0.008 0.012 0.001 0.004 -600% -176% 10/50-1b 0.008 0.013 0.003 0.005 -172% -182%

2/50 0.015 0.024 0.006 0.016 -158% -51% 10/50-2 0.009 0.014 0.003 0.007 -178% -94%

Table 4.9 – Comparison of the simulated to measured maximum plastic rotation in 2nd

floor exterior column 2nd Floor Ext. Column Hinge (2C4) – Max. Plastic Rotation (rad)


Upper Hinge

Lower Hinge

Upper Hinge

Lower Hinge

Upper Hinge

50/50 0.007 0.005 0.002 0.005 -294% 0% 10/50-1a 0.013 0.013 0.003 0.008 -374% -68% 10/50-1b 0.012 0.013 0.003 0.007 -333% -77%

2/50 0.014 0.021 0.004 0.029 -268% 28% 10/50-2 0.013 0.013 0.002 0.017 -706% 26%

219

Table 4.10 – Comparison of the simulated to measured maximum plastic rotation in 1st floor beam.

1st Floor Beam Hinge (1B1) – Max. Plastic Rotation (rad) OpenSees Measured Error Event

South Hinge

North Hinge

South Hinge

North Hinge

Lower Hinge

Upper Hinge

50/50 0.008 0.004 0.003 0.001 -204% -322% 10/50-1a 0.014 0.014 0.012 0.008 -14% -78% 10/50-1b 0.013 0.012 0.007 0.005 -86% -176%

2/50 0.015 0.017 0.063 0.017 76% 3% 10/50-2 0.012 0.010 0.010 0.001 -24% -818%

Table 4.11 – Comparison of the simulated to measured maximum plastic rotation in

2nd floor beam. 2nd Floor Beam Hinge (2B3) – Max. Plastic Rotation (rad) OpenSees Measured Error Event

South Hinge

North Hinge

South Hinge

North Hinge

Lower Hinge

Upper Hinge

50/50 0.005 0.007 0.003 0.003 -73% -132% 10/50-1a 0.005 0.018 0.003 0.004 -66% -349% 10/50-1b 0.004 0.015 0.002 0.003 -91% -347%

2/50 0.005 0.016 0.003 0.004 -57% -261% 10/50-2 0.004 0.013 0.002 0.002 -54% -641%

Table 4.12 – Summary of OpenSees input parameters for definitions of Concrete02 materials (uniaxialMaterial Concrete02)

Variable Name Concrete Core Concrete Cover Concrete Slab '

ccf Equation 4.1 –

using 0.85 ',c nomf 0.85 '

,c nomf 1.3 ',c nomf

ccε Equation 4.2 -0.002 -0.002

'2cf

Equation 4.3 – using 0.85 '

,c nomf 0.0 0.2*1.3 ',c nomf

2cε Equation 4.4-4.5 -0.010 -0.050

cu EE=λ 0.1 0.1 0.1 ft Equation 4.4 0.0 Equation 4.4

Ets Stevens (1991)

or Linear Approx. 0.0 Stevens (1991) or Linear Approx.

220

Table 4.13 – Summary of OpenSees input parameters for definitions of Steel02 materials

(uniaxialMaterial Steel02) Variable Name Longitudinal Rebar Steel Beam Joint Shear Spring

Fy 1.25Fy,rebar 1.1Fy,beam Mps Equation 2.33

E 200,000MPa 200,000MPa Kes Equation 4.9

b 0.02 0.02 0.02 Ro 18.5 18.5 18.5 cR1 0.925 0.925 0.96 cR2 0.15 0.15 0.15 a1 0 0 0 a2 1 1 1 a3 0 0 0 a4 1 1 1

Table 4.14 – Summary of OpenSees input parameters for definitions of Hysteretic

materials (uniaxialMaterial Hysteretic) Variable Name Vertical Bearing

+M1 0.9Mvb

Equation 2.34

+θ1 0.9Mvb/Keb

Equation 2.34, 4.8

+M2 Mvb

Equation 2.34 +θ2 0.05

+M3 0.65Mvb

Equation 2.34 +θ3 0.10

-M1,-θ1, -M2,-θ2, -M3,-θ3,

Negative of above values

xη 0.2

yη 0.5 dΔ 0.015

Ed 0.0

221

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-600

-400

-200

0

200

400

600

Str

ess

(MP

a)

Strain Figure 4.1– Hysteretic response for the OpenSees Steel02 material model.

-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-70

-60

-50

-40

-30

-20

-10

0

10

Str

ess

(MP

a)

Strain

(f'c2

, εc2

)

(f'cc

, εcc

)

(ft)

Core ConcreteCover Concrete

Figure 4.2 – Hysteretic response for the OpenSees Concrete02 material model.

222

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

4

Mom

ent

(kN

-mm

)

Rotation (rad)

(d1, f

1) →

(d2, f

2) →

(d3, f

3)

Hysteretic Modelη

x = η

y = 0.5

dδ = 0.01d

E = 0.0

Figure 4.3 – Backbone and cyclic response of Hysteretic model in OpenSees.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10-3

0

1

2

3

4

5

6

7

8

(εcr

, fcr

)

Tensile Strain

Con

cret

e S

tres

s (M

Pa)

Carrasquillo/StevensLinear Approx.

Figure 4.4 – Typical tensile softening response of reinforced concrete.

223

Δslip

Gap opens (

σs>σy

σy β

Figure 4.5 – Representation of deformations from bond slip and yield penetration.

Fiber section element is used in series with

bond slip spring

Δslip) due to yield penetration

and bond slip

σy = yield stress of rebar σs = stress in rebar including strain hardening

Figure 4.6 – Idealized backbone response of elastic reinforcing bar pull out. (Fillipou et

al. 1983)

20

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18P

Confined Concrete

Elastic Reba

Slip, u (mm)

Bon

d S

tres

s, q

(M

Pa)

r

→ Bar Pull Out

224

-250 -150 -50 0 50 150 250-2.5

-1.5

-0.5

0

0.5

1.5

2.5x 10

6

Mom

ent(

kN-m

m)

Drift (mm)

Tsai 2002FFH08

OpenSeesTest

Figure 4.7 – RC Column calibration against subassembly test: Tsai 2002-FFH08, base

springs included.

-250 -150 -50 0 50 150 250-2.5

-1.5

-0.5

0

0.5

1.5

2.5x 10

6

Mom

ent(

kN-m

m)

Drift (mm)

Tsai 2002FFH08No Base Springs

OpenSeesTest

Figure 4.8 – RC Column calibration against subassembly test: Tsai 2002-FFH08, no base

springs.

225

-250 -150 -50 0 50 150 250-2.5

-1.5

-0.5

0

0.5

1.5

2.5x 10

6

Mom

ent(

kN-m

m)

Drift (mm)

Tsai 2002FFL08

OpenSeesTest

Figure 4.9 – RC Column calibration against subassembly test: Tsai 2002-FFL08, grouted

splice within hinge zone.

-150 -100 -50 0 50 100 150-4

-3

-2

-1

0

1

2

3

4x 10

5

Mom

ent(

kN-m

m)

Drift (mm)

Tsai 2002FRL08

OpenSeesTestOS-Backbone w/ Couplers

Figure 4.10 – RC Column calibration against subassembly test: Tsai 2002-FRL08,

grouted splice within hinge zone (OS model with coupler influence shown as backbone).

226

-150 -100 -50 0 50 100 150-6

-4

-2

0

2

4

6x 10

5

Mom

ent(

kN-m

m)

Drift (mm)

Tsai 2002FRL60

OpenSeesTest

Figure 4.11 – RC Column calibration against subassembly test: Tsai 2002-FRL60,

grouted splice within hinge zone, high axial load.

Figure 4.12 – Schematics of the cantilever and double-ended test setup with respect to

bond slip and OpenSees modeling.

Depending on d1, the bond slip in one column may be affected by the other column

d2

Cantilever Tsai 2002

Tension stress goes to zero

d1

Tension stress

Double-Ended Tanaka and Park 1990

OpenSees Model

Bond-Slip Spring

227

-100 -50 0 50 100 150-200

-150

-100

-50

0

50

100

150

200

For

ce (

kN)

D isplacement (mm)

Tanaka and Park 1990, No. 4

OpenSeesTest

(a) Bond slip spring included.

-100 -50 0 50 100 150-200

-150

-100

-50

0

50

100

150

200

For

ce (

kN)

D isplacement (mm)


OpenSeesTest

(b) No bond slip spring.

Figure 4.13 – RC Column calibration against subassembly test: Tanaka et al. (1990) test #4.

228

-80 -60 -40 -20 0 20 40 60 80-200

-150

-100

-50

0

50

100

150

200

For

ce (

kN)

D isplacement (mm)


OpenSeesTest

Figure 4.14 – RC Column calibration against subassembly test: Tanaka et al. (1990) test

#3.

-100 -50 0 50 100 150-200

-150

-100

-50

0

50

100

150

200

For

ce (

kN)

D isplacement (mm)


OpenSeesTest

Figure 4.15 – RC Column calibration against subassembly test: Tanaka et al. (1990) test

#2.

229

Figure 4.16 – Definition of effective slab width showing both AISC-LRFD and the column width.

(a) Test setup and specimen – Tagawa et al.1989 (1in=25.4mm)

47.24”

0.79”1.97”2.75”

8 bars - φ0.47”

IPE 330

Concrete slab

IPE 330

HE 360B

P, Δ

157.48”

55.1

2”

(b) Test setup and specimen – Bursi and Ballerini 1996 (1in=25.4mm)

30”

0.56”1”1”

M 6x4.4

Wire meshφ0.0625” @ 1”

Concret e slab

M 6x4.4

P, Δ

45”

(c) Test setup and specimen – Uang 1985 (1in=25.4mm)

Loading Beam

ReactionFrame

P, Δ

Concret e slab

W 14x30

W 16x57

Point A

295” 118”

134”

41”

147.6”

1.18”3.54”2.95”

W 14x30

Wire meshφ0.236” @ 3.94”Point B

bAISC bcol

tslab

RC Column

Concrete Slab

230

47.24”

1.2”3.5”3”

W 18x35

Wire meshφ0.214” @ 4”

P, ΔConcrete slab

W 18x35

90.55”

66.9

3”66

.93”

W 12x65(weak axis)

(d) Test setup and specimen – Lee 1987 (1in=25.4mm)

(e) Test setup and specimen (ICLCS, INUCS, ICLPS) – Cheng 2002

Figure 4.17 – Composite beam subassembly dimensions and cross-section details.

-3 -2 -1 0 1 2 3-6

-4

-2

0

2

4

6

8

Tip Displacement (in)

Tip

For

ce (

kips

)

Uang 1985f'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Figure 4.18 – Composite beam calibration against subassembly test: Uang (1985) test.

(1kip = 4.448kN, 1in = 25.4mm)

207575

596x199x10x15

Wire meshφ7mm @ 100mm

2000

All dimensions are in millimeters

P,Δ P,Δ

2700 2700

1600 1600

concrete slab

596x199x10x15

650mm square RC 12#36 bars

231

-5 -4 -3 -2 -1 0 1 2 3 4 5-80

-60

-40

-20

0

20

40

60

80


Tip

For

ce (

kips

)

Bursi & Ballerini 1996f'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Figure 4.19 – Composite beam calibration against subassembly test: Bursi and Ballerini

(1996) test. (1kip = 4.448kN, 1in = 25.4mm)

-80 -60 -40 -20 0 20 40 60 80 100-500

-400

-300

-200

-100

0

100

200

300

400

500

Displacement at pt. A (mm)

Hor

izon

tal F

orce

(kN

)

Tagawa 1989f'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Figure 4.20 – Composite beam calibration against subassembly test: Tagawa (1989) test –

horizontal force versus displacement at A.

232

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02-4

-3

-2

-1

0

1

2

3

4

5x 10

5

Beam Rotation (rad)

Bea

m M

omen

t (k

N-m

m)

Tagawa 1989f'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Figure 4.21 – Composite beam calibration against subassembly test: Tagawa (1989) test –

beam moment versus rotation.

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-50

-40

-30

-20

-10

0

10

20

30

40

50


Tip

For

ce (

kips

)

Lee 1987f'

c=1.3f'

c & b

slab=b

colε

C2=0.012

Figure 4.22 – Composite beam calibration against subassembly test: Lee (1987) test.

(1kip = 4.448kN, 1in = 25.4mm)

233

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002INUCS - East Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)

Figure 4.23 – Composite beam calibration against subassembly test: Cheng (2002),

specimen INUCS-East Beam.

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002INUCS - West Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)


specimen INUCS-West Beam.

234

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002ICLCS - East Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)


specimen ICLCS-East Beam.

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002ICLCS - West Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)


specimen ICLCS-West Beam.

235

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002ICLPS - East Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)


specimen ICLPS-East Beam.

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 106

Cheng 2002ICLPS - West Beamf'

c=1.3f'

c & b

slab=b

colε

C2=0.05

Beam Rotation (rad)

Mom

ent

(kN

-mm

)


specimen ICLPS-West Beam.

236

Node 2

Figure 4.29 – Schematic of OpenSees joint element used in this study.

Figure 4.30 – Panel shear hysteretic model (backbone and cyclic model).

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

MP

anel

She

ar

Rotation

Joint Panel Shear Rotation

Mps

→

Kinitial

= 2Mps

/0.01K

hardening = 0.02K

initial

(Mps/Kes, Mps)

0.02Kes

Node 1

ode 4Center Node Rotational Spring

Frame ElementNode 3

N

Frame Element

Frame Element

Frame Element

Fixed-end Multipoint Constraint

237

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Mvb

Rotation (rad)

Joint Bearing Rotation

(4.5e-3, 0.9Mvb

)(0.05, M

vb)

(0.10, 0.65Mvb

)

Figure 4.31 – Vertical bearing hysteretic model (backbone and cyclic model).

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Total Joint RotationOJB1-0M

ps = 10106 kN-mm

Mvb

= 7327 kN-mm

TestOpenSees

Figure 4.32 – Calibration results for joint specimen OJB1-0, which primarily fails in

vertical bearing.

238

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 10098 kN-mm

Mvb

= 7301 kN-mm

TestOpenSees


vertical bearing.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 10102 kN-mm

Mvb

= 8326 kN-mm

TestOpenSees


vertical bearing.

239

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 9988 kN-mm

Mvb

= 6976 kN-mm

TestOpenSees


vertical bearing.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Total Joint RotationOJS1-1M

ps = 4436 kN-mm

Mvb

= 4801 kN-mm

TestOpenSees

Figure 4.36 – Calibration results for joint specimen OJS1-1, which primarily fails in panel

shear.

240

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 3309 kN-mm

Mvb

= 4463 kN-mm

TestOpenSees


shear.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 6789 kN-mm

Mvb

= 9453 kN-mm

TestOpenSees


shear.

241

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 6789 kN-mm

Mvb

= 9453 kN-mm

TestOpenSees


shear.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 6276 kN-mm

Mvb

= 10834 kN-mm

TestOpenSees


shear.

242

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 7040 kN-mm

Mvb

= 10279 kN-mm

TestOpenSees


shear.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 7040 kN-mm

Mvb

= 10279 kN-mm

TestOpenSees


shear.

243

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Total Joint RotationHJS1-0M

ps = 9561 kN-mm

Mvb

= 15848 kN-mm

TestOpenSees

Figure 4.43 – Calibration results for joint specimen HJS1-0, which primarily fails in panel

shear.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Total Joint RotationHJS2-0M

ps = 9561 kN-mm

Mvb

= 15848 kN-mm

TestOpenSees

Figure 4.44 – Calibration results for joint specimen HJS2-0, which primarily fails in panel

shear.

244

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Joint Panel Shear RotationOJS3-0

TestOpenSees

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)

Joint Bearing RotationOJS3-0

TestOpenSees

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


TestOpenSees

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


TestOpenSees

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


TestOpenSees

-0.1 0 0.1

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


TestOpenSees

Figure 4.45 – Contributions from panel shear and vertical bearing spring for joint

specimen OJS3-0, OJS4-1, and OJS5-0.

245

Figure 4.46 – Schematic of the analytical model of the test frame.

Figure 4.47 – Ramp and hold phases of pseudo-dynamic testing and the concept of force

relaxation.

nΔT

(n+1)ΔT

Force

Disp.

Force Relaxation

dn dn+1

(n+2)ΔT

dn+2

nΔT

(n+1)ΔT

Real Time

(n+2)ΔT

Hold Ramp Ramp

dn

dn+1

dn+2

Disp.

RC column fiber element

Bond slip base springs Zero length

Composite beam fiber element

Composite RCS joint element

4m

4m

4m

Rigid link

7m 7m 7m

Released end

Node Leaning column

246

0 5 10 15 20 25 30 35 40 45-200

-150

-100

-50

0

50

100

150

200

Time (sec)

Roo

f D

isp.

(m

m)

TCU082 50/50TestOpenSees

0 5 10 15 20 25 30 35 40 45-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (sec)

Bas

e S

hear

(kN

)


-6 -4 -2 0 2 4 60

1

2

3

IDR

Flo

or

-4 -3 -2 -1 0 1 2 3 40

1

2

3

Story Shear (1000kN)

Flo

or

Figure 4.48 – OpenSees versus test frame response for 50/50 event: (a) roof

displacement, (b) base shear, (c) peak IDR, and (d) peak story shear.

247

0 1 2 3 4 5 6 7-300

-200

-100

0

100

200

300

400

Time (sec)

Roo

f D

isp.

(m

m)

LP89G04 10/50 1a

TestOpenSees

0 1 2 3 4 5 6 7-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (sec)

Bas

e S

hear

(kN

)

LP89G04 10/50 1a

TestOpenSees

-6 -4 -2 0 2 4 60

1

2

3

IDR

Flo

or

-4 -3 -2 -1 0 1 2 3 40

1

2

3


Flo

or

Figure 4.49 – OpenSees versus test frame response for 10/50-1a event: (a) roof


248

0 5 10 15 20 25 30 35 40-300

-200

-100

0

100

200

300

Time (sec)

Roo

f D

isp.

(m

m)

LP89G04 10/50 1bTestOpenSees

0 5 10 15 20 25 30 35 40-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (sec)

Bas

e S

hear

(kN

)

LP89G04 10/50 1bTestOpenSees

-6 -4 -2 0 2 4 60

1

2

3

IDR

Flo

or

-4 -3 -2 -1 0 1 2 3 40

1

2

3


Flo

or

Figure 4.50 – OpenSees versus test frame response for 10/50-1b event: (a) roof


249

0 5 10 15 20 25 30 35 40 45 50-600

-400

-200

0

200

400

Time (sec)

Roo

f D

ispl

acem

ent

(mm

)


Frame test stoppedat 28 seconds

0 5 10 15 20 25 30 35 40 45 50-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (sec)

Bas

e S

hear

(kN

)


-6 -4 -2 0 2 4 60

1

2

3

IDR

Flo

or

-4 -3 -2 -1 0 1 2 3 40

1

2

3


Flo

or

Figure 4.51 – OpenSees versus test frame response for 2/50 event: (a) roof displacement,

(b) base shear, (c) peak IDR, and (d) peak story shear.

250

0 5 10 15 20 25 30 35 40-300

-200

-100

0

100

200

300

Time (sec)

Roo

f D

isp.

(m

m)

LP89G04 10/50 2TestOpenSees

0 5 10 15 20 25 30 35 40-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time (sec)

Bas

e S

hear

(kN

)

LP89G04 10/50 2TestOpenSees

-6 -4 -2 0 2 4 60

1

2

3

IDR

Flo

or

-4 -3 -2 -1 0 1 2 3 40

1

2

3


Flo

or

Figure 4.52 – OpenSees versus test frame response for 10/50-2 event: (a) roof


251

Figure 4.53 – Contours of the power spectral density for the frequency of the analytical

response throughout the time history (10/50-1) using a 10-second sliding window.

Figure 4.54 – Contours of the power spectral density for the frequency of the measured


10 15 20 25 30 350.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2TCU082 - 50%in50yrAnalytical Results

time (sec)

freq

(H

z)

T = 1.15sec

T = 1.05sec

10 15 20 25 30 350.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2TCU082 - 50%in50yrExperimental Results

time (sec)

freq

(H

z) T = 1.15sec

T = 1.3sec

252

Figure 4.55 – Contours of the power spectral density for the frequency of the analytical


Figure 4.56 – Contours of the power spectral density for the frequency of the measured


5 10 15 20 25 30 350.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 LP89G04 - 10%in50yr - 1Analytical Results

time (sec)

freq

(H

z)

T = 1.3sec

10 15 20 25 300.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2LP89G04 - 10%in50yr - 1Experimental Results

time (sec)

freq

(H

z)

T = 1.4sec

253

0 5 10 15 20 25 30 35 401

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

LP89G04 - 0.8*10%in50yr - 1

time (sec)

Pre

dom

inat

e P

erio

d (s

ec)

AnalyticalExperimental

Figure 4.57 – Plot of the predominate period of a sliding 10-second window over the

displacement time history of the first 10/50 event.

0 5 10 15 20 25 301

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

TCU082 - 2%in50yr

time (sec)

Pre

dom

inat

e P

erio

d (s

ec)

AnalyticalExperimental

Figure 4.58 – Plot of the predominate period of a sliding 10-second window over the

displacement time history of the 2/50 event.

254

0 5 10 15 20 25 30 35 400.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

LP89G04 - 0.8*10%in50yr - 2

time (sec)

Pre

dom

inat

e P

erio

d (s

ec)

Figure 4.59– Plot of the predominate period of a sliding 10-second window over the

displacement time history of the second 10/50 event.

Figure 4.60– Analytical versus experimental comparison of the roof drift versus base

shear during the final static pushover of the test frame.

0 1 2 3 4 5 6 7 80

500

1000

1500

2000

2500

3000

3500

Roof Drift Ratio (%)

Bas

e S

hear

(kN

)

TestOpenSees

kos

ktest

kos/ktest = 1.9 7%

255

0 5 10 15 20 25 30 35 40-300

-200

-100

0

100

200

300

Roo

f D

ispl

acem

ent

(mm

)

Time (sec)

Test Frame Results

1st Event2nd Event

Figure 4.61 – Comparison of the roof displacement response measured from the test frame

for the first (1b) and second 10/50 (2) event.

0 5 10 15 20 25 30 35 40-300

-200

-100

0

100

200

300

Roo

f D

ispl

acem

ent

(mm

)

Time (sec)

OpenSees Results

1st Event2nd Event

Figure 4.62 – Comparison of the roof displacement response predicted by OpenSees for

the first (1b) and second 10/50 (2) event.

256

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2B3N050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.63 – Analytical versus measured response of beams during 50/50 event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1N050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2B3S050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

Figure 4.64 – Analytical versus measured response of beams during 10/50-1a event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2B3N050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.65 – Analytical versus measured response of beams during 10/50-1b event.

257

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2B2N050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.66 – Analytical versus measured response of beams during 2/50 event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1B1S050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

2B3N050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.67 – Analytical versus measured response of beams during 10/50-2 event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C2d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C4d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.68 – Analytical versus measured response of columns during 50/50 event.

258

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C2d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C4d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.69 – Analytical versus measured response of columns during 10/50-1a event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C2d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C4d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.70 – Analytical versus measured response of columns during 10/50-1b event.

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C1d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C4d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.71 – Analytical versus measured response of columns during 2/50 event.

259

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C2d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000)

-80 -60 -40 -20 0 20 40 60 80-3

-2

-1

0

1

2

3

1C4d050

Mom

ent

(10

3 kN-m

)

Rotation (rad/1000) Figure 4.72 – Analytical versus measured response of columns during 10/50-2 event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

2J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000) Figure 4.73 – Analytical versus measured response of joints during 50/50 event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

2J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000) Figure 4.74 – Analytical versus measured response of joints during 10/50-1a event.

260

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

2J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000) Figure 4.75– Analytical versus measured response of joints during 10/50-1b event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

2J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000) Figure 4.76– Analytical versus measured response of joints during 2/50 event.

-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

1J3

Join

t S

hear

(10

3 kN)


-30 -20 -10 0 10 20 30-6

-4

-2

0

2

4

6

2J3

Join

t S

hear

(10

3 kN)

Total Rot. (rad/1000) Figure 4.77 – Analytical versus measured response of joints during 10/50-2 event.

261

-60 -40 -20 0 20 40 600

1

2

3

Flo

or 50/50 Event1st Fl: 199% err.

2nd Fl: -1% err.3rd Fl: 40% err.

-60 -40 -20 0 20 40 600

1

2

3

Flo

or 10/50-1a Event1st Fl: 33% err.

2nd Fl: -22% err.3rd Fl: -19% err.

-60 -40 -20 0 20 40 600

1

2

3

Flo

or 10/50-1b Event1st Fl: 77% err.2nd Fl: 60% err.3rd Fl: 45% err.

-60 -40 -20 0 20 40 600

1

2

3

Flo

or 2/50 Event1st Fl: 96% err.2nd Fl: 95% err.3rd Fl: 97% err.

← δ1 = -135

← δ2 = -244

← δ3 = -329

-60 -40 -20 0 20 40 600

1

2

3

Flo

or 10/50-2 Event1st Fl: 107% err.2nd Fl: 122% err.3rd Fl: 134% err.

Residual Displacement (mm)

Figure 4.78– Comparison of the residual displacements from the analytical (thin line) and

experimental (thick line) model after each pseudo-dynamic event.

262


vertical bearing.

30 44 44 30

44

50

67

36

36

52

36

43

66

36

44

68

35

36

49

43

49

67

TCU082-EW: 50%in50year

Figure 4.80 – Damage index values (>30%) after 50% in 50 year event.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-400

-300

-200

-100

0

100

200

300

400

Bea

m S

hear

(kN

)

Rotation (rad)


ps = 10106 kN-mm

Mvb

= 7327 kN-mm

diff. in peak strength

negative backbone

kunloading zero load

difference in resid. drift

difference in strength

degradation

TestOpenSees

263

49

46

50

45

39 57

31

57

31

39

56

56

73

51

42

58

51

50

72

53

52

74

51

42

56

66

60

76

LP89G04-NS: 10%in50year-1a

Figure 4.81 – Damage index values (>30%) after 10% in 50 year – 1a event.

50

50

30

50

50

30

60

39

32

78

54

50

78

54

50

60

37

31

76

76

93

73

67

81

73

71

91

73

73

93

74

66

79

84

82

94

LP89G04-NS: 0.8*10%in50year-1b

Figure 4.82– Damage index values (>30%) after 10% in 50 year -1b event.

264

41

43

72

73

48

71

73

49

39

41

77

61

54

92

31

77

76

30

92

31

77

76

77

59

53

90

89

101

89

82

93

88

84

99

89

86

101

90

81

91

97

93

102

TCU082-EW: 2%in50year

Figure 4.83 – Damage index values (>30%) after 2% in 50 year event.

53

57

39

87

87

63

86

87

64

53

55

40

85

70

64

30

97

37

86

84

38

33

97

37

85

84

37

33

85

69

63

96

95

104

95

90

98

95

92

103

95

93

104

96

89

97

101

98

105

LP89G04-NS: 0.8*10%in50year-2

Figure 4.84 – Damage index values (>30%) after final 10% in 50 year event.

265

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e)0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

1C3

DIθ: Lower HingeDIθ: Upper Hinge

(f)0 20 40 60 80 100 120 140 160 180

0

0.1

0.2

0.3

0.4

Time (sec)

Dam

age

Inde

x DImaxExc

: Lower HingeDI

maxExc: Upper Hinge

(g) 0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

1C3

Figure 4.85 – (a-d) Photos of damage progression in the 1st floor int. column after each main event. Evolution of damage indices using (e,f) OpenSees and (g) measured data.

266

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e)0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

1C4

DIθDI

maxExc

(f)0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

1C4

Figure 4.86 – (a-d) Photos of damage progression in the 1st floor exterior column after

each main event. Evolution of damage index using (e) OpenSees and (f) measured data.

267

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e) 0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

2C3

DIθDI

maxExc

(f) 0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

2C3

Figure 4.87 – (a-d) Photos of damage progression in the 2nd floor interior column after


268

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e) 0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

2C4

DIθDI

maxExc

(f) 0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

2C4

Figure 4.88– (a-d) Photos of damage progression in the 2nd floor exterior column after


269

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e)0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

1B1

DIθDI

maxExc

(f)0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

1B1

Figure 4.89 – (a-d) Photos of the damage progression in the 1st floor beam after each main

event. Evolution of damage index using (e) OpenSees and (f) measured data.

270

(a) 50/50 (b) 10/50-1b (c) 2/50 (d) 10/50-2

(e) 0 20 40 60 80 100 120 140 160 180

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50 II

LP89G0410/50-2

2B3

DIθDI

maxExc

(f) 0 20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

Time (sec)

Dam

age

Inde

x

TCU08250/50 I

LP89G0410/50-1b

TCU0822/50

LP89G0410/50-2

2B3

Figure 4.90 – (a-d) Photos of the damage progression in the 1st floor interior column after each main event. Evolution of damage index using (e) OpenSees and (f) measured data.

271

Chapter 5: Applications

5.1 Introduction

In this chapter, the design recommendations proposed in Chapter 2 are implemented and

evaluated in the designs of three case study buildings. These include a 3, 6, and 20-story

buildings with perimeter frame systems. Each of these buildings are modeled using the

recommendations outlined in Chapter 4 and then subjected to multiple ground motions

representing a range of earthquake intensities up through the 2% in 50 year hazard level.

The results from this study are used to evaluate the performance of composite RCS

moment frames as influenced by the current and proposed design recommendations. The

performance of the 3-story building also provides further insights into the performance of

the test frame discussed in Chapter 3.

5.2 Case Study Buildings

The moment frame of the 3-story case-study building is identical to the test frame

discussed in Chapter 3. Pertinent details of this frame design are briefly reviewed in this

chapter; for complete details the reader is referred to Chapter 3. The 6 and 20-story

designs are more representative of the building heights where RCS systems are most

competitive with conventional steel or RC systems.

The layout of the 6-story building is presented in Fig. 5.1 and follows the general layout

of the theme structure proposed as part of the US-Japan program on hybrid structures.

For the perimeter frame configuration, two additional columns (columns B1/B7 and

E1/E7 on Fig. 5.1) have been added to the original theme structure plan. The layout of

the 20-story case study building (Fig. 5.2) is well known to the research community as

one of three buildings that has been exhaustively studied as part of the SAC Joint Venture

investigation on Steel Framed Buildings (Gupta and Krawinkler, 1999). In the 20-story

building, the beams framing into the corner columns are released in one direction to

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avoid complicated three-dimensional joint details and biaxial bending in the corner

columns.

All three building systems have been designed as perimeter moment resisting RCS frame

systems according to the recommended design provisions presented in Chapter 2. The

unit floor loads used in the design and modeling of each of the case study buildings are

summarized in Table 5.1. The live load is based on typical office floor load requirements

from the ASCE 7-02 standards. An additional concentrated wall weight of 1.0kPa is also

considered along the perimeter of the building (1.2kPa was assumed for the 3-story

building). Seismic design forces are based on a highly seismic site representative of Los

Angeles or San Francisco with mapped spectral accelerations of and

, using IBC 2003. The soil condition at the building location is assumed to be

that of the site class D. The buildings are assigned a Seismic Use Group I, which

together with the seismic hazard level classifies the building into Seismic Design

Category D (as per IBC 2003).

1.5sS = g

g1 0.72S =

The calculated seismic mass (including the weight of the structural members) and the

natural periods for each of the case study buildings are summarized in Table 5.1. The

natural periods are computed from the OpenSees model with gravity loads applied and

zero tensile strength in the concrete to represent cracked conditions. These natural

periods are consistent with those calculated using elastic models with averaged positive

and negative composite beam stiffness, 50% rigid panel zones, and effective cracked

column stiffness according to equation 2.5. The periods calculated according to the

simplified equation in the IBC 2003 (equation 2.3) (Ta) for the 3, 6, and 20-story frames

are 0.44, 0.68, and 2.43 seconds, respectively. Given that the computed periods from the

analytical models are greater than the code defined values, the IBC 2003 permits one to

use an effective period of 1.2Ta for calculating the design base shear. Thus, the base

shears are determined using periods of 0.53, 0.82, and 2.91 seconds for the 3, 6, and 20-

story building, respectively. Each of these periods is marked on the IBC (2003) design

hazard spectra in Fig. 5.3 with the corresponding design base shear coefficient (not

including the provision for accidental torsion). Note that the resulting base shear for the

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20-story frame falls below the lower limit of the design base shear (represented by the

dashed line in Fig. 5.3). Therefore, the 20-story frame is designed based on the minimum

base shear coefficient of 0.044V W = . The calculated building weights and governing

design base shear coefficient, including the accidental torsion effect, are presented in

Table 5.1.

Member dimensions and properties for the 6 and 20-story frames are shown in Tables 5.2

and 5.3, respectively; properties of the 3-story frame are reported in Chapter 3. Rolled W

shapes of grade 50 steel ( 345yF MPa= ) are used for the beams and ' 41 (6 )cf MPa ksi=

normal strength concrete is used for the reinforced concrete columns. The longitudinal

and transverse steel reinforcement in the columns is designed according to the seismic

details and recommendations as given in ACI-318 Chapter 21 with a nominal yield

strength of . The general layout of the transverse reinforcement is

shown in Fig. 5.4 and 5.5 for the 6 and 20 story frames, respectively. The restraining

bars are provided to meet the clear span distance requirements of crossties (≤356mm or

14in) from ACI-318 and may vary depending on whether a steel erection column is

needed in the construction process. The slab is normal weight concrete with a minimum

specified compression strength of

414 (60 )yF MPa k= si

' 27.6 (4 )cf MPa ksi= . The controlling aspects of the

design of the buildings are presented in the following sections.

5.2.1 Beam Design

The beam sizes in all frames are controlled by the negative bending strength requirements

for the 1.2D+0.5L+1.0E load combination (IBC 2003). As recommended in Chapter 2,

the shear studs are designed to develop the full composite strength according to the

AISC-LRFD (2002) and the AISC Seismic Provisions (2002). The latter reference

applies a 25% reduction factor on the strength of the shear studs defined in the first

reference in order to account for the cyclic demands in seismic design.

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5.2.2 Column Design

The design of the RC columns in each of the case study frames is controlled by the

strong-column weak-beam criteria. Table 5.4 lists the computed nominal strengths of the

interior and exterior columns, the plastic strength of the composite beams (according to

Section 2.3.2.2.1), and the corresponding strong-column weak-beam ratios according to

equation 2.46 for the 3-story frame. These ratios are slightly different than those

presented in Chapter 3 due to the fact that tributary gravity loads are now considered in

the columns and, therefore, additional strength is provided based on the column

interaction diagram. The two exterior columns are handled separately due to overturning

effects, which vary the axial loads and leads to large differences in strength. The beam

that frames into the exterior column with the larger strength (compressive overturning

force) will be in negative bending (i.e. steel only), while the opposite exterior column that

is weaker must resist composite action associated with positive beam bending. This is

the reason for the two SCWB ratios for the exterior columns in Table 5.4. The average

SCWB ratios over the floor considering composite beam action are 1.2, 1.1, and 1.0,

indicating that the spirit of the code is met by satisfying the SCWB criterion over the

entire floor. Considering only the bare steel beam strength, the SCWB criterion is met at

every joint with the average ratios increasing by about 20%. The alternative SCWB

criteria proposed by the SEAOC Blue Book are also specified in Table 5.4. This reveals

that both the 1st and 2nd floor are approximately 40% under-designed based on the

requirements of the alternative (proposed SEAOC) SCWB check (considering composite

beam strength).

Table 5.5 presents the SCWB information for the 6-story building for the frame lines 1

and 7. This direction of framing, as opposed to frame lines A and F, is modeled and

simulated in OpenSees later in this chapter. The SCWB design for the 6-story frame

pushes the minimum limits of the specified criteria, similar to the design for the 3-story

frame. The average ratios over each floor are 1.10, 0.96, 1.09, 1.02, 1.14, and 0.57 for

the first through roof level, in order. Again, if only the steel beam is considered, the

average SCWB ratios increase by about 17%, implying that there is some conservatism in

275

the design of the columns. The alternative SEAOC Blue Book SCWB ratios are also

reported considering composite beam action, which reveals that the strength of the

columns would have to be increased by almost 50% in order to satisfy this proposed

criterion.

Table 5.6 presents the same SCWB information for the 20-story building for the frame

lines A and F. Again, this represents this framing direction is modeled and simulated in

OpenSees later in this chapter. The SCWB ratios for this frame are much more

conservative than the two previous designs, with the average ratios over the each floor

equal approximately 1.60 (compared to ~1.0 for the other two building designs). Despite

this conservatism, this design would still require about a 20% additional strength in the

columns in order to satisfy the proposed alternative SEAOC Blue Book SCWB criterion.

While this conservative SCWB design was originally a result of miscalculation of the

plastic strength of the composite beams, this resulting frame design provides some insight

into the influence on the SCWB criteria.

5.2.3 Composite Joint Design

The composite beam-column joints in these frames are designed with the following

standard details: (1) face bearing plates, (2) band plates, and (3) joint ties within the beam

depth. The strength of the joints in the 3, 6, and 20-story frames, calculated according to

the updated strength model discussed in Chapter 2, are presented in Tables 5.7, 5.8, and

5.9, respectively. The ratio of the nominal joint strength to the nominal strengths of the

beams (i.e. strong-joint weak-beam ratio) is also reported. The design of the joints for

these case study buildings shows that the standard joint details will usually provide

sufficient strength to automatically satisfy the strong-joint weak-beam criterion.

A plan view of the column and a typical beam column joint in the 20-story frame is

shown in Fig. 5.6. Notice that in this detail the joint ties are allowed to pass directly

through the web of the main girder and the gravity beams. This is clearly seen in Fig.

5.7, which represents cross section A-A from Fig. 5.6. The band plate detail is utilized

276

both above and below the beam along with the face bearing plates (FBP) for both the

main girder and the gravity beam (Fig. 5.8). This detail is representative of the details in

the 6-story frame as well. The joint details in the 3-story frame are discussed in Chapter

3 and include a transverse beam framing into both sides of the column and without

through-web joint ties.

5.2.4 Drift Limitations

When checking the drift limitations for each of the frames, it should be noted that IBC

(2003) and ASCE 7 (2002) allow the designer to compute the base shear based on the

calculated period of the frame rather than the code-defined value. In addition, the lower

limit of the design base shear, represented by the dashed line in Fig. 5.3 does not apply to

the drift check. For these case-study buildings, this resulted in a reduction of the base

shear by approximately 25, 40, and 50% for the 3, 6, and 20-story frames. Using these

reduced forces, all of the frames automatically satisfy the 2% interstory drift limits set by

the IBC (2003) and ASCE 7 (2002) and no further resizing of the members is required.

While this is not always the case in the design of RCS frames, it does highlight the

efficiency of composite beams and RC columns to satisfy both strength and stiffness

requirements concurrently. This is in contrast to conventional RC or steel moment

resisting frames, where the sizes of the beams are typically controlled by the drift

criterion.

5.3 Nonlinear Dynamic Time History Analyses

Second-order inelastic dynamic analyses are performed on the three case study buildings

using the OpenSees analysis platform. Three analytical models are generated using the

recommendations presented in Chapter 4. A stripe analysis technique, described in

Section 5.3.1, is implemented in this study to investigate the performance of the three

case study buildings at a variety of hazard levels.

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5.3.1 Ground Motion Scaling Techniques

The approach taken in the nonlinear time history analyses is to subject the analytical

model to measured ground motions, each of which represents a particular hazard level for

the building under investigation, and then report the engineering demand parameters of

interest, such as interstory drift ratio (IDR) and floor accelerations. The result of these

analyses can be represented as a scatter plot between the earthquake ground motion

intensity and the engineering demand parameter of interest. This strategy is shown in

Figure 5.9a, where each point represents the building response (maximum IDR) from a

single earthquake ground motion. One problem with this approach is that there is often a

lack of substantial data in the less frequent hazard levels (i.e. 2%in50years), because

there are very few recorded events that can provide these high intensities. This lack of

high intensity ground motions is why other approaches, such as the incremental dynamic

analysis (IDA) method (Vamvatsikos 2002), were developed.

A key assumption of most techniques that utilize recorded ground motions as input for

nonlinear response analyses is that it is reasonable to scale existing records to represent a

range of earthquake intensities. Shome (1999) has shown that scaling ground motion

records by the spectral acceleration at the first natural period of a structure is appropriate

to represent various earthquake intensity levels and does not introduce a bias into the

results. This conclusion is limited to first-mode dominated structures and does not

necessarily apply to frames that have significant higher mode effects. The higher-mode

limitation poses a problem for the 20-story frame and discussion on an alternate scaling

technique for this building is provided in Section 5.3.4.

If one accepts the legitimacy of scaling ground motions, one approach to organize the

analyses is to incrementally scale a single earthquake to a variety of ground motion

intensities resulting in what is often called an IDA curve. This can be thought of as the

dynamic equivalent of the static pushover curve for a single ground motion. This process

can be repeated for a number of different earthquake events and results in a series of IDA

278

curves, as is represented in Figure 5.9b. These curves are often taken up to collapse of

the structure and can exhibit nonlinear hardening and softening prior to collapse.

An alternate approach to the IDA concept is to select and scale different records, which

are more suitable to represent different hazard levels for a particular building and site.

This is in contrast to scaling one record to a wide range of intensities. This method,

which can be referred to as the stripe analysis technique, involves selecting a specific

number of appropriate ground motions and scaling each of them to the same hazard level,

thereby creating a stripe of response points. This is represented in Figure 5.9c for three

hazard levels. The appropriateness of a record depends on several factors, all of which

attempt to gauge how suitable the record is to represent the particular hazard level. This

topic will be discussed further in Section 5.3.3 when records are selected for each of the

case study frames. The process results in a series of stripes at various hazard levels, from

which a statistical analysis can be performed to find the mean and coefficient of variation

at each level. It is not appropriate nor is it necessary to connect the dots between each

stripe since it is not likely that the same set of earthquakes is repeated for each hazard

level. What is often reported are the curves that connects the means and a plus and minus

standard deviations for each stripe level. This stripe analysis approach is adopted in this

study.

5.3.2 Limitations of Analytical Models

As discussed in Chapter 4, the fiber beam-column element models can accurately capture

the flexural hinging response in composite steel beams and RC columns when it is

limited to steel yielding and concrete crushing and cracking. When pushed to larger

inelastic rotations, the response of these hinges begin to be dominated more by other

effects such as local buckling in the steel beams and reinforcing bar bond deterioration

and buckling in the RC columns. Given the fundamental assumptions of these fiber

models, these types of degrading behaviors are not captured in the response. Therefore,

when the response exceeds about 4% interstory drift, it is unlikely that the fiber models

are accurately capturing the complete behavior. It is for this reason that the analyses

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presented in this chapter will not push these buildings out to very large drifts by scaling

the records up to simulate global collapse. Rather the limits of the model will be

acknowledged and the results presented in this chapter will be limited to earthquake

record intensities slightly above the 2% in 50 year event (or the maximum considered

event), where drifts will likely reach the limits of the validity of the fiber elements.

5.3.3 Ground Motion Selection

The earthquake records used in these analyses were selected from a suite of 80

earthquake ground motions. This suite of records was originally compiled by Medina

(2001) from the Pacific Earthquake Engineering Research (PEER) Center strong motion

database, where all records are consistently processed. All ground motions were

recorded on free-field sites that can be classified as site class D according to the IBC

2000 provisions. Figure 5.10 shows the distribution of the magnitude (Mw) and distance

(R) pairs for each of the 80 records.

In this study, 15 unique earthquake records are chosen for each stripe level, where each

record is scaled to a common spectral acceleration ( ( )1aS T ) to represent a specific hazard

level for the building. Each of these records has been selected from the suite of 80

records using the following criteria:

1. The spectral acceleration of the unscaled record should be as close as possible to

the desired Sa-level, such that the scaling factor applied to the record is as near as

possible to unity. Adhering to this will avoid scaling records by very large or

very small factors. Unfortunately, this criterion cannot always be satisfied since

there is only a limited range of ground motions available for use. For this reason,

when larger scaling is required, a second criterion (#2) is also considered.

2. The epsilon of the earthquake record, which is defined by Baker (et al. 2005) as

the number of standard deviations by which an observed logarithmic spectral

acceleration differs from the mean logarithmic standard deviation, is also

considered in the selection of ground motions. Epsilon is computed by

subtracting the mean predicted )(ln 1TSa from the record’s unscaled )(ln 1TSa and

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dividing by the logarithmic standard deviation (Baker et al. 2005). Both the mean

predicted )( and the logarithmic standard deviation are calculated from

attenuation relationships given the magnitude and distance to the rupture zone for

the record of concern. Baker et al. points out that at low mean annual frequency

of exceedance the ground motions are generally associated with positive-epsilon

events. Baker et al. argue that the scaling of zero or negative epsilon events to

achieve larger intensity records may not be appropriate and will likely over

estimate the demand on the structure. Therefore, they recommended to select

records with appropriate epsilon values for the type of scaling that one wishes to

perform. This means that when selecting records to scale up to represent lower

frequency events, records with positive epsilons should be used.

ln 1TSa

3. The records from the PEER strong motion database have been filtered for noise

using causal Butterworth filters with high-pass (HP) and low-pass (LP)

frequencies. The useable bandwidth of the records for the purpose of engineering

analysis is within 0.8 of the LP frequency and 1.25 of the HP frequency. The

limit on the low pass frequency is not of concern for the frames under

investigation given their long natural periods. On the other hand, the high pass

frequency of the record should be sufficiently lower than the natural frequency of

the structure, or rather the high pass period should be larger than the natural

period of the structure. This is particularly important considering that the natural

period of the frames will elongate as the structure becomes more nonlinear at

lower hazard levels. This criterion was most critical for the 20-story frame,

resulting in the elimination of 40 of the records in the ground motion suite, which

have high pass frequencies of 0.2Hz (5 seconds) that were considered too close to

the natural frequency of the frame (0.25 Hs, 4 seconds).

Figures 5.11 through 5.13 provide a graphical representation of the first two steps of the

ground motion selection process by plotting the spectral acceleration versus the epsilon of

each of the records for a period of 1.0, 1.5, and 4.0 seconds1. These figures shows that a

1 Note that the records for the 6-story building were chosen and scaled based on a natural period of 1.5 seconds, whereas Table 5.1 reports the period as 1.4 seconds. This difference reflects a change in the

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large number of the earthquakes fall within the low spectral acceleration and low epsilon

region, which is expected since these are the more common events. The more intense

events (i.e. lower frequency) are represented by the data points that have both a large

spectral acceleration and large epsilon. Using the information in these graphs and the

selection criteria presented in steps 1-3, records are selected for each frame and stripe

level. The final scaled events for the 3-story frame through the 0.6g stripe level are

shown in Figs. 5.14a-g. For all stripes above 0.6g, the records used for the 0.6g stripe are

repeated given the lack of recorded ground motions in these higher intensity regions. The

results for the 6-story frame up through the 0.4g stripe level are shown in Figs. 5.15a-f,

where all stripes above 0.4g were created by re-scaling the 0.4g stripe. The records for

the 20-story frame were selected using the same technique presented here, however,

scaling of these records was performed in slightly a different manor, as described in the

next section.

5.3.4 Weighted 20-story Scaling Technique

One of the fundamental assumptions of scaling records based on is that the

structural response is largely dominated by the first-mode of vibration. This is clearly not

the case for a 20-story building, where the influence of higher modes is likely to be

significant. This suggests that an alternative scaling technique should be implemented to

account for the effects of the higher modes. This issue has been investigated by Shome

(1999) who recommends that a weighted-average scaling technique be used in the cases

where more than one mode has a large impact on the final response of a structure. The

number of modes that one should consider and their corresponding weighted values can

be determined from the modal-mass participation factors of the elastic structure. Table

5.10 lists the modal properties of the 20-story frame and their corresponding modal-mass

participation factors. Based on these participation factors, it seems reasonable to consider

the first three modes of the frame in the earthquake scaling procedure. The weighted

( )1aS T

model between selecting the records and the final analysis model and is presumed to be small enough not to have a large impact on the final results.

282

factors (WFi) are interpreted from these mass participation ratios and are presented in the

last column of Table 5.10.

# modesconsidered

Target

1 Record

( )( )

a ii

i a i

S TScale Factor WF

S T=

= ∑ (0.1)

The solid line in Fig. 5.16 is an example of an unscaled response spectrum (IV79e12).

The white circles are points on the IBC equal hazard curve for the first three modes of the

20-story frame, each of which represent a ( )Targeta iS T value. The corresponding points

on the unscaled record at these three periods represent the ( )recorda iS T values. Using

these data points and the weight values proposed in Table 5.10, a weighted scale factor of

4.14 can be obtained for this record from equation (0.1). The results of the record

selection (presented in Section 5.3.3) and the weighted average scaling for the 20-story

frame are shown in Figs. 5.17a-f for stripe levels up through .

Beyond , the records are repeated with only a difference in scaling

factors.

( )1 Target0.20aS T g=

( )1 Target0.20aS T g=

Whereas the scaled records for the 3 and 6-story frames are all scaled to a common

spectral acceleration value, ( )1aS T ; using this weighted average scaling technique, the

scaled records for the 20-story building do not share a common spectral value. Rather

there is some variability in the hazard level that corresponds to the weight factor used at

each specific period. As seen in Fig. 5.17f, the variability is small around 4 seconds

where the weight factor corresponds to 75%. This variability increases dramatically at

the 1.5 and 0.8 seconds where the weight factors are only 15 and 10%, respectively. In

order to organize the analysis results for the 20-story frame, the engineering demand

parameters used to evaluate the performance of the 20-story frame will be plotted against

, despite the fact that there exists a small amount of variation at this period. ( )1 TargetaS T

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5.4 3-Story Perimeter Frame Results

This section will first begin by subjecting the analytical model of the test frame,

developed in Chapter 4, to the stripe analysis at four different hazard levels

corresponding to the levels tested in the laboratory. These results are investigated to give

us some insight to the response of the test frame and how this compares to other events.

The OpenSees model will then be adjusted from the laboratory conditions to represent the

case-study building with appropriate gravity loads and damping. Using this updated

model, a complete stripe analysis is simulated up to hazard levels just beyond the 2% in

50year event, defined by the IBC 2003 ( ( )1aS T =1.08g). Important engineering demand

parameters are then calculated at each stripe level to evaluate the frame performance.

5.4.1 Interpreting the Test Frame Results

The measured maximum interstory drift ratios from the test frame are represented in Fig.

5.18 with the inverted triangle for the first four pseudo-dynamic events (discussed in

Chapter 3). These records are as follows:

1. 1999 Chi-Chi record scaled to 50/50 hazard level ( ( )1aS T =0.41g)

2. 1989 Loma Prieta record scaled to 10/50 hazard level ( ( )1aS T = 0.68g, “1a”)

3. 1989 Loma Prieta record scaled to 80% of the 10/50 hazard level ( ( )1aS T = 0.54g,

“1b”)

4. 1999 Chi-Chi record scaled to the Taiwanese 2/50 hazard level ( ( )1aS T = 0.92g)

The simulated results from the analytical model of the test frame developed in Chapter 4

are also shown in Fig. 5.18 with the diamond marker. Recall that this model simulates

the laboratory conditions of the test frame, with zero viscous damping and where the full

gravity load is applied to the leaning column. This figure shows that the measured drift

for the first three loading events is captured very well by the analytical simulations. In

the fourth event (2/50), there is a large difference between the predicted and measured

maximum drifts, which can be largely attributed to the limitations in the fiber model

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discussed in Section 5.3.2. This figure is one of the primary motivations for questioning

the validity of the fiber models beyond about 4% interstory drift.

Using this same analytical model, nonlinear earthquake time history analyses are

simulated using the ground motions selected in Section 5.3.3 corresponding to the

following four hazard levels: (1) ( )1aS T = 0.40g, (2) ( )1aS T = 0.60g, (3) = 0.72g,

and (4) = 0.9g. These levels represent the range of the Taiwanese spectral hazard

levels of 50, 10, and 2% in 50 years that were simulated in the composite RCS test frame

described in Chapter 3. In Fig. 5.19, the maximum interstory drifts for each scaled

ground motion are plotted against the intensity of the record, which is represented by the

intensity measure . The median and the 16th and 84th percentile response values

are also represented in this figure by the dashed lines. Note that the response points

described in Fig. 5.18 are repeated in Fig. 5.19. These stripe analyses of the test frame

provides the opportunity to (1) consider the performance of the test frame under different

input ground motions, and (2) evaluate the severity of the records that were used in the

test.

( )1aS T

( )1aS T

( )1aS T

Before comparing the response of the test frame at each stripe level with that of the

measured and simulated test response, it is important to make a couple of key distinctions

between the two. Recall that the test frame was not repaired after each earthquake event,

so therefore the damage accumulates throughout all the loading events, making the frame

more flexible and susceptible to further damage. Contrast this to stripe analysis response

points, where each of the simulations represents a single event that is subjected to an

undamaged frame. In addition, there are several aspects of the pseudo-dynamic testing

methodology that could lead to larger drifts than would be experienced under actual

earthquake loading conditions (discussed in Chapter 4).

Now focusing on Fig. 5.19, it is apparent that the first three loading events fall within the

median and 84th percentile of the predicted response points. This implies that the records

selected for use in the test were representative of ground motions that were slightly more

285

severe than the median at their respective stripe levels and produced larger deformation

demands. At the = 0.9g stripe level, it is interesting to note that the predicted test

response point falls on the median of the stripe analysis response points. This was

intentional in the selection of this event, given that this record was carefully selected to

produce a moderate amount of damage and remain within the capabilities of the

laboratory. Given the limitations of the fiber beam-column, it is likely that the response

points in Fig. 5.19 which are equal to or larger than 4% interstory drift are beginning to

diverge from the actual response. This accounts for 6 of the 15 total records that were

analyzed at this hazard level. Despite these modeling limitations, there are important

implications that can be deduced from the analyses at the

( )1aS T

( )1aS T = 0.9g hazard level.

These are discussed in a subsequent section after the local response comparisons.

Figure 5.20 plots the simulated maximum response for selected columns, beams, and

joints as well as the corresponding measured values from the test frame. For the column

plastic rotations (Figs. 5.20a-b), the measured response of the test frame falls within the

range of simulated results for the first three events, but differences occur during the 2/50

event when measured response points fall in the tail of the predicted distribution in Figs.

5.20a. Similar trends are apparent in the beam plastic rotation plots in Figs. 5.20c-d,

where maximum measured plastic rotations for an interior and exterior beam hinge are

represented on these plots with an inverted triangle. Again, the maximum values from

the 2/50 event correspond to the excursion where severe local buckling had increased the

flexibility of the test frame. In addition to this, there is some measurement error when

attempting to track the large plastic rotations that occurred in these hinges in the test

frame, particularly in the measured point in Fig. 5.20c that shows plastic rotations up to

6% in the beam. While the 2nd floor joint response in Fig. 5.20f is also captured

relatively well, there are some noticeable differences in the simulated versus measured

response of the 1st floor joint (Fig. 5.20e). While some of this may be due to deficiencies

in the models, these particular joints measurements are prone to error because the data is

inferred from beam and column tiltmeters that likely includes additional rotation from

these members.

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There are a few important conclusions to draw from the results shown in Figs. 5.19 and

5.20:

1. While the full-scale test presented in Chapter 3 provided a unique opportunity to

evaluate the performance of the frame under a series of earthquakes, Fig. 5.19

reveals that the performance exhibited in this test is not a definitive estimate of

performance. Rather it is but one instance within a larger distribution of possible

random earthquake ground motions.

2. The 1999 Chi-Chi record (TCU082) was initially chosen because the OpenSees

models predicted that this motion would produce a moderate amount of damage to

the test frame and stay within the limitations of the laboratory. This is confirmed

in Fig. 5.19, which shows that the analytical prediction of the test response lies on

the median of the 15 records analyzed at this level. One might consider what

would have happened if instead of selecting the TCU082 event, the LP89hda

record (1989 Loma Prieta), which is labeled on Fig. 5.19, was selected for the test

at the 2/50 hazard level? The peak drift in this event (2.2%) is well within the

capabilities of the analytical models, so it is reasonable to suspect that the test

frame would have matched the predicted response rather well. It also reveals that

there would have been much less damage under this LP89hda event than what

was observed in the test frame (under the TCU082 event). This would have likely

led to much different conclusions regarding the performance and modeling of

composite RCS frames. On the other hand, what if the LP89g03 record (marked

on Fig. 5.19) was selected to represent the 2/50 hazard level event on the test

frame? Predicted drifts for this event are very large (6.4%) and beyond the

limitations of the fiber models. In this case, it is likely that if local buckling and

general stiffness degradation was incorporated into the frame performance, this

record has caused enough damage and drift to lead to global collapse of the frame.

3. What would the response of the frame to the 2/50 event have been if it was

subjected to an undamaged frame. In other words, how significant to the final

response of the test frame was the fact that the frame had already experienced the

equivalent of two major earthquakes (50/50 and 10/50 event)? Note that a

moderate amount of local buckling had already occurred in most of the steel beam

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hinges during the first two events, which leads local buckling at much earlier

stages in the 2/50 event. This would increase the flexibility and reduce the

capacity of the beam hinges in negative bending as compared to an undamaged

beam hinge and ultimately lead to larger interstory drifts.

5.4.2 Modeling Variations for Realistic Building Case Study

The following adjustments are made to the 3-story model of the test frame in order to

account for more realistic conditions in an actual building:

1. In the pseudo-dynamic frame test, the only gravity load on the frame test was that

of the frame itself. All other gravity loads that were tributary to the frame and to

gravity columns supported by the frame were modeled in the pseudo-dynamic

algorithm with a leaning column. This same distribution of loading was

implemented in the analytical model of the test frame. For the model results

described later in this chapter, which are intended to represent the real building,

the gravity loads are distributed between the perimeter frame and gravity column

according to the actual floor framing plan. Roughly one-third of the gravity (full

dead and 25% live load) is applied to the moment frame and two-thirds is applied

to the leaning columns. This does not change the effective P-delta effects on the

structure, but the shift of gravity load to the RC columns will increase their

moment capacity by approximately 10% and increase the effective stiffness by

approximately 15%.

2. As discussed in Chapter 3, there was no viscous damping included in the pseudo-

dynamic algorithm for the test frame. Accordingly, viscous damping was set to

zero in the analytical model presented in Chapter 4. The building model in this

chapter does, on the other hand, include 2% viscous damping at the 1st and 3rd

modes of the structure. Given that the natural period of this structure (Tn = 1sec)

falls within the velocity-sensitive region of response spectrum, damping is

expected to result in a noticeable decrease in the response of system as compared

to structures that fall within the acceleration or displacement-sensitive regions of

the spectrum (Chopra 1995).

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In order to highlight the differences of the laboratory versus the realistic building

analytical model, the test frame loading protocol is analyzed using the revised model and

compared to the original model. Results for the two analysis models, as well as the

measured results, are summarized in Table 5.11. The results show that the adjustments

to the mold reduce the maximum interstory drifts by about 20% in the larger earthquakes,

which is primarily due to the viscous damping added to the realistic model. This effect

will be investigated further in Section 5.4.2.2.

Both models incorporate the measured material properties of the test frame, as described

in Chapter 3. The measured steel and concrete strengths are presented in Tables 5.12 and

5.13, respectively. These tables show that the measured values all exceed the expected

strength values. While there is a very large material overstrength of the concrete in the

RC columns, this only leads to approximately a 10% increase in the moment capacity of

these columns given that they are largely controlled by the yielding of the longitudinal

reinforcement. The measured yield strength of the steel in the 2nd floor beams is

approximately 30% higher than the expected yield strength (1.1Fy), which has the

potential to have a large impact on the balance of strength between the beams and the

columns. Fortunately, given that the measured strength of the concrete and the rebars

were also found to be higher than the expected values, these differences do not severely

impact the capacity design criteria (e.g. SCWB provisions) and the performance of the

frame. One could imagine a case where these measured properties could adversely affect

the system performance and shift the hinging from the beams into the columns, perhaps

leading to an undesirable story mechanism. While these results are based on a single test

frame, this does highlight the potential problems that one could face in the design,

analysis, and performance prediction of real building systems. One way to approach the

analysis of this type of problem is implement a sensitivity analysis of several of the key

properties of the frame that could affect the system performance.

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5.4.2.1 Static Pushover Response

Figure 5.21 shows the roof drift ratio versus the base shear from a static pushover

analysis on the 3-story building using the IBC 2003 force distribution. This figure shows

that the building has a maximum strength of approximately 2.4 times the design base

shear. This overstrength is within the range expected (2-3) of buildings designed per

current standards. In Fig. 5.22, the interstory drift profile of the building is plotted at

various stages of the pushover analysis. The expected levels of deformation can be

computed using the so-called “displacement-coefficient” method from FEMA 273. This

method determines the target displacement, δt, to which the structure is expected to be

pushed during a design level earthquake. For the 3-story frame, the 10/50 target

displacement level is approximated as 1.9% roof drift. From Figs. 5.21 and 5.22, at this

level of drift, the building is expected to reach its maximum strength with deformations

tending to concentrate in the 2nd floor. As the frame is pushed further, deformations

continue to concentrate in the first two floors, indicating that the 2-story mechanism

observed in the test frame is also captured in the analytical model.

5.4.2.2 Derivation of Damping and Effects on Maximum Response

Initially, the analytical models used in this study contained no damping so as to mimic

conditions in the test frame. In order to more accurately model the conditions of a real

building, 2% damping is included in this updated model. In OpenSees, damping is

assumed to be linearly proportional to the mass and stiffness matrix, according to the

Rayleigh equation (Chopra, 1995).

C M Kα β= + (0.2)

where:

M, K = Mass and stiffness matrix of the MDOF structure

α, β = mass and stiffness parameters of proportionality determined by to the

following equations:

290

( )2 2

2

2

2

j j i i

j i

i i i

ω ξ ω ξβ

ω ω

α ω ξ βω

−=

−

= −

where damping ratios, ξi and ξj, are assumed at two frequencies, ωi

and ωj, of the structure.

In modeling moment resisting frames, the mass matrix is typically defined as a diagonal

matrix with the mass of each floor along the diagonal. In OpenSees, the stiffness matrix

used to calculate the damping matrix per (0.2) can be defined as one of three variations:

(1) the current iteration of the model ( ), (2), the last committed state of the model

( ), or (3) the initial state of the model ( ). The first and second options

are roughly the same in a time history analysis since the load steps are small, although the

later seems to make more sense given that the stiffness is based on a converged step

rather than the current Newton iteration. Both of these variations of the Rayleigh

damping equation will cause the damping matrix to continually change as nonlinearities

in the system occur, which maintains an effective equivalent damping, but would result in

equilibrium imbalances that could ultimately be detrimental to the reliability of the

computed results (Bernal, 1994; Kannan and Powell, 1973). The third option is to use

, which implies a constant damping matrix over the entire time history analysis

according to equation

currentK

lastCommittedK initialK

initialK

(0.2). This approach leads to the potential for the development of

spurious forces at degrees of freedom with small (or zero) inertias, which is a result of the

loss of orthogonality of the damping matrix when yielding occurs in the structure (Bernal,

1994). This effect only occurs as the frame experiences inelasticity, and has a larger

effect on the computed forces than the maximum displacements, given that the plastic

excursions typically occur over short periods of time. This approach would also lead to a

change in effective damping according to the amount of nonlinearity that occurs during

the time history. There are ways to condition the damping matrix such that these

spurious forces are not introduced into the system (Bernal, 1994), but these methods are

currently not implemented in OpenSees.

291

The effects of the different formulations of the damping matrix, as well as zero damping,

are compared in Fig. 5.23. This figure shows the median response of the model at the

three stripe levels ( = 0.40, 0.72, and 0.90g) with four different assumptions for

damping: (1) zero damping, (2) , (3) , and (4) . The results show

that the constant damping matrix based on the initial stiffness causes the biggest

reduction of the maximum response (approximately 20%), which is likely a combination

of the increase in relative damping as the structure gets more nonlinear and the effect of

the spurious forces. The damping shows about 5% larger response than the

, but also leads to convergence problem as 5 of the records were unable to converge

(~10% of events). This problem gets worse when the damping is based on

causing a total of 10 records to fail to converge, thereby making the median response

unreliable.

( )1aS T

currentK lastCommitK initialK

lastCommitK

initialK

currentK

In this study, it was decided to base the damping matrix on . This study accepts the

spurious nodal forces at the massless degrees of freedom, in exchange for better global

convergence of the model. It also is based on the assumption that the inherent damping

in the building is associated with physical properties that would be present throughout an

earthquake. As discussed later in Chapter 6, this problem with damping is something that

needs to be resolved in OpenSees. For now, the differences shown in the median drift

response are small enough to accept this problem.

initialK

The alpha and beta coefficients (equation (0.2)) for the 3-story frame are computed

according to the 1st and 3rd modal frequencies of the frame assuming a cracked stiffness

of the columns and beams, anticipating some elongation of the period during the

earthquake excitation. Figure 5.24 depicts the damping ratio as a function of the

frequency by assuming 2% damping at 6.11 and 40.65 rad/sec, which correspond to the

square root of the 1st and 3rd eigenvalues of the cracked stiffness of the 3-story RCS

frame. The frequency corresponding to the initial uncracked stiffness of the frame is also

marked on this figure at approximately 8 rad/sec, which corresponds to a damping ratio

of approximately 1.7%.

292

5.4.2.3 Global Response

The stripe analysis results are plotted in Fig. 5.25 with the EDP as the maximum

interstory drift ratio (the maximum IDR that occurred in any floor of the frame). Each

stripe contains the results for 15 ground motions corresponding to the events chosen in

Section 5.3.3. The median, 16th, and 84th percentiles for each stripe level are connected

by the solid and dotted lines, respectively. This figure reveals that the response of the

structure with respect to increasing earthquake intensities remains relatively proportional

to the intensity up to the design hazard level ( ( )1aS T = 0.72g). At this hazard level, larger

nonlinearities in the frame begin to increase the variability of the response, with the

predicted median response just above 2.5% interstory drift and a dispersion ( ln |idr Saσ ) of

17.5%. Note that this median exceeds the design drift limit of 2% set by the IBC 2003

and the ASCE-7 (2002). With an implicit lognormal assumption, these results indicate

that there is a probability of 78% that the frame will exceed the design limit of 2% drift in

a design level event. As the frame is pushed to the 2% in 50 year level ( = 1.08g),

the median response increases out to 3.5% interstory drift with a dispersion of 28.9%.

Note that 6 of the 15 records at this hazard level exceed 4% interstory drift, implying that

the assumptions in the fiber models are beginning to diverge from what would be the true

response (e.g., due to local buckling in the steel beams, bond slip in the RC columns,

etc.).

( )1aS T

Figure 5.26 contains six plots corresponding to the first 6 IDA stripe levels ( ( )1aS T =

0.045-0.5g) each depicting the instantaneous drift profile of the frame at the time of the

maximum interstory drift. The dark circle on each of the drift profiles indicates the floor

at which the maximum interstory drift occurred. Figure 5.27 depicts the same

information for the remaining 6 IDA stripes ( ( )1aS T =0.6-1.15g). These plots show that

the frame responds primarily in a first mode of vibration during the lower level IDA

stripes. As the intensity is increased to the design level ( ( )1aS T =0.72g) and higher, the

293

maximum drifts begin to occur in the 2nd story, implying that the nonlinearities are

beginning to concentrate in this floor. This behavior is a bit different from the test frame,

where the drift concentrated in the 1st and 2nd story, but was largest in the 1st. Figures 5.28

and 5.29 reevaluate this interstory drift information by plotting the absolute maximum

value for each floor given each event at each IDA stripe level. These maximum IDR

values do not necessarily correspond to the same time in the record. The median, 16th,

and 84th percentiles are also plotted in these figures. The maximum median drift at the

design level ( =0.72g) is 2.3%, indicating that the drift limitations of 2% defined

by the ASCE 7 (2002) has been exceeded. These figures also confirm that deformations

are starting to concentrate in the 2nd floor of the frame at the higher intensity levels. This

is evident at the 2/50 level (

( )1aS T

( )1aS T =1.08g), where the median drift at the 2nd floor is

3.6% interstory drift (84th percentile of 4.9%). The concentration of deformation in the

2nd floor was also captured in the static pushover analysis described in Section 5.4.2.1.

5.4.2.4 Member Plastic Rotations

Figure 5.30 contains six plots that show the maximum plastic rotations in the lower and

upper hinges of the interior columns of each floor as a function of increasing earthquake

intensity. As expected, the base hinges in the 1st story columns experience the most

significant plastic rotations in all column hinges, with the median values of 0.013 and

0.020 rad of plastic rotation for the 10/50 and 2/50 hazard events. These figures also

show that the plastic rotation in the 2nd story column reach 0.007 and 0.011rad in the

lower hinge and 0.004 and 0.007rad in the upper hinge for the 10/50 and 2/50 hazard

levels, respectively. Similar trends exist for the exterior columns in Fig. 5.31. This

reinforces the trends seen in the maximum IDR plots (Figs. 5.28-5.29) and confirms that

hinging occurs in the upper and lower hinges of the 2nd story columns.

The absolute maximum plastic rotations in the composite beams of each floor are shown

in Fig. 5.32 as a function of increasing earthquake intensity. This figure shows that

plastic rotations are distributed fairly evenly throughout all floors with median values of

0.010, 0.011, and 0.012rad in each of the three floors for the 10/50 hazard level. These

294

values increase to 0.018, 0.020, and 0.020 for the 2/50 hazard level. This shows that

despite the yielding that is occurring in the columns, the beams at each floor are also

experiencing a significant amount of hinging.

Rather than plotting the absolute maximum plastic rotation in the beams, consider the

maximum positive (i.e., composite beam) and negative (i.e., steel only) plastic rotations

separately, as shown in Fig. 5.33. This figure reveals that there is very little positive

plastic rotation (corresponding to composite action) in the events less than the 10/50

hazard level, and the median response at higher earthquake intensities (2/50) reaches

approximately one-half of the negative plastic rotation (i.e., steel only). This confirms

that the plasticity of the beams is dominated by the response in negative bending and that

the slab prevents large plastic rotations in positive bending. This reveals that more of the

rotation demand is placed on the columns when the beams are in positive bending, which

further substantiates the consideration of the composite strength of the beams in the

strong-column weak-beam design of the RC columns.

The maximum joint rotations for the interior and exterior beam-column joints are shown

in Figs. 5.34 and 5.35, respectively. A line is marked at 2% joint rotation on each of

these plots because this is recognized as the deformation level at which the joint attains

its maximum strength. These figures further substantiate other data which show that the

composite RCS joints are inherently strong and capable of forcing hinging to occur in the

surrounding beams and columns.

In order to get a better appreciation of the relative distribution of these plastic

deformations, the median and the 16th and 84th percentile for the response at the 10/50

hazard level in Figs. 5.30 through 5.35 are re-plotted in a more compact way in Fig. 5.36.

This new figure shows side-by-side comparisons of the median plastic rotations

(represented by the heavy black bars) for the interior and exterior columns (upper and

lower hinge), the beams, and the interior and exterior joints. In addition, the 16th and 84th

percentile values are represented by the white circles connected by a horizontal line. This

shows that for the 10/50 hazard level, the most severe plastic rotations occur in the 1st

295

floor interior and exterior base hinges. The lower hinge in the 2nd floor is experiencing

about half the plastic rotation seen at the base hinges. Again, the distribution of plastic

hinging is relatively even in the beams for each floor and approximately the same

magnitude as the 1st floor column base hinges. The joints all remain relatively elastic.

These same damage trends extend to the 2/50 hazard level, as shown in Fig. 5.37.

5.4.2.5 Damage Indices

As discussed in Chapter 4, the Mehanny damage index (2001) has been shown to

correlate the history of plastic rotations in a component with the severity of damage and

the repairability. These damage indices provide a better measure of damage since they

account for both the maximum plastic excursions as well as the cumulative damage

caused by repeated excursions. The monotonic plastic rotation capacities of the

components of the frame are computed using the methods described in Section 4.4.1 and

are summarized in Table 5.14. Note that the predicted plastic rotation capacities for the

RC columns are rather large, particularly in the exterior columns. Recall the discussion

in Section 4.4.1, which, based on work by Fardis et al. (2001), argued that the rotation

capacities for the interior columns are reasonable, but acknowledged that those for the

exterior columns are excessively large given that the model used in this study does not

consider all possible failure modes in the column (e.g., reinforcing bar buckling or

fracture).

The plastic rotation history of each of the components in the frame has been processed

with the Mehanny damage index for each of the time history analyses. These results are

plotted in a similar manner as the maximum plastic rotations plots that have been already

presented in Section 5.4.2.4. The computed damage indices for in the interior and

exterior columns are presented in Figs. 5.38 and 5.39, respectively. The damage index

plots for the composite beams are shown in Fig. 5.40 and the interior and exterior joints

are shown in Fig. 5.41 and 5.42, respectively. On each of these plots are three vertical

lines that separate the negligible to moderate (0.5), moderate to significant (0.7), and

significant to loss of capacity (0.95) damage states. Each of these damage states are

296

described in Table 5.15. Also, two horizontal lines are drawn on these figures to indicate

the 10/50 and 2/50 hazard levels.

The first thing that stands out about these plots is the extreme outliers that first appear at

the = 0.3g stripe and continue up through the maximum = 1.15g stripe.

These response points belong to a single event, a record from the 1979 Imperial Valley

event (IV79dlt), which is scaled throughout the range of this stripe levels. This record is

particularly damaging because the event lasts about 100 seconds with approximately 50

seconds of strong motion, which leads to a significant number of plastic excursions.

Compare this to the more modest events that last about 40 seconds and have strong

motion durations that range from 10-20 seconds. This shows that these damage indices

are able to capture the duration effect of a longer event, something which is not reflected

in the maximum plastic rotations.

( )1aS T ( )1aS T

Shifting the focus to the median values, the damage indices indicate that the 1st story

column base hinges experience the most damage of all the column hinges (Fig. 5.38).

The 84th percentile damage index of these hinges cross into the moderate damage state

just below the 10/50 hazard level while the median crosses into this region at the 2/50

hazard level. From the distribution at 10/50 hazard level, it is estimated that there is an

18% probability that these hinges fall within the moderate damage state and only a 5%

chance of exceeding this damage state. These probabilities increase to 32 and 18%,

respectively, at the 2/50 hazard level. The only other column hinges that experiences

noteworthy damage is the lower and upper hinges of the 2nd story columns, which have

approximately a 15 and 7% probability of exceeding the negligible damage level at the

2/50 level, respectively. The damage in the lower hinge of these columns is counter to

the assumption of the SEAOC SCWB provision that presumes that columns will tend to

incur damage in the upper column hinge of the story.

The damage indices for the composite beams (Fig. 5.40) predict much earlier and more

significant damage than seen in the columns. Table 5.16 breaks down the probability of

the beam hinges in each floor being within moderate, significant, and loss of capacity

297

damage state levels for the 10/50 and 2/50 hazard levels. This table shows that (1) there

are much higher probabilities of damage that requires some sort of repair than what was

seen for the RC column hinges and (2) despite the damage seen in some of the upper

story columns (suggesting the formation of a story mechanism), the beam hinges are still

experiencing high inelastic rotations.

The damage indices for the interior and exterior beam-column joints are shown in Figs.

5.41 and 5.42. Other than the outlier data points from the IV79dlt record, the predicted

damage indices for the joints all remain within the negligible damage state.

Figure 5.43 summarizes the median and 16th and 84th percentile values for the damage

indices in the columns, beam, and joints at the 10/50 hazard level. This figure shows that

the median damage is indicative of a side sway frame mechanism where the column base

hinges and the beam hinges in each floor experience the most damage, which is

representative of the damage observed in the test frame after the design level event. The

level of damage in these hinges is indicative of the performance expected by FEMA 356,

with the 84th percentile levels entering the moderate damage region.

Figure 5.44 summarizes this same data for the 2/50 hazard level, which exhibits a similar

trend as the 10/50 hazard level. This shows that the beams are much more likely to

experience moderate to significant damage, which would imply that local buckling is

becoming more prevalent in these hinges. These damage states correlate to those

observed in the test frame and should be expected given the higher level of drifts at this

hazard level (median interstory drift of 3.5%). The median damage in the base hinges of

the 1st floor column is within the moderate level while the 84th percentile falls within the

significant level. This figure also shows that the predictions imply that the lower hinge of

the second floor column is beginning to reach moderate levels of damage (84th

percentile). Recall that the test frame showed more damage in the upper hinge of the 2nd

floor than in the lower hinge, while the analytical model is predicting the opposite. This

may be attributed to the fact that the predicted drifts of the frame are exceeding the

limitations set on the fiber models, with 6 of the 15 events surpassing 4% maximum drift.

298

Given that local buckling is not being adequately captured in the 1st floor beam at these

drift levels, the analytical models of the beams are not capturing the strength degradation

in these hinges. The result may be that the beams are imposing unrealistically high forces

into the columns, leads to hinging in the lower hinges of the 2nd story columns.

Another interesting difference between the test behavior and the response of the

analytical models is that the 2nd floor beams are experiencing roughly the same amount of

damage (moderate to significant) as the 1st and 3rd floor beams, which was not observed

in the test. The damage in the 2nd floor beam was limited to minor yielding in the test

frame. This difference is likely attributed to the fact that the axial loads (from the

tributary gravity loads) have increased the capacity of the RC columns, thereby

increasing the average SCWB ratio by approximately 15% from the original test frame

model. This change has the potential to shift more of the damage into the 2nd floor beams

than what was observed in the test frame.


The performance assessment of the 6-story building will focus on lateral resisting frames

corresponding to frame lines 1 and 7 from the building plan presented in Fig. 5.1. This

frame is modeled in OpenSees according to the recommendations in Chapter 4 and

subjected to a complete stripe analysis up through the hazard level associated with the

maximum considered event, which is defined by IBC 2003 as =0.72g and can be

assumed as the intensity of a 2% in 50 years ground motion. The performance of the

frame is evaluated in a similar manner as the 3-story frame presented in the previous

section. Damping is defined as 2% at the first and third modes of the frame, which

corresponds to an alpha and beta coefficients of 0.16 and 1.36x10-3 (equation

( )1aS T

(0.2),

shown graphically in Fig. 5.45). Tributary gravity loads (full dead and 25% live load) are

imposed on the moment frame and the remaining loads are imposed upon a leaning

column. The ground motion records used at each hazard level have been discussed in

Section 5.3.3.

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5.5.1 Static Pushover Response

The results from a static pushover of the 6-story building model are shown in Fig. 5.46.

This figure shows that the maximum strength of the building is approximately 2.9 times

the design base shear. The drift profiles of the frame at the several stages of the pushover

are shown in Fig. 5.47. At the design base shear, interstory drifts remain below 0.5%,

with a relatively even level of deformation demand throughout all stories. The maximum

strength of the building occurs at approximately 2.0% drift. The target displacement, δt,

from FEMA 273 is computed as 1.6% for a design level earthquake. At this drift level,

deformations are beginning to concentrate in the middles stories, with the most

pronounced drifts in 3rd and 4th stories. This localization of damage continues in these

floors as the frame is pushed to higher drift demands.

5.5.2 Global Response

Maximum interstory drifts versus the hazard level, as defined by , are plotted for

the 6-story frame in Fig. 5.48. The median response of the 6-story frame exhibits a slight

hardening effect with increasing earthquake intensities. At this design hazard level, the

median value is approximately 1.9% interstory drift with a dispersion (

( )1aS T

ln |idr Saσ ) of about

13%. Note that the median response is just below the 2% drift limit set by the IBC 2003

and the ASCE-7 (2002). Assuming a lognormal distribution, this corresponds to a

probability of 32% that the frame will exceed the 2% drift limit in a design level event.

At the 2/50 hazard level ( ( )1aS T = 0.72g), the frame is pushed to a median drift of 2.5%

with a dispersion of approximately 20%. Note that the drift ratios for all of the 2/50

records are less than 4%, which suggests that the fiber beam-column elements can

accurately simulate the response. In fact, only two events exceed this threshold as the

earthquake intensity is increased to the largest intensity analyzed in this stripe analysis,

= 0.8g. ( )1aS T

300

Figures 5.49 and 5.50 shows the instantaneous drift profiles of each analysis at each

stripe hazard level. These plots show that the maximum drift (marked by the dark circle)

typically occurs within the 3rd, 4th, or 5th story for all hazard levels. As the earthquake

intensities are increased, it is apparent that there is a bulging effect of the middle stories

indicating that a localization of response in this region is beginning to control the

response of the building. Figures 5.51 and 5.52 show the absolute maximum interstory

drifts for each floor over each of the earthquakes at each hazard level. These plots show

similar trends in that the middle 4 stories display the largest displacement demands. This

concentration of demands is also captured in the static pushover response described in

Section 5.5.1. The 1st-story only reaches a median drift of 1.8%, indicating that rotation

demand at the base hinges of the 1st-story column is likely much less than what was seen

in the 3-story building.

5.5.3 Member Plastic Rotations

For brevity, only the median, 16th and 84th percentile summary plots are examined for

general trends and insights into the performance of the 6-story frame. Figure 5.53 shows

the summary plot for the 10/50 stripe level ( ( )1aS T = 0.48g). This figure shows that the

bulging effect of the middle stories is apparent in the maximum beam plastic rotations,

with median values reaching as high as 1% in the 3rd floor beams. The base column

hinges are subjected to median plastic rotations of only 0.6% and 0.8% in the interior and

exterior columns, respectively. This is approximately half of the demand that was seen in

the 10/50 level for the 3-story frame. This difference is likely attributed to the

localization of the response in the middle stories, which alleviates the demands on the

lower story. This figure also shows that the median joint rotations are generally larger

than what was seen in the 3-story frame, but are still well within their maximum capacity.

A summary of the plastic rotation demands for the 2/50 hazard level is shown in Fig.

5.54. The 3rd-floor beam is subjected to the highest deformation demand, with the

median plastic rotation reaching approximately 1.5%. The bulging effect of the middle

floors is still apparent in the maximum beam plastic rotations. The demand in the interior

301

and exterior base column hinges are approximately 1.0 and 1.2%, respectively, which

again is low compared to the demands seen in the 3-story frame. There are also

comparable plastic rotations occurring in the lower hinges of the 3rd story columns, and to

a lesser degree in the upper hinges of the 4th and 5th story columns. While damage is

occurring in the upper story columns, there are no signs of development of story

mechanisms at these hazard levels. The deformation demands in the composite joints

remain within the same limits that were seen in the 10/50 hazard level (0.5-1.0%).

5.5.4 Damage Indices

The damage index developed by Mehanny et al. (2001) is used to process the plastic

rotation histories from each of frame components, which can then be correlated to a

specific physical damage state level according to the relationships in Table 5.15. The

plastic rotation capacities (θpu) for each of the components in the 6-floor frame are

computed according to the methods outlined in Section 4.4.1 and are summarized in

Table 5.17. As with the hinge rotation demands, only the overall trends are reviewed

through the median, 16th and 84th percentile summary plots.

Figure 5.55 shows the summary of the damage indices in each of the components of the

frame for the 10/50 hazard level. The median damage in the 3rd and 4th floor beams

remain within the negligible damage state but the 84th percentiles are pushed to the

moderate damage state, which is comparable to what was seen in the results of the 3-story

frame. The 1st story column base hinges remain within the negligible damage state and is

less severe than what was seen in the 3-story frame. This again can be attributed to the

higher mode effects on the 6-story frame that tend to push the middle stories to larger

deformations than the lower stories. The composite joints all remain within the

negligible damage state, but do tend to experience more damage than the joints in the 3-

story frame.

Summary of the damage indices for the 2/50 hazard level are shown in Fig. 5.56. This

figure shows that the 3rd and 4th floor beams experience the most damage of all the

302

components in the frame, with medians of moderate damage and the 84th percentiles

approaching significant damage. Damage in the 1st story base hinges remains limited

with only the 84th percentile of the exterior columns experiencing moderate levels of

damage. Similar to the 10/50 hazard level, the lower hinge of the 3rd story exterior

column is also showing comparable damage to the 1st story base hinges. The 84th

percentile of the 5th story columns are also on the verge of moderate damage. The

damage in the composite joints has not changed much from what was predicted in the

10/50 hazard level.


The performance assessment of the 20-story building will focus on lateral resisting

frames corresponding to frame lines A and F from the building plan presented in Fig. 5.2.

The analytical modeling will follow the recommendations presented in Chapter 4 and

subjected to a complete stripe analysis up through the 2% in 50year hazard level, which is

defined by IBC 2003 as =0.18g. Recall that in Section ( )1 TargetaS T 5.3.4, an alternative

weighted average scaling technique was implemented in the scaling of the ground

motions for the 20-story building. The performance of the frame is evaluated in a similar

condensed manner as the 6-story frame presented in the previous section. Damping is

defined as 2% at the at the first and fourth mode of the building, which corresponds to an

alpha and beta coefficients of 0.049 and 2.88x10-3 (equation (0.2), shown graphically in

Fig. 5.57). Note that the damping at the first mode is approximately 1.8%, which is due

to a change in the model that was not accounted for in the Rayleigh coefficients. This is

only a small error and the impact on the final results should be insignificant. Tributary

gravity loads (full dead and 25% live load) are imposed on the moment frame and the

remaining loads are imposed upon a leaning column. The ground motion records used at

each hazard level have been discussed in Section 5.3.3.

303

5.6.1 Static Pushover Response

It should be acknowledged that the static pushover of the 20-story building is less likely

to capture the realistic deformation and damage pattern of the dynamic response of the

building. Nevertheless, the results of the static pushover are shown in Fig. 5.58 for

comparison to the trends observed later in the dynamic analyses. This figure shows that

the building reaches a maximum strength of approximately 1.9 times the design base

shear, which is substantially lower than the overstrengths in the 3 and 6-story frame. At

the design base shear, the deformation demands push the middle stories more that the

upper and lower stories (Fig. 5.59). As the frame is pushed further, deformations begin

to concentrate in the lower stories, particularly in the 1st through 5th floors. These types

of results highlight the limitations of the equivalent static lateral load approach used in

design to capture higher mode effects often found in taller structures. Comparison to the

actual dynamic response will be made in the following section.

5.6.2 Global Response

Maximum interstory drifts are plotted against the hazard level, represented by

, for the 20-story frame in Fig. 5.60. The median, 16th and 84th percentile

response are also shown with the solid and dashed lines, respectively. The median shows

a slight hardening response with increasing earthquake intensities, which is similar to the

results of the 6-story building. At the design hazard level, the median value is 2.2% with

a dispersion (

( )1 TargetaS T

ln |idr Saσ ) of 19%. Assuming a lognormal distribution, this corresponds to a

67% probability that the ASCE-7 (2002) drift limit of 2% will be exceeded in this frame

during a design level event. At the 2/50 hazard level ( ( )1 TargetaS T = 0.27g), the frame

experiences a median drift of 2.9% with a dispersion of 15%. The drift limitations (4%

interstory drift) set on the fiber beam-column models is exceeded only under one ground

motion at = 0.3g, suggesting that the analysis results are fairly accurate.. ( )1 TargetaS T

304

From the onset of this study, it was recognized that higher mode effects would influence

the response of this building. These effects are highlighted in Figs. 5.61 and 5.62, which

show the maximum instantaneous drift profiles of each time history analysis at each

hazard level. The floors that experience the maximum interstory drift are marked by the

dark circle. Under very low excitations ( ( )1 TargetaS T = 0.01 and 0.02g in Fig. 5.61), the

building experiences an upper story whiplash effect, with maximum drifts occurring in

the 17th and 18th floors. As the earthquake intensities are increased, the shape of the drift

profile changes from record to record, with no real distinct pattern. At the design level

hazard, the maximum drifts occur throughout the 9th through 13th floor and the 3rd floor.

This trend continues at the two longest intensities ( ( )1 TargetaS T = 0.27 and 0.3g), where six

of the fifteen events produce maximum drifts in the 3rd floor, with the rest distributed

throughout the 9th through 18th floor.

Figures 5.63 and 5.64 show the absolute maximum drifts of each floor for each hazard

level in a non-synchronous manner. These data show similar trends as the instantaneous

drift profiles. At higher intensities, the maximum drifts occur in the 1st through 4th floors

and the 10th through the 17th floors. Contrast this to the predicted deformation demands

in the static pushover analysis, where only high demands in the lower floors were

captured. This shows that evaluating the response of a taller building solely on the static

pushover results will likely underestimate the demand in the upper stories associated with

higher mode effects.

5.6.3 Member Plastic Rotations

The median summary plots of the maximum plastic rotations in the columns, beams, and

joints are shown in Figs. 5.65 and 5.66 for the 10/50 and 2/50 hazard levels, respectively.

Focusing on the 10/50 level (Fig. 5.65), it is interesting to observe that the plastic

deformations in the upper story columns are very small. Even at the 84th percentile

response, the columns in the upper floors remain below 0.4% plastic rotation. Similarly,

at the 2/50 hazard level, the median plastic rotations in the upper story columns remain

305

below 0.5%. Contrast this to the to the upper story columns in the 3 and 6-story frames

that experienced moderate levels plastic rotation and damage, even in the design level

event. This behavior is likely attributed to relatively stronger columns in this frame

compared to the two previously discussed frames. The SCWB ratios in this 20-story

frame were, on average, 60% larger than the code minimum, considering the composite

strength of the beams. Recall that the alternate SEAOC Blue Book SCWB criterion

would still require approximately 20% more strength in the columns.

The 1st story column base hinges do experience moderate plastic rotation demands,

although not quite as high as those predicted in the 3-story building. Recall that the 6-

story building experienced very low inelastic demands at the base column hinges and that

the largest demands were in the middle stories. While the 20-story building has

significant higher mode effects, they tend to produce larger deformation demands in the

lower stories of the frame (as described in Section 5.6.2). At the both the 10/50 (Fig.

5.65) and 2/50 hazard levels (Fig. 5.66), the exterior column base hinges experience

much larger plastic rotation demands than the interior columns. The primary reason for

this is that during the large excursions where the building is being pushed in one

direction, the exterior columns experience large compressive and tensile forces in order

to resist the overturning moment. The tension force dramatically reduces the moment

capacity of the column thereby leading to very large plastic rotation demands. On the

opposite column, the compressive force increases the moment capacity of the columns,

thereby reducing the plastic rotation demand. Given that both of these columns are

considered together in the summary plots, this is also the reason for the large amount of

scatter in the exterior column plastic rotation demands. It should also be recognized that

the rotation capacity of the column would also change given the large change in axial

loads (e.g. increasing the axial load beyond the balance point of the column interaction

diagram would reduce its deformation capacity). This effect is rather interesting

considering that it could not be captured using nonlinear hinge models that must be

calibrated at a particular axial load.

306

The maximum plastic rotations in the composite beams follow the drift profiles seen in

Section 5.6.2, where larger demands occur in the lower four stories and between the 10th

and 16th floor. The median plastic rotations remain below 1% in the 10/50 hazard level

(Fig. 5.65) and 2% in the 2/50 hazard level (Fig. 5.66), both of which are well within the

rotation capacity of these composite beam hinges.

Joint deformations are approaching 1% distortion in the 9th through 14th floors at both the

10/50 and 2/50 hazard level. This is comparable to the demand in the joints for the 6-

story frame and again larger than the demands in the 3-story frame. Recall that the

maximum joint strength is expected to occur at approximately 2% joint distortion, which

again demonstrates the large relative strength of composite joints to the surrounding

members.

5.6.4 Damage Indices

Similar to the two previous frames, damage indices are used to interpret the plastic

rotation histories from each of the analyses. The monotonic plastic rotation capacities

(θpu) for each of the components in the 20-floor frame are summarized in Table 5.18.

Similar to the interior columns of the 3-story frame, the predicted θpu–values for the RC

columns tend be on the higher side with an average of approximately 0.15 radians. While

these are high, they are not unreasonable considering the work of Fardis et al. (Fardis et

al. 2003; Panagiotakos et al. 2001). Again, in future work, alternative definitions of RC

column capacities will be considered (see Section 5.4.2.5). Nevertheless, there is a very

limited amount of plastic rotations in the columns in this building, so this should not have

a large impact on the results. The general trends from the median, 16th and 84th percentile

summary plots for the 10/50 and 2/50 hazard levels are discussed herein.

Figure 5.67 and 5.68 shows the median summary plot for the damage indices in each of

the components of the frame at the 10/50 and 2/50 hazard level, respectively. These

figures follow similar trends that were found in the plastic rotation summary plots.

Damage in the upper story columns is predicted as negligible in both hazard levels. The

307

median response of the 1st story base column hinges fall within the moderate damage

state, with slightly more damage occurring in the exterior columns due to the large

changes in axial load and moment capacity. Despite attaining moderate levels of plastic

rotations (1-2%) at the 2/50 hazard level, the damage in these hinges remain relatively

low. This implies that the number of inelastic cycles that these hinges experience during

these events is relatively small.

These figures show that the beams experience the greatest amount of damage, which is

more concentrated in the 2nd through 5th floors and the 15th through 20th floors. At the

10/50 level, the median response remains just below the threshold of moderate damage.

At the 2/50 level, the level of predicted damage is increased, particularly in the 2nd, 3rd

and 19th floors, which have a 84th percentile response that falls in the significant damage

state (implying extensive hinge formation and a high probability of local buckling).

Under both hazard levels, the damage in the joints remains negligible.

5.7 Conclusions

5.7.1 Seismic Design

The case study buildings highlight the efficiency of design that is possible with

composite RCS frames. For all three case study buildings, the composite beam designs

are controlled by strength requirements and the RC columns according to the strong-

column weak-beam criterion. Drift is automatically satisfied in each of the frames, which

highlights the inherent stiffness that composite RCS systems possess over conventional

steel or concrete frames. Using fairly standard details, the composite joints in all three

case study buildings were able to satisfy the strong-joint weak-beam criterion. This is in

contrast to conventional RC frames where the column sizes are often controlled by the

beam-column joint design requirements. Alternatively, seismically designed steel frames

typically require the use of fully welded connections with web doubler plates.

308

5.7.2 General Seismic Performance

All frames exhibit excellent seismic performance up through the 2/50 hazard level. The

predicted damage is comparable to what was observed in the test frame described in

Chapter 3 and meets the spirit of the life-safety (10/50) and collapse-prevention (2/50)

performance states as defined by FEMA 356. Predicted plastic rotations in the beams are

well within the rotation capacities observed in the test frame and RCS subassembly tests.

Damage in the RC columns is within the limits of the damage states observed in the test

frame; moreover, the column deformation demands and damage appear to be less in the

taller buildings, as compared to the 3-story test frame.

5.7.3 Drift Criterion

Figure 5.69 plots the maximum interstory drifts from each frame at their corresponding

design level hazard (10/50). The IBC (2003) and ASCE-7 (2002) design drift limit of 2%

is also marked on this figure for comparison with the predicted inelastic drifts. As

mentioned earlier, the probability that the 3, 6, and 20-story buildings exceed this design

level drift is approximately 78, 32, and 67%, respectively. One could argue that the

intention of the drift criterion is to ensure that the median response falls approximately on

or below 2% interstory drift. Given the empirical nature of the structural modification

factors (R and Cd) that are used in the design process, it is interesting to see that the

inelastic deformations are actually not that far off the drift limit. In fact, if more

conservatism was implemented in the design of these frames, the medians of the 3 and

20-story frame may shift closer to the 2% drift limit.

An important point regarding these results is that the frames are all designed (for strength

and drift) according to a design base shear that is distributed up the height of the frame

according to the IBC equivalent static loading pattern. This loading pattern can vary

from linear to parabolic up the height of the structure, but ultimately, it cannot capture the

type of higher mode effects seen in this study for the 6 and 20-story buildings. This

309

highlights the inherent limitations of the equivalent static lateral load approach used in

design.

5.7.4 Composite Joint Performance

The composite joints experienced negligible amounts of damage in each of the frames.

In the 3-story frame, the joints remained relatively elastic up through the 2/50 hazard

level. While this is also true for the 6 and 20-story frames up to the 10/50 hazard level,

the joints in these frames begin to show some minor nonlinearity at the 2/50 level. This

implies that the joint demand in the taller buildings is higher than that in low-rise

buildings.


Based on comparisons to the composite strength of the beams, RC columns in the 3 and

6-story buildings were designed to the minimum limits of the strong-column weak-beam

(SCWB) criteria considering the composite beam strength. This design approach resulted

in some hinging in the upper story columns, but it did not lead to any significant story

mechanisms in the range of hazard levels investigated in the stripe analyses. This implies

that while the current SCWB ratio does not prevent damage in the upper story column

hinges, it does seem to provide sufficient protection from the formation of a story

mechanism at the 10/50 and 2/50 hazard levels. However, the uncertainties introduced

by variability in the measured material strengths, unaccounted changes in member sizes,

and other construction issues could potentially alter the column and beam strength

enough to alter this observation. In addition to this, the static pushover results revealed

that deformations in both the 3 and 6-story frames began to concentrate in a couple of

floors at higher demand levels, implying the likelihood of the formation of a story

mechanism at even higher intensity ground motions.

The 20-story building adopted a different (albeit inadvertent) design approach where the

columns were conservatively sized to provide, on average, 60% more strength than what

310

is required by the minimum limits of the traditional SCWB. Recall that this design still

does not meet the more stringent requirements of the proposed SEOAC Blue Book

provision, which essentially increases the SCWB ratio to 2.0. The predicted damage in

the upper story columns in this building is negligible, with the columns remaining

relatively elastic throughout all the considered hazard levels. These results imply that for

this case the SEOAC Blue Book provision may in fact be too conservative and that a

more reasonable SCWB ratio may be somewhere between the two cases considered in

this study. On the other hand, if the composite strength of these beams were ignored in

the SCWB calculations, the strength of the columns would be close to satisfying a

strength ratio of 2.0.

5.7.6 Damage Distribution

The 3-story building experienced damage that is consistent with a first-mode sway

motion, with damage concentrating in the 1st story column base hinges and the beam

hinges in each floor. This is also fairly representative of the damage seen in the test

frame response described in Chapter 3. There were some differences including some

predicted damage in the lower hinge of the of the 2nd story columns that was not seen in

the test. Recall that six of the fifteen 2/50 ground motions push this building beyond the

threshold of the fiber models, implying that local buckling would occur in these events.

This lack of strength deterioration in the 1st floor beams is likely the reason that damage

is predicted in these 2nd story lower column hinges. In addition, the predicted damage in

the 2nd floor beams was found to be generally larger than what was observed in the test.

The distribution of damage in the 6 and 20-story buildings are controlled by localization

of inelastic demands in the mid-region stories and associated higher mode effects. For

the 6-story frame, this results in much less demand on the 1st story column base hinges

and more damage in the middle story columns and beams. The 20-story frame has two

regions of higher amounts of damage; one in the lower stories (1st-4th floor) and the

second in the upper floors (10th-16th floors).

311

In the 20-story building, the drastic change in axial load in the exterior columns due to

the overturning moment proved to have a large impact on the plastic rotation demand and

damage that occurred in the exterior column hinges. This is something that was not seen

in the 3 and 6-story frames, presumably because the overturning moment is not as

significant as in taller buildings. This effect shows the importance of being able to

capture the interaction between moment capacity and axial loads. This can be accurately

modeled with elements using either fiber sections or P-M interaction yield surfaces.

Traditional moment versus rotation hinge models are not able to capture this effect.

The influence of higher modes in taller buildings and the resulting distribution of damage

provide some perspective to what was observed in the 3-story test frame:

1. Damage in the base column hinges for taller structures may not be as significant

as what was observed in the 3-story test.

2. It is much more difficult in taller structures to achieve an even distribution of

damage over all of the floors.

3. Axial loads due to overturning in the RC columns can lead to more damage in the

exterior columns. As most RC frame columns are designed below the balance

point, induced tension forces can dramatically reduce the bending resistance and

lead to more significant column hinging.

312

313

Table 5.1 – Summary of design values for each of the case study buildings 3-Story RCS 6-Story RCS 20-Story RCS

Floor 4.41kPa 92psf

3.64kPa 76psf

4.12kPa 86psf

Dead Load Roof 4.26kPa

89psf 3.21kPa

67psf

3.64kPa, (5.22kPa) 76psf, (109psf) (w/penthouse)

Live Load 2.40kPa 50psf

2.40kPa 50psf

2.40kPa 50psf

Typical Floor Mass 585 kN-s2/m 40 k-s2/ft

701 kN-s2/m 48 k-s2/ft

686 kN-s2/m 47 k-s2/ft

Roof Mass 585 kN-s2/m 40 k-s2/ft

556 kN-s2/m 38 k-s2/ft

628 kN-s2/m 43 k-s2/ft

Total Weight 17,241 kN 3,876 kips

39,836 kN 8,956 kips

133,990 kN 30,120 kips

Vdesign/W (+torsion) 0.134 0.097 0.046

Calculated Natural Period, Tn

1.0sec 1.4sec* 4.0sec

*Note that the earthquake hazard level and ground motion selection and scaling are based on a period of 1.5seconds, which represents a slightly older model. This difference is presumed to be negligible in the final results.

Table 5.2 – Member design schedule of 6-story case study building.

PERIMETER COLUMNS PERIMETER BEAMS Floor

# A1,F1,A7,F7 A1,B1,C1,D1,E1,A7,B7,C7,D7,E7

A2,A3,A4,A5,A6F2,F3,F4,F5,F6

Frame Line 1 & 7

Frame LineA & F

1 - 2

650x650 mm 12#32 bars 25.6"x25.6" 12#10 bars

650x750 mm 8#43,4#36 bars

25.6"x29.5" 8#14,4#11 bars

650x750 mm 8#32,4#29 bars

25.6"x29.5" 8#10,4#9 bars

W 690x125 W 27x84

W 610x101W 24x68

3 - 4

650x650 mm 12#29 bars 25.6"x25.6" 12#9 bars

650x750 mm 8#36,4#32 bars

25.6"x29.5" 8#11,4#10 bars

650x750 mm 12#29 bars 25.6"x29.5" 12#9 bars

W 610x101 W 24x68

W 530x92 W 21x62

5 - 6

600x600 mm 12#25 bars 23.6"x23.6" 12#8 bars

600x700 mm 12#36 bars 23.6"x27.6" 12#11 bars

600x700 mm 12#25 bars 23.6"x27.6" 12#8 bars

W 530x92 W 21x62

W 460x89 W 18x60

Notes: (1) Column reinforcement: Fy = 414MPa (60ksi) (2) Column concrete: f’c = 41.4MPa (6ksi) (3) Slab concrete: f’c = 27.6MPa (4ksi) (4) Steel beams: Fy = 345MPa (50ksi)

314

Table 5.3 – Member design schedule of 20-story case study building. PERIMETER COLUMNS PERIMETER BEAMS

Floor # A1,F1,A7,F7 B1,C1,D1,E1;

B7,C7,D7,E7 A2,A3,A4,A5,A6; F2,F3,F4,F5,F6;

Frame Line 1 & 7

Frame Line A &

F B2

B1

1

1016x762mm 12#36 bars

40"x30" 12#11 bars

2

3

4

5

W 760x147W 30x99

6

7

762x762mm 12#43 bars

30"x30" 12#14 bars

1016x762mm 12#36 bars

40"x30" 12#11 bars 889x762mm

12#32 bars 35"x30"

12#10 bars

8

W 690x125 W 27x84

9

10

11

12

W 760x134W 30x90

13

889x762mm 12#36 bars

35"x30" 12#11 bars

W 610x113 W 24x76

14

762x762mm 12#36 bars

30"x30" 12#11 bars

15

16

762x762mm 12#32 bars

30"x30" 12#10 bars

W 530x101W 21x68

17

762x762mm 12#32 bars 30"x30"

12#10 bars

W 530x92W 21x62

18

762x762mm 12#32 bars

30"x30" 12#10 bars W 460x74

W 18x50

19

20

762x762mm 12#25 bars

30"x30" 12#8 bars

762x762mm 12#25 bars

30"x30" 12#8 bars

762x762mm 12#25 bars

30"x30" 12#8 bars

W 460x52 W 18x35

W 460x52W 18x35

Notes: (1) Column reinforcement: Fy = 414MPa (60ksi) (2) Column concrete: f’c = 41.4MPa (6ksi) (3) Slab concrete: f’c = 27.6MPa (4ksi) (4) Steel beams: Fy = 345MPa (50ksi)

315

Table 5.4 – Summary of column and beam strengths with the corresponding SCWB ratios for the 3-story perimeter frame. (units: kN,mm)

Mc,col (1x106)

Mp,beam (1x106) ΣMc,col/ΣMp,beam ΣMc,colFloor/ΣMp,beamFloor

Traditional SCWB Floor Interior Ext (t) Ext (c) Comp. Steel Interior Ext (t) Ext (c) SEAOC SCWB

1 1.76 1.12 1.33 1.91 1.28 1.09 0.89 1.59 0.62 2 1.72 0.59 0.70 1.65 1.11 1.23 0.72 1.2 0.57

1.67 3 1.20 0.60 0.63 0.84 0.49 0.9 0.71 1.3 0.91

Table 5.5 – Summary of column and beam strengths with the corresponding SCWB ratios

for the 6-story perimeter frame (frame line 1 and 7). (units: kN,mm) Mc,col

(1x106) Mp,beam (1x106) ΣMc,col/ΣMp,beam ΣMc,colFloor/ΣMp,beamFloor

Traditional SCWB Floor Interior Ext (t) Ext (c) Comp. Steel

Interior Ext (t) Ext (c) SEAOC SCWB

1 2.01 0.86 1.39 2.19 1.64 1.05 0.81 1.66 0.54 2 2.01 0.91 1.33 2.19 1.64 0.91 0.75 1.34 0.54 3 1.48 0.74 0.88 1.67 1.19 1.03 0.91 1.48 0.53 4 1.48 0.78 0.88 1.67 1.19 0.93 0.91 1.45 0.53 5 1.19 0.75 0.84 1.37 0.97 1.01 1.1 1.7 0.54 6 1.18 0.77 0.80 1.37 0.97 0.5 0.56 0.83 0.54

316

Table 5.6 – Summary of column and beam strengths with the corresponding SCWB ratios for the 20-story perimeter frame (frame line A and F). (units: kN,mm)

Mc,col (1x106)

Mp,beam (1x106) ΣMc,col/ΣMp,beam ΣMc,colFloor/ΣMp,beamFloor

Traditional SCWB Floor Interior Ext (t) Ext (c) Comp. Steel

Interior Ext (t) Ext (c) SEAOC SCWB

1 3.44 1.89 3.46 2.27 1.64 1.53 1.69 4.24 1.03 2 2.54 1.95 3.51 2.27 1.64 1.28 1.75 4.31 0.83 3 2.48 2.01 3.57 2.27 1.64 1.26 1.8 4.35 0.82 4 2.43 2.07 3.59 2.27 1.64 1.23 1.85 4.33 0.82 5 2.37 2.13 3.54 2.27 1.64 1.2 1.9 4.27 0.80 6 2.32 2.18 3.49 2.27 1.64 1.18 1.94 4.21 0.79 7 2.28 2.23 3.44 2.27 1.64 1.12 1.58 3.67 0.78 8 2.10 1.34 2.60 2.27 1.64 1.06 1.2 3.11 0.66 9 2.06 1.37 2.51 1.90 1.35 1.25 1.44 3.64 0.78 10 2.02 1.38 2.41 1.90 1.35 1.23 1.46 3.5 0.77 11 1.99 1.39 2.31 1.90 1.35 1.21 1.47 3.34 0.75 12 1.95 1.40 2.21 1.90 1.35 1.19 1.47 3.18 0.73 13 1.91 1.40 2.09 1.90 1.35 1.16 1.23 2.7 0.72 14 1.88 0.94 1.55 1.45 0.97 1.43 1.3 3.07 0.88 15 1.57 0.94 1.44 1.45 0.97 1.28 1.29 2.85 0.76 16 1.52 0.93 1.33 1.45 0.97 1.24 1.27 2.61 0.73 17 1.48 0.91 1.21 1.45 0.97 1.01 1.25 2.35 0.70 18 0.96 0.90 1.08 0.80 0.45 1.5 2.22 4.6 0.97 19 0.90 0.87 0.98 0.80 0.45 1.41 2.14 4.15 0.91 20 0.85 0.83 0.88 0.80 0.45 0.68 1.05 1.96 0.85

Table 5.7 – Strength of composite joints and the strong-joint weak-beam ratios for the 3-

story case study frame. (units: kN,mm) Mp,beamNom

(1x106) Mjoint,Nom (1x106) SJWB Ratios

Floor Comp. Steel Interior Exterior Interior Exterior

Comp. Exterior

Steel 1 1.77 1.16 2.95 2.05 1.00 1.16 1.76 2 1.53 1.01 2.46 1.72 0.97 1.12 1.70 3 0.79 0.44 1.68 1.12 1.36 1.42 2.53

317

Table 5.8 – Strength of composite joints and the strong-joint weak-beam ratios for the 6-story case study frame. (units: kN,mm)

Mp,beamNom (1x106)

Mjoint,Nom (1x106) SJWB Ratios


Comp. Exterior

Steel 1 1.96 1.36 4.09 2.34 1.23 1.19 1.72 2 1.96 1.36 4.09 2.34 1.23 1.19 1.72 3 1.49 0.98 3.42 1.94 1.38 1.30 1.97 4 1.49 0.98 3.42 1.94 1.38 1.30 1.97 5 1.22 0.80 2.62 1.47 1.30 1.21 1.83 6 1.22 0.80 2.62 1.47 1.30 1.21 1.83

Table 5.9 – Strength of composite joints and the strong-joint weak-beam ratios for the 20-

story case study frame. (units: kN,mm) Mp,BeamNom

(1x106) Mjoint,Nom (1x106) SJWB Ratios


Comp. Exterior

Steel 1 1.95 1.36 6.04 4.04 1.83 2.07 2.97 2 1.95 1.36 5.15 3.45 1.56 1.77 2.54 3 1.95 1.36 5.15 3.45 1.56 1.77 2.54 4 1.95 1.36 5.15 3.45 1.56 1.77 2.54 5 1.95 1.36 5.15 3.45 1.56 1.77 2.54 6 1.95 1.36 5.15 3.45 1.56 1.77 2.54 7 1.95 1.36 5.15 3.45 1.56 1.77 2.54 8 1.95 1.36 4.28 2.87 1.29 1.48 2.12 9 1.64 1.12 3.64 2.44 1.32 1.49 2.19 10 1.64 1.12 3.64 2.44 1.32 1.49 2.19 11 1.64 1.12 3.64 2.44 1.32 1.49 2.19 12 1.64 1.12 3.64 2.44 1.32 1.49 2.19 13 1.64 1.12 3.64 2.44 1.32 1.49 2.19 14 1.24 0.80 3.03 2.03 1.48 1.64 2.52 15 1.24 0.80 3.03 2.03 1.48 1.64 2.52 16 1.24 0.80 3.03 2.03 1.48 1.64 2.52 17 1.24 0.80 3.03 2.03 1.48 1.64 2.52 18 0.69 0.37 2.22 1.46 2.09 2.11 3.97 19 0.69 0.37 2.22 1.46 2.09 2.11 3.97 20 0.69 0.37 2.22 1.46 2.09 2.11 3.97

318

Table 5.10 – Modal properties of 20-story frame and corresponding weights for record scaling.

Mode ωi (rad/s) Ti (sec) Mass Participation

Weighted Values

1 1.55 4.04 71.8% 75% 2 4.32 1.45 12.8% 15% 3 7.45 0.84 4.2% 10% 4 11.17 0.56 3.1% 0% 5 15.15 0.42 2.3% 0%

Table 5.11 – Comparison of IDRMAX of two OpenSees models with test frame.

IDRMAX

Earthquake Event Measured Response

OS: Lab

Conditions

OS: Realistic Building

Difference in Models

50%in50yr 1999 ChiChi

( )1aS T =0.408g 1.91% 1.52% 1.35% 11%

10%in50yr-1a 1989 Loma Prieta

( )1aS T =0.68g 3.10% 3.18% 2.37% 25%

10%in50yr-1b 1989 Loma Prieta

( )1aS T =0.544g 2.67% 2.48% 1.98% 20%

2%in50yr 1999 ChiChi

( )1aS T =0.92g 5.78% 3.79% 2.93 % 23%

10%in50yr-2 1989 Loma Prieta

( )1aS T =0.544g 2.75% 2.60% 2.14% 18%

Table 5.12 – Measured strengths of steel tension coupons.

Steel Fy (MPa)

Percent Difference from Fy,exp

Flange 409 8% 1st Floor Web 442 16%

Flange 484 28% 2nd Floor Web 517 36%

Flange 407 7% 3rd Floor Web 431 14%

#11 bars 527 6%

319

Table 5.13 – Measured crushing strength of concrete cylinders.

Concrete 'cf (MPa) Percent Difference from

Nominal Strength

1st Floor Columns 89.0 (lower) 70.8 (upper)

115% 71%

2nd Floor Columns 68.2 65%

3rd Floor Columns 68.4 65%

Slab 31.0 12%

Table 5.14 – Plastic rotation capacity of 3-story case study frame components. puθ (rad)

Floor RC Columns Steel Beams Comp. Joints

Inner 0.150 1st Outer 0.306 0.072 0.087

Inner 0.161 2nd Outer 0.415 0.093 0.093

Inner 0.162 3rd Outer 0.418 0.098 0.102

Table 5.15 – Correlation between the Mehanny damage index and the expected damage

in the component. Dθ Range Anticipated Damage State

0.00-0.50 Negligible: Little to no damage in element and corresponds to immediate occupancy damage level

0.50-0.70

Moderate: Structural element experiences noticeable damage, such as spalling of cover concrete and minor shear cracking in RC columns, and hinging and some local buckles in steel beams. In terms of the component damage and necessary repairs, this region of the damage index roughly corresponds to a life safety limit state.

0.70-0.95

Significant: Structural element is assumed to be at a near collapse state, with extensive cracking and hinge formation in RC columns and significant hinging and local buckles for the steel beams.

>0.95 Loss of Capacity: The damage is so extensive that the capacity of the element is assumed to be compromised.

320

Table 5.16 – Probability of beam hinges being in a specific damage state given a 10/50 and 2/50 hazard level.

Pr( x | 10/50 hazard) x =

Pr( x | 2/50 hazard) x =

Moderate Significant Loss Moderate Significant Loss Beams

0.5<DI<0.7 0.7<DI<0.95 DI<0.95 0.5<DI<0.7 0.7<DI<0.95 DI<0.95 1st

Floor 20% 6% 1% 32% 21% 11%

2nd Floor 22% 3% 0.2% 49% 21% 3%

3rd Floor 25% 7% 1% 44% 24% 5%

Table 5.17 – Plastic rotation capacity of 6-story case study frame components.

puθ (rad) Floor

RC Columns Steel Beams Comp. Joints Inner 0.089 0.070 1st, 2nd Outer 0.088 0.052 0.077 Inner 0.096 0.073 3rd, 4th Outer 0.082 0.060 0.080 Inner 0.089 0.074 5th, 6th Outer 0.079 0.094 0.081

321

Table 5.18 – Plastic rotation capacity of 20-story case study frame components. θpu (rad)

RC Columns Comp. Joints Floor Inner Outer

Steel Beams Inner Outer

1st 0.126 2nd

0.079 0.089

3rd 4th 5th 6th 7th

0.125 0.154

8th

0.075 0.086

9th

0.054

10th 0.070 0.081

11th 12th 13th 14th

0.145 0.077

15th

0.073 0.083

16th

0.172

17th 18th

0.166 0.090

19th

0.076 0.087

20th 0.188

0.187 0.077

0.079 0.089

Figure 5.1 – Typical floor plan of 6-story case study building.

Figure 5.2 – Typical floor plan of 20-story case study building.

6 @ 6.10m = 35.60m (6 @ 20’ = 120’)

5 @

6.1

m =

30.

5m (5

@ 2

0’ =

100

’)

63.5mm Normal Weight Concrete over 76mm Metal Deck

A

B

C

D

E

F

1 2 3 4 5 6 7

Released End

6 @ 6.40m = 38.40m (6 @ 21’ = 126’)

2 @

6.4

0m (2

@ 2

1’)

2 @

6.4

0m (2

@ 2

1’)

9.60

m (3

1.5’

)

35.2

0m (1

15.5

’)

F 83mm Normal Weight

Concrete over 51mm Metal Deck

E

D

C

B

A 1 2 3 4 5 6 7

322

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

(T = 0.53 sec, V/W = 0.125)

(T = 0.82 sec, V/W = 0.111)

(T = 2.91 sec, V/W = 0.031)

(T = 2.91 sec, V/W = 0.044)

IBC 2003/ASCE 7-02 Design Spectra

Period (sec)

V/W

- B

ase

She

ar D

esig

n C

oeff

icie

nt

Figure 5.3 – IBC 2003 design hazard spectra with the code-defined periods (1.2Ta) for the 3, 6, and 20-story frames labeled on the curve.

323

Figure 5.4 – Schematic of typical transverse reinforcement in RC columns for 6-story

perimeter frame.

600mm

600mm

#4-75mm o.c. #5-75mm o.c. #4-75mm o.c.

700mm

Restraining Bars

650mm

#5-75mm o.c. #4-75mm o.c.

750mm

324

Figure 5.5 – Schematic of typical transverse reinforcement in RC columns for 20-story

perimeter frame.

762mm

Restraining Bars

762mm

#4-100mm o.c. #5-100mm o.c. #4-100mm o.c.

Restraining Bars

889mm

#5-100mm o.c. Restraining Bars

1016mm

762mm

325

Figure 5.6 – Typical plan view of the column section just below the beam and in the

beam-column joint. (section A-A and B-B in Figs. 5.7 and 5.8)

889mm

A

Restraining Bars

Steel Erection Column (Optional)

762mm

Column Section (Below Beam)

889mm 38mm

13mm

B

B

85mm

A

W760x147

48mm

Gravity Beam

Column Section (Beam Level)

326

Figure 5.7 – Cross-section of typical beam-column joint depicting the location of the

joints ties.

Figure 5.8 – Cross-section of typical beam-column joint with band plate and face bearing

plate details.

Section A-A from Fig. 5.6 Holes in web

Ties within Joint

W760x147

265mm Band Plate

FBP

Gravity Beam

Section B-B from Fig. 5.6

W760x147 FBP: 16mm thick

Band Plate 16mm thick

762mm

327

(a) (b)

(c)

Figure 5.9 – (a) The traditional cloud approach of nonlinear time history analyses and two alternative concepts for scaling ground motions using (b) incremental scaling of

gle ground motions and (c) the stripe analysis techniqusin e.

10 15 20 25 30 35 40 45 50 55 60 65

5.6

5.8

6

6.2

6.4

6.6

6.8

7

R (km)

Mw

Figure 5.10 – Magnitude and distance to the rupture pairs for ground motion records used in this study.

IDRmax

EQ Intensity

IDRmax

EQ Intensity

IDRmax

EQ Intensity

328

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-3

-2

-1

0

1

2

3

4

Sa(1sec) (g)

Eps

ilon

(1se

c)

R. Medina's EQ Database

Figure 5.11 – Epsilon versus spectral acceleration at a period of 1 second for the 80 ground motions considered in this study.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Sa(1.5sec) (g)

Eps

ilon

(1.5

sec)


Figure 5.12 – Epsilon versus spectral acceleration at a period of 1.5 seconds for the 80 ground motions considered in this study.

329

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Sa(4.04sec) (g)

Eps

ilon

(4.0

4sec

)


Figure 5.13 – Epsilon versus spectral acceleration at a period of 4 seconds for the 80 ground motions considered in this study.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.05gNR94glp - 0.75IV79e13 - 0.63IV79pls - 0.76BO42elc - 0.95NR94bad - 0.59IV79vct - 0.65WN87cat - 1.04WN87flo - 0.68PS86h06 - 0.98MH84cap - 0.67CO83c08 - 0.58WN87cts - 0.93PS86ino - 0.63WN87sse - 0.57LV80stp - 0.55

Figure 5.14a – Response spectrum for selected ground motions at 0.05g stripe hazard level for the 3-story building.

330

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.09gIV79wsm - 0.94NR94nya - 1LP89sjw - 1.06IV79e01 - 0.87LP89fms - 0.96IV79cmp - 0.95NR94cas - 0.89MH84sjb - 1.04NR94sor - 0.89LV80srm - 0.99IV79cc4 - 0.86LV80kod - 0.96WN87har - 1.03LV80stp - 1.1WN87stc - 1.09

Figure 5.14b – Response spectrum for selected ground motions at 0.09g stripe hazard level for the 3-story building.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.2gSH87bra - 1.13IV79e12 - 1.27SF71pel - 1.29LP89hvr - 1.36SH87wsm - 0.82NR94fle - 1.26NR94pic - 1.35MH84g03 - 1.21NR94php - 1.34NR94hol - 0.86PS86psa - 1.29NR94jab - 1.29NR94dwn - 1.3NR94lh1 - 0.85PM73phn - 0.91

Figure 5.14c – Response spectrum for selected ground motions at 0.2g stripe hazard level for the 3-story building.

331

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.3gLP89cap - 1.08NR94stc - 1.02SH87icc - 0.97LP89g04 - 0.88LP89g03 - 0.79NR94hol - 1.29LP89svl - 1.16NR94lh1 - 1.28IV79chi - 1.07IV79qkp - 0.89NR94cen - 0.88LP89a2e - 1.17IV79dlt - 1.15WN87cas - 0.77WN87bir - 0.71

Figure 5.14d – Response spectrum for selected ground motions at 0.3g stripe hazard level for the 3-story building.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.4gNR94stc - 1.36SH87icc - 1.29LP89g04 - 1.18LP89g03 - 1.06LP89svl - 1.54NR94cnp - 0.8IV79chi - 1.43IV79qkp - 1.19NR94cen - 1.17IV79dlt - 1.54LP89hch - 0.79LP89hda - 0.73LP89slc - 0.72WN87cas - 1.03WN87bir - 0.95

Figure 5.14e – Response spectrum for selected ground motions at 0.4g stripe hazard level for the 3-story building.

332

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.5gLP89g04 - 1.47LP89g03 - 1.32LP89svl - 1.93NR94lh1 - 2.14NR94cnp - 1IV79chi - 1.79IV79qkp - 1.49NR94cen - 1.47LP89a2e - 1.95IV79dlt - 1.92LP89hch - 0.99LP89hda - 0.91LP89slc - 0.9WN87cas - 1.29WN87bir - 1.19

Figure 5.14f – Response spectrum for selected ground motions at 0. 5g stripe hazard level for the 3-story building.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.6gSH87icc - 1.94LP89g04 - 1.77LP89g03 - 1.59LP89svl - 2.31NR94cnp - 1.2IV79chi - 2.14IV79qkp - 1.79NR94cen - 1.76LP89a2e - 2.34IV79dlt - 2.31LP89hch - 1.19LP89hda - 1.1LP89slc - 1.09WN87cas - 1.55WN87bir - 1.42

Figure 5.14g – Response spectrum for selected ground motions at 0.6g stripe hazard level for the 3-story building.

333

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.03gLV80kod - 0.82MH84gmr - 0.81WN87cat - 1.41WN87flo - 1.44NR94glp - 1.48NR94lv2 - 0.75NR94sor - 0.79NR94sse - 0.73CO83c05 - 0.73IV79vct - 0.93MH84cap - 0.95MH84sjb - 0.87PS86h06 - 0.98WN87cts - 1.24WN87har - 1.18


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.06gMH84agw - 1.08MH84g02 - 0.9WN87w70 - 1.03WN87wat - 1.11SF71pel - 0.97SH87bra - 1LP89hvr - 0.93NR94bad - 1.15NR94del - 0.85NR94lh1 - 0.98BO42elc - 0.86IV79cmp - 1.01IV79nil - 0.88LV80stp - 0.92PS86ino - 0.86


334

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.1gIV79e13 - 0.92PM73phn - 1.01PS86psa - 1.14WN87cas - 0.88LP89agw - 0.94NR94far - 1.18NR94fle - 0.94LP89fms - 1.04LP89sjw - 1.17NR94dwn - 0.9NR94loa - 1.12NR94php - 0.97NR94pic - 1.15NR94ver - 1.08MH84hch - 0.98


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.2gIV79chi - 1.01IV79qkp - 0.82WN87cas - 1.77LP89cap - 0.72LP89hch - 0.81LP89hda - 1.14LP89svl - 0.91NR94hol - 0.95SH87pls - 0.87BM68elc - 1.46LP89a2e - 1.19LP89slc - 0.85NR94cen - 0.93IV79dlt - 0.94WN87bir - 1.62


335

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.3gIV79chi - 1.51IV79qkp - 1.23LP89cap - 1.08LP89g03 - 0.85LP89g04 - 0.81LP89hch - 1.21LP89svl - 1.36NR94hol - 1.43NR94stc - 0.8SH87icc - 1.03SH87pls - 1.31LP89a2e - 1.79LP89slc - 1.28NR94cen - 1.4IV79dlt - 1.41

Figure 5.15e – Response spectrum for selected ground motions at 0. 3g stripe hazard level for the 6-story building.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Period (s)

Sa (

g)

Sa,Target

= 0.4gIV79chi - 2.02IV79qkp - 1.65LP89cap - 1.44LP89g03 - 1.13LP89g04 - 1.07LP89hch - 1.62LP89svl - 1.81NR94cnp - 0.82NR94hol - 1.9NR94stc - 1.07SH87icc - 1.37SH87pls - 1.75LP89slc - 1.71NR94cen - 1.86IV79dlt - 1.88

Figure 5.15f – Response spectrum for selected ground motions at 0.4g stripe hazard level for the 6-story building.

336

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Period (s)

Sa (

g)

IV79e12 - UnscaledIV79e12 - 4.14IBC Hazard Curve

Scale factor = 4.14

Figure 5.16 – Example of weighted average scaling technique.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.01g

Period (s)

Sa (

g)

WN87bir - 0.47WN87cas - 0.55NR94loa - 0.57MH84g03 - 0.62NR94del - 0.64NR94sse - 0.69SH87bra - 0.71NR94far - 0.72NR94jab - 0.78IV79pls - 0.83NR94nya - 0.87NR94lh1 - 0.9NR94ver - 0.92PS86ino - 1.05LV80stp - 1.32


337

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.02g

Period (s)

Sa (

g)

IV79chi - 0.49IV79wsm - 0.61LP89sjw - 0.62LP89fms - 0.62IV79cal - 0.71NR94fle - 0.87IV79nil - 0.91WN87bir - 0.95WN87cas - 1.09NR94loa - 1.13MH84g03 - 1.25NR94del - 1.27NR94sse - 1.38SH87bra - 1.42NR94far - 1.44


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.05g

Period (s)

Sa (

g)

IV79cal - 1.59IV79chi - 1.1IV79e01 - 1.34IV79e12 - 1.16IV79qkp - 0.85IV79wsm - 1.38LP89g03 - 0.75LP89hda - 0.71NR94cnp - 0.62NR94stc - 0.88SH87wsm - 0.73LP89fms - 1.39LP89sjw - 1.39IV79dlt - 0.77IV79nil - 2.04


338

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.1g

Period (s)

Sa (

g)

IV79chi - 2.19IV79e01 - 2.67IV79e12 - 2.33IV79qkp - 1.71IV79wsm - 2.76LP89g03 - 1.5LP89hch - 1LP89hda - 1.41LP89svl - 1.18NR94cnp - 1.23NR94stc - 1.76SH87icc - 1.09SH87wsm - 1.45LP89sjw - 2.78IV79dlt - 1.54


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.18g

Period (s)

Sa (

g)

IV79chi - 3.9IV79e01 - 4.75IV79e12 - 4.14IV79qkp - 3.04IV79wsm - 4.91LP89g03 - 2.68LP89hch - 1.78LP89hda - 2.52LP89svl - 2.09NR94cnp - 2.19NR94stc - 3.13SH87icc - 1.94SH87wsm - 2.59LP89sjw - 4.95IV79dlt - 2.75

Figure 5.17e – Response spectrum for selected ground motions at 0.18g stripe hazard level for the 20-story building.

339

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2T

1T

2T

3

Sa,Target

= 0.2g

Period (s)

Sa (

g)

LP89hch - 2SH87icc - 2.18LP89svl - 2.35NR94cnp - 2.46LP89hda - 2.83SH87wsm - 2.91LP89g03 - 3.01IV79dlt - 3.09IV79qkp - 3.41NR94stc - 3.52IV79chi - 4.39IV79e12 - 4.65IV79e01 - 5.34IV79wsm - 5.52LP89sjw - 5.57

Figure 5.17f – Response spectrum for selected ground motions at 0.2g stripe hazard level for the 20-story building.

0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.2

0.4

0.6

0.8

1

1.2

IDRMAX

Sa (

g)

3-Story RCSPerimeter Frame

TCU082-50/50

LP89G04-10/50 1a

LP89G04-10/50 1b

TCU082-2/50

OS: Test ConditionsTest Results

Figure 5.18 – Plot of the measured and simulated maximum IDR from the first four events of the pseudo-dynamic loading protocol.

340

0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.2

0.4

0.6

0.8

1

1.2

IDRMAX

Sa (

g)


TCU082-50/50

LP89G04-10/50 1a

LP89G04-10/50 1b

TCU082-2/50

OS: Test ConditionsTest Results

LP89g03 IDRmax=6.4%

LP89hda IDRmax=2.2%

Figure 5.19 – Comparison of stripe analysis study and the measured and simulated drift from the test frame.

341

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)

Column Int. Lower HingeFloor: 1

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)

Column Int. Upper HingeFloor: 2

(a) (b)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

Composite BeamsFloor: 1

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


θp (rad)

Sa (

g)

(c) (d)

0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2

Maximum Joint Rotation

Sa (

g)

Interior JointsFloor 1

0 0.01 0.02 0.03

0

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


(e) (f)

Figure 5.20 – Simulate IDA stripe response for selected columns (a,b), beams (c,d), and joints (e,f) compared to the measured response from the frame test.

342

0 0.005 0.01 0.015 0.02 0.025 0.030

0.5

1

1.5

2

2.5

Roof Drift Ratio

VB

aseS

hear

/ V

Des

ign

3-Story Perimeter Frame

Figure 5.21 – Static pushover curve for 3-story frame using IBC 2003 force distribution.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.5

1

1.5

2

2.5

3

IDR

Flo

or

Vdesign

RDR = 0.01RDR = 0.02RDR = 0.029

Figure 5.22 – IDR profile of 3-story frame during the pushover at the design base shear and selected roof drift ratios.

343

0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

IDRMAX

Sa (

g)

β - Last Committed Kβ - Initial Kβ - Current KZero Damping

0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

Ratio of Medians to Zero Damping

Non-c

– **

– *

onverged Events β - Last Com. K: *3, **2 events β - Current K: *4, **6 events

Figure 5.23 – Comparison of the median response of 3-story RCS frame with zero damping and 2% damping based on initial and last committed stiffness matrix.

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

ω, Frequency (rad/s)

ξ, P

erce

nt C

ritic

al D

ampi

ng

ω1

ω2

ω3

ω1,initial

α = 0.2126β = 0.0008554

Figure 5.24 – Relationship between damping ratio and frequency for the 3-story RCS frame as defined by the Rayleigh equation.

344

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.2

0.4

0.6

0.8

1

1.2

IDRMAX

Sa (

g)


IBC 10%in50yr 0.72g

IBC 2%in50yr 1.08g

Figure 5.25 – Stripe analysis plot of maximum interstory drift versus hazard level for the 3-story RCS frame.

345

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.045g)

Flo

or

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.09g)

Flo

or

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.2g)

Flo

or

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.3g)

Flo

or

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.4g)

Flo

or

-0.04 -0.02 0 0.02 0.040

0.5

1

1.5

2

2.5

3

IDR (Sa =0.5g)

Flo

or

Figure 5.26 – Drift profile of 3-story frame at the time of maximum drift during each event scaled to the common hazard level labeled in the x-axis. (Sa=0.045g-0.5g)

346

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.6g)

Flo

or

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.72g)

Flo

or

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.8g)

Flo

or

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.9g)

Flo

or

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =1.08g)

Flo

or

-0.06 -0.03 0 0.03 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =1.15g)

Flo

or


347

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.045g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.09g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.2g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.3g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.4g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

IDR (Sa =0.5g)

Flo

or

Figure 5.28 – Maximum drift at each floor of 3-story frame during each event in the corresponding stripe level (bold lines: median, 16th, and 84th percentile).

348

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.6g)

Flo

or

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.72g)

Flo

or

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.8g)

Flo

or

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =0.9g)

Flo

or

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =1.08g)

Flo

or

0 0.02 0.04 0.060

0.5

1

1.5

2

2.5

3

IDR (Sa =1.15g)

Flo

or


349

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


Figure 5.30 – Relationship between the maximum plastic rotation in the interior columns and the scaled spectral acceleration.

350

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)

Column Ext. Lower HingeFloor: 1

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)

Column Ext. Upper HingeFloor: 1

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

θp (rad)

Sa (

g)


Figure 5.31 – Relationship between the maximum plastic rotation in the exterior columns and the scaled spectral acceleration.

351

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


θp (rad)

Sa (

g)

Figure 5.32 – Relationship between the maximum plastic rotation in the beams and the scaled spectral acceleration.

352

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

Composite Beams, θp+

Floor: 1

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

Composite Beams, θp-

Floor: 1

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


Floor: 2

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


Floor: 2

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


Floor: 3

θp (rad)

Sa (

g)

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2


Floor: 3

θp (rad)

Sa (

g)

Figure 5.33 – Relationship between the maximum positive (left column) and negative (right column) plastic rotation in the beams and the scaled spectral acceleration.

353

0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


Figure 5.34 – Relationship between the maximum rotation for the interior joints and the scaled spectral acceleration.

354

0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)

Exterior JointsFloor 1

0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


0 0.01 0.02 0.030

0.2

0.4

0.6

0.8

1

1.2


Sa (

g)


Figure 5.35 – Relationship between the maximum rotation for the exterior joints and the scaled spectral acceleration.

355

0 0.02 0.04

1

2

3

θp (rad)

Flo

or

Int. Cols .(Low/Upp)

Sa=0.72g

0 0.02 0.04

1

2

3

θp (rad)

Ext. Cols .(Low/Upp)

0 0.02 0.04

1

2

3

θp (rad)

Beam s

0 0.02 0.04

1

2

3

θtotal (rad)

Joints(Int/Ext)

Figure 5.36 – Summary of the median and ± standard deviation of plastic rotations of 3-story frame members at the 10%in50year level (Sa = 0.72g).

0 0.02 0.04

1

2

3

θp (rad)

Flo

or


Sa=1.08g

0 0.02 0.04

1

2

3

θp (rad)


0 0.02 0.04

1

2

3

θp (rad)

Beam s

0 0.02 0.04

1

2

3

θtotal (rad)

Joints(Int/Ext)


356

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


Figure 5.38 – Relationship between the final value of the damage index for the interior columns and the scaled spectral acceleration.

357

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


Figure 5.39 – Relationship between the final value of the damage index for the exterior columns and the scaled spectral acceleration.

358

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

M S LC

10/50

2/50


DI

Sa (

g)

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

M S LC

10/50

2/50


DI

Sa (

g)

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

M S LC

10/50

2/50


DI

Sa (

g)

Figure 5.40 – Relationship between the final value of the damage index for the beams and the scaled spectral acceleration.

359

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


Figure 5.41 – Relationship between the final value of the damage index for the interior joints and the scaled spectral acceleration.

360

0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

DI

Sa (

g)

M S LC

10/50

2/50


Figure 5.42 – Relationship between the final value of the damage index for the exterior joints and the scaled spectral acceleration.

361

0 0.5 1.0

1

2

3

DI

Flo

or

M S LC


Sa=0.72g

0 0.5 1.0

1

2

3

DI

M S LC


0 0.5 1.0

1

2

3

DI

M S LC

Beam s

0 0.5 1.0

1

2

3

DI

M S LC

Joints(Int/Ext)

Figure 5.43 – Summary of the median and ± standard deviation of damage indices of frame members in 3-story frame at the 10%in50year level (Sa = 0.72g).

0 0.5 1.0

1

2

3

DI

Flo

or

M S LC


Sa=1.08g

0 0.5 1.0

1

2

3

DI

M S LC


0 0.5 1.0

1

2

3

DI

M S LC

Beam s

0 0.5 1.0

1

2

3

DI

M S LC

Joints(Int/Ext)

Figure 5.44 – Summary of the median and ± standard deviation of damage indices of frame members in 3-story frame at the 2%in50year level (Sa = 1.08g).

362

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04


ξ, P

erce

nt C

ritic

al D

ampi

ng

ω1

ω2

ω3

ω4

ω5

ω6

α = 0.16129β = 0.00136


0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.5

1

1.5

2

2.5

3

Roof Drift Ratio

VB

aseS

hear

/ V

Des

ign



363

0 0.01 0.02 0.03 0.04 0.05 0.060

1

2

3

4

5

6

IDR

Flo

or

Vdesign

RDR = 0.01RDR = 0.02RDR = 0.03



0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

IDRMAX

Sa (

g)

6-Story RCS Perimeter Frame

IBC 10%in50yr 0.48g

IBC 2%in50yr 0.72g

364

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.03g)

Flo

or

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.06g)

Flo

or

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.1g)

Flo

or

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.2g)

Flo

or

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.3g)

Flo

or

-0.04 -0.02 0 0.02 0.040

1

2

3

4

5

6

IDR (Sa =0.4g)

Flo

or


365

-0.1 -0.05 0 0.05 0.10

1

2

3

4

5

6

IDR (Sa =0.48g)

Flo

or

-0.1 -0.05 0 0.05 0.10

1

2

3

4

5

6

IDR (Sa =0.6g)

Flo

or

-0.1 -0.05 0 0.05 0.10

1

2

3

4

5

6

IDR (Sa =0.72g)

Flo

or

-0.1 -0.05 0 0.05 0.10

1

2

3

4

5

6

IDR (Sa =0.8g)

Flo

or


366

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.03g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.06g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.1g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.2g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.3g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

1

2

3

4

5

6

IDR (Sa =0.4g)

Flo

or


367

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

IDR (Sa =0.48g)

Flo

or

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

IDR (Sa =0.6g)

Flo

or

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

IDR (Sa =0.72g)

Flo

or

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

IDR (Sa =0.8g)

Flo

or


368

0 0.02 0.04

1

2

3

4

5

6

θp (rad)

Flo

or


Sa=0.48g

0 0.02 0.04

1

2

3

4

5

6

θp (rad)


0 0.02 0.04

1

2

3

4

5

6

θp (rad)

Beam s

0 0.02 0.04

1

2

3

4

5

6

θtotal (rad)

Joints(Int/Ext)


0 0.02 0.04

1

2

3

4

5

6

θp (rad)

Flo

or


Sa=0.72g

0 0.02 0.04

1

2

3

4

5

6

θp (rad)


0 0.02 0.04

1

2

3

4

5

6

θp (rad)

Beam s

0 0.02 0.04

1

2

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4

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6

θtotal (rad)

Joints(Int/Ext)


369

0 0.50 1.0

1

2

3

4

5

6

DI

Flo

or

M S LC


Sa=0.48g

0 0.50 1.0

1

2

3

4

5

6

DI

M S LC


0 0.50 1.0

1

2

3

4

5

6

DI

M S LC

Beam s

0 0.50 1.0

1

2

3

4

5

6

DI

M S LC

Joints(Int/Ext)

Figure 5.55 – Summary of the median and ± standard deviation of damage indices of 6-story frame members at the 10%in50year level (Sa = 0.48g).

0 0.50 1.0

1

2

3

4

5

6

DI

Flo

or

M S LC


Sa=0.72g

0 0.50 1.0

1

2

3

4

5

6

DI

M S LC


0 0.50 1.0

1

2

3

4

5

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DI

M S LC

Beam s

0 0.50 1.0

1

2

3

4

5

6

DI

M S LC

Joints(Int/Ext)


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0 5 10 15 20 250

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04


ξ, P

erce

nt C

ritic

al D

ampi

ng

ω1

ω2

ω3

ω4

ω5

α = 0.04889β = 0.00288


0 0.005 0.01 0.015 0.02 0.025 0.030

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Roof Drift Ratio

VB

aseS

hear

/ V

Des

ign



371

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

2

4

6

8

10

12

14

16

18

20

IDR

Flo

or

Vdesign

RDR = 0.01RDR = 0.02RDR = 0.025



0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

0.05

0.1

0.15

0.2

0.25

0.3

0.35

IDRMAX

Sa (

g)

20-Story RCS Perimeter Frame

IBC 10%in50yr 0.18g

IBC 2%in50yr 0.27g

372

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.011125g)

Flo

or

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.02225g)

Flo

or

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.05g)

Flo

or

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.1g)

Flo

or

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.178g)

Flo

or

-0.04 -0.02 0 0.02 0.040

5

10

15

20

IDR (Sa =0.2g)

Flo

or


373

-0.05 -0.025 0 0.025 0.050

5

10

15

20

IDR (Sa =0.267g)

-0.05 -0.025 0 0.025 0.050

5

10

15

20

IDR (Sa =0.3g)

Flo

or


374

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.011125g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.02225g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.05g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.1g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.178g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.2g)

Flo

or


375

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.267g)

Flo

or

0 0.01 0.02 0.03 0.04 0.050

5

10

15

20

IDR (Sa =0.3g)

Flo

or


376

0 0.02 0.040

2

4

6

8

10

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14

16

18

20

22

θp (rad)

Flo

or


Sa=0.178g

0 0.02 0.040

2

4

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18

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22

θp (rad)


0 0.02 0.040

2

4

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22

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Beam s

0 0.02 0.040

2

4

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22

θtotal (rad)

Joints(Int/Ext)


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0 0.02 0.040

2

4

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22

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Flo

or


Sa=0.267g

0 0.02 0.040

2

4

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20

22

θp (rad)


0 0.02 0.040

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θp (rad)

Beam s

0 0.02 0.040

2

4

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θtotal (rad)

Joints(Int/Ext)


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0 0.50 1.00

2

4

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10

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14

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18

20

22

DI

Flo

or

M S LC

Int. Cols.(Low/Upp)S

a=0.178g

0 0.50 1.00

2

4

6

8

10

12

14

16

18

20

22

DI

M S LC

Ext. Cols.(Low/Upp)

0 0.50 1.00

2

4

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22

DI

M S LC

Beams

0 0.50 1.00

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M S LC

Joints(Int/Ext)


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0 0.50 1.00

2

4

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8

10

12

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18

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22

DI

Flo

or

M S LC

Int. Cols.(Low/Upp)S

a=0.267g

0 0.50 1.00

2

4

6

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22

DI

M S LC

Ext. Cols.(Low/Upp)

0 0.50 1.00

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22

DI

M S LC

Beams

0 0.50 1.00

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DI

M S LC

Joints(Int/Ext)


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0.01 0.015 0.02 0.025 0.03 0.035

3-story

6-story

20-story

10% in 50 year Hazard Level

IDRMAX

IDRMAX

|EQ Record

Median,16th,84th perc.IBC/ASCE7 Drift Limit

P(IDRMAX≥0.02) = 67%

P(IDRMAX≥0.02) = 32%

P(IDRMAX≥0.02) = 78%

Figure 5.69 – Maximum interstory drift response for each case study building at the 10/50 hazard level.

381

Chapter 6: Conclusions

The main objective of this research is to assess the seismic performance of composite

RCS frames and, thereby, validate provisions for the seismic design of these systems. An

underlying goal is to fill the knowledge gaps in design and construction of composite

RCS systems and to facilitate their acceptance as a viable alternative to traditional steel or

concrete construction. This research employs complementary full-scale experimental

testing and comprehensive analytical studies to evaluate seismic design criteria and the

overall system response. In addition to providing insight into composite RCS systems,

this work has broader implications toward the development of a general methodology and

enabling tools for performance based earthquake engineering.

In this chapter, a summary of the work done throughout this research highlighting the

main contributions is presented, followed by conclusions and recommendations.

Suggestions for future research are also included.

6.1 Summary

Design Provisions: A detailed review and interpretation of the seismic design criteria

for composite RCS frames is provided in Chapter 2. Given that these systems combine

reinforced concrete (RC) columns and steel (or composite) beams, the design criteria for

these moment frames are compiled from several different sources. In addition, a

literature search on the latest research on the design and performance of RC columns,

composite beams, and composite joints is compiled. Final recommendations for the

design of composite RCS frames are proposed and later exercised and validated in the

design of a full-scale test (Chapter 3) and subsequent case-study building designs

(Chapter 5).

Updated Joint Design Model: A proposed update to the 1994 ASCE beam-column joint

design guidelines (ASCE 2004) is developed, which incorporates information from

several of the latest studies on composite joints as well as results from the full-scale

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testing program (Chapter 3). These updated guidelines extend the 1994 ASCE model to

include a wider variety of joints details, reduce the requirements for transverse ties within

the joint height, differentiate the strength of interior and exterior joints, and incorporate

performance-based requirements to limit deformation and demand in joints. Based on

observations from subassembly tests, the updated model identifies the strength of the

inner and outer panel separately, considering both shear and vertical bearing deformation

mechanisms. Using a database of RCS composite joint tests, predicted strengths from

both of these models are compared to the measured values from subassembly tests. The

updated guidelines are implemented in the design of the three case-study buildings and

are used to define the backbone of the rotational springs in the analytical models of the

composite joints.

Full-Scale Testing: A full-scale 3-story composite RCS frame is designed, constructed,

and tested in collaboration with researchers at the National Center for Research on

Earthquake Engineering in Taipei, Taiwan. Designed with the intention of pushing the

minimum limits of the recommendations presented in Chapter 2, the test frame is pseudo-

dynamically subjected to a series of four earthquake ground motions, ranging in

intensities from what is considered a frequent event (50%in50year) up through a rare

event (2%in50year probability of exceedance). Peak transient drifts during the design

level and maximum considered earthquake loading events reached as high as 3.0% and

5.5%, respectively. Upon completing the pseudo-dynamic tests, the frame is then quasi-

statically loaded to interstory drift ratios as high as 10%. Global and local behavior

results are examined for each test and performance and design implications are discussed.

Results of the frame test provide the basis for assessing the effectiveness of design

recommendations from Chapter 2 and to evaluate the validity of analytical models from

Chapter 4. In addition, differences in observed behavior between connection

subassembly tests and the frame test provide evidence that the subassembly tests tend to

exaggerate the amount of damage that will occur in real buildings subjected to large

earthquakes.

383

Analytical Modeling Recommendations: Modeling recommendations are provided to

accurately simulate to the performance of composite RCS frames within the structural

analysis software, OpenSees. Using fiber beam-column elements, RC columns and

composite beams are calibrated against a series subassembly tests and recommendations

for material models are presented, considering the effects such as confined and

unconfined concrete and effective stress and width of composite slabs. Composite joints

are represented by a finite joint model with two nonlinear springs to simulate the vertical

bearing and panel shear deformation mechanisms. Using the updated strength model in

Chapter 2 to define the backbone of the joint behavior, the simulation models are

calibrated against a series of subassembly tests. General recommendations on improving

convergence are also provided.

Damage Indices: A damage index developed by Mehanny et al. (2001) is used to

process the plastic rotation histories from the analytical models and the measured results

to obtain information on the predicted damage states and necessary levels of repair.

These predictions are compared to the observed damage in the test frame, which provides

implications on the validity of the damage model and also how well the analytical models

capture the distribution and extent of the damage observed in the test frame.

Case Study Building Design and Performance: The different aspects of this study

regarding design, testing, and analysis are brought together and applied in the seismic

design and performance assessment of three case study buildings. Standing 3, 6, and 20

stories tall, these buildings are designed with the intent to examine the key design aspects

of these frames as well as to assess the performance of RCS systems in the range of

heights that they are expected to be competitive with other structural systems. The

building designs highlight the efficiency of composite RCS systems to concurrently

satisfy strength, stiffness, and strong-column and strong-joint weak-beam requirements.

These frames are simulated in OpenSees using static pushover and nonlinear time history

analyses under multiple hazard levels up through the maximum considered event (2% in

50 year). The results of these simulations help provide insight and perspective into the

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performance of the test frame as to inform conclusions regarding the design

recommendations and general performance of composite RCS frames.

6.2 Major Findings and Conclusions

The main finding and general conclusions from this work are summarized in the

following sections.

6.2.1 Seismic Performance of Composite RCS Frames

Designed to interrogate the minimum limits of current building code requirements, the

full-scale test frame exhibited excellent seismic performance up through the maximum

considered earthquake level. The damage patterns after each pseudo-dynamic earthquake

event were representative of the performance expected in moment resisting frames

designed by current building codes. The columns, beams, and joints all performed in a

ductile manner and did not experience any sudden or unexpected failures. The fact that

the test frame performed well through four major earthquake loadings and still

maintained most of its strength (2.8 times the design base shear) through large ductilities

during the final pushover test demonstrates the robustness of RCS moment frames. The

composite joints maintained their strength and stiffness throughout the entire loading

protocol and experienced very limited damage. This sort of behavior is expected by these

composite joints given their inherent strength compared to the surrounding beams and

columns.

The performance assessment of the case study buildings reinforce the observations from

the test frame, with all frames demonstrating excellent seismic performance up through

the 2/50 hazard level. Predicted median plastic rotations and damage indices are within

the limits observed in the test and meet the spirit of the life-safety (10/50) and collapse-

prevention (2/50) performance states as defined by FEMA 356.

385

6.2.2 Performance of Precast Splices

The grouted RC column splices and the bolted steel beam splices exhibited adequate

strength and stiffness to provide equivalent behavior to cast-in-place concrete or welded

steel systems throughout all of the pseudo-dynamic loading events. The flange plates on

the 1st floor steel beam did experience ductile rupture in the final stages of the quasi-static

pushover test (at a drift ratio of 10%); however, this behavior is considered as acceptable

under the design intent. Moreover, with little additional cost, the splice could be

designed to either eliminate or further postpone this failure mode.

6.2.3 Structural Period Elongation

The stiffness deterioration of the frame resulted in a significant amount of period

elongation during each of the pseudo-dynamic earthquakes. After the first earthquake

loading (corresponding to the 50% in 50 year event), the effective stiffness of the frame

reduced to 60% of its initial value, as indicated by a shift in period from 1.0 second to 1.3

seconds. After the design level (10% in 50 year) event, the period further lengthened to

1.5 seconds, indicating that the stiffness had reduced to 45% of its original value. After

the maximum considered event (2% in 50 year), the period of the frame was 1.7 seconds

or 35% of its original stiffness. This elongation of the period was shown to have a large

influence in changing the spectral demand on frame under subsequent earthquake events.

This type of behavior has implications in both scaling and selection of ground motions

for future testing and also reinforces the idea of including spectral shape information into

the intensity measures anticipating the elongation of the period (Cordova et al. 2001,

Baker and Cornell, 2005).

6.2.4 SCWB

Despite satisfying the strong-column weak-beam criteria, a two-story mechanism

between the 1st and 2nd-floor of the test frame began to develop during the maximum

considered event and became even more pronounced in the final static pushover. Based

386

on this response, the current SCWB criteria appear unable to prevent this mechanism

from occurring in the test frame. An alternative SCWB provision proposed for the

SEAOC Blue Book (Maffei et al. 2004) shows promise in that it was able to identify the

weakness of the columns in the 2nd-floor. However, the frame studies also suggested that

the proposed SEAOC provisions are probably more conservative than necessary to

provide reasonably good performance.

6.2.5 Top Floor Joints

The proposed reinforcing bar plate detail for the roof beam-column joint of a composite

RCS frame has been shown in both subassembly tests and the full-scale testing program

to possess adequate strength and stiffness to force hinging to occur in the surrounding

beams. This joint performed well in both tests and is recommended as a practical detail

for use in top floor (roof) joints.

6.2.6 IBC 2003/ASCE 7-2002 Drift Criterion

Despite meeting the stiffness criterion set by the IBC 2003 and ASCE 7 (2002), which

limits the interstory drift ratios under the design earthquake loads to 2%, the test frame

reached drift ratios of 3% during the design level event. In the case study buildings, the

3, 6, and 20-story frame experience a median drift at the design level earthquake of

approximately 2.5, 1.9, and 2.2%, respectively. If one interprets the drift criterion to

imply that the median response of the building falls approximately on or below 2%

interstory drift, then these results show that the case study buildings, which pushed the

minimum limits of the design, are relatively close to meeting this expectation.

6.2.7 Full-scale System versus Subassembly Test Behavior

The boundary conditions enforced in typical beam-column subassembly tests exaggerate

the amount of damage and deterioration that occurs in the hinges as compared to the

response of full-scale structural systems. The severity of steel beam flange and web local

387

buckling was limited in the frame test by the continuity of the steel beam and the

continuous top flange support of the composite slab. Local buckling of the steel beam

tends to be exaggerated in subassembly tests where the steel beam is allowed to

physically shorten, leading to an “accordion” effect where local buckles build up over

cycles.

Composite action of the slab was maintained throughout the entire loading protocol with

no occurrence of shear stud fracture in the test frame. This can be attributed to (1) the

continuity of the slab and beams and (2) the realistic introduction of load through the

floor system that alleviates the tension stresses in the slab due to flexural bending. The

typical beam-column subassembly setup is not able to capture this effect and tends to

induce higher stresses in the slab and impose excessive slip on the shear studs than what

may be present in real buildings. This effect leads to the prediction of an excessive

amount of damage in slab and therefore more strength and stiffness degradation in the

beam.

6.2.8 Validity of Fiber Beam-Column Models

The fiber beam-column elements used to model the RC columns and composite steel

beams were shown to capture the test frame behavior quite well up through

approximately 3% drifts. As the frame was pushed into larger excursions during the 2%

in 50 year event, the analytical models could not accurately capture the response where

local buckling in the hinge zone of the steel beams began to dominate the frame behavior.

Given the fundamental principals behind the fiber element models (i.e., plane sections

remain plane and uniaxial material behavior), one must recognize that there are some

limitations to the type of behavior that they can accurately model. While these models

can accurately capture the response of flexural hinging, problems occur as the hinges are

pushed to large plastic rotations when their behavior begins to deviate from the plane

sections remain plane assumption with the occurrence of local buckling in the beam

flange, followed by web buckling in the beam and deterioration of the concrete, bond

slip, and possibly rebar buckling in the RC column. Therefore, the validity of the

388

standard beam-column fiber models is questionable as the drift exceeds values of 4%,

which implies that they are inaccurate in simulating excessively large drifts or collapse.

6.2.9 Mehanny Damage Index

A damage index proposed by Mehanny et al. (2001) was validated using interpreted

plastic rotations from the hinge response measured in the frame. These results showed

that the index correlates well with the observed damage in the test frame. While there are

some differences between predicted and observed damage in some of the lightly damaged

hinges, these can be attributed to the estimation process used to interpret the plastic

rotations in these components.

The fiber beam-column models combined with the Mehanny damage index accurately

predicted the regions of the test frame that experienced severe damage over the duration

of the pseudo-dynamic loading events. However, there were instances where the model

tended to overestimate the amount of damage compared to what was observed in the test

frame. This is likely due to the inability of the fiber elements to capture the softening

behavior (i.e. local buckling) that would lead to damage concentration in highly loaded

regions, which will shield damage in other regions. What this shows is that while these

damage models are useful to detect levels of damage, their accuracy is limited by the

accuracy of the fiber beam-column element.

6.2.10 Perspective on the Performance of the Test Frame

The full-scale test presented in Chapter 3 provided a unique opportunity to evaluate the

performance of a composite RCS frame under a series of earthquakes representing a

range of hazard levels. It is important to recognize that this is not the definitive estimate

of performance, but rather, only one instance within a larger distribution of possible

random earthquake ground motions. Subsequent analytical simulations of the test frame

(Chapter 5) emphasize the inherent variability in the structural response when subjected

to different ground motions. These results demonstrate that the response of the frame

389

could have been quite different than what was observed in the test. More specifically,

given a sample of 15 ground motions representative of the maximum considered

earthquake hazard, the response of the test frame could have ranged from relatively minor

damage (IDRMAX ≈ 2%), up to, conceivably, global collapse of the frame.

6.3 Design and Analytical Modeling Recommendations

The full-scale testing program and the complementary analytical studies provided the

opportunity to investigate several key design features of current building codes. Based

on the results from these studies, the recommendations in the following sections are

made.


The case study building simulations reinforce the results observed in the test frame

(Section 6.2.4), showing that when the SCWB design was pushed to its minimum limits,

damage in the upper floor columns occurred during the more intense loading events

(around the 2/50 hazard level). Despite incurring some damage, there were no signs of

pronounced story mechanism in the time history analyses at the hazard levels

investigated. The static pushover, on the other hand, was able to pick up some of the

weakness of the 3 and 6-story frame, with deformation demands beginning to localize in

just a couple of the stories as the frame was pushed to higher drifts. This suggests that at

higher intensity events, a story mechanism may develop and begin to dominate the

response of these frames. This implies that while the current SCWB ratio does not

prevent damage in the upper story column hinges, it does seem to provide a sufficient

amount protection from the formation of a story mechanism at the 10/50 and 2/50 hazard

levels. However, the uncertainties introduced during the design and construction stages

(i.e. measured versus expected strengths, unaccounted changes in member sizes, etc.)

could potentially shift the balance of column and beam strengths and lead to excessive

column hinging in the upper stories.

390

The more conservatively designed 20-story frame, which was approximately 60%

stronger than the minimum SCWB limit, did not experience any sort of damage in the

upper floor columns. Despite this good behavior, the columns are still 20% under-

designed based on the proposed SEAOC provisions, implying that this alternative

approach is overly conservative for this building.

6.3.2 Bolted Beam Splice Design

Based on the performance of the bolted beam splices in the test frame, it is recommended

that the location of the edge of the splice be at least two times the depth of the steel beam

away from the column face to avoid interaction of the splice and the hinging zone of the

beam. This beam splice can be designed as a simple bolted connection with flange plates

and a shear tab designed with a strength to develop the expected plastic moment of the

steel beam (1.1 y pR M ), which is described in detail in Chapter 2. While the bolts in this

splice can be designed for bearing resistance, it should be recognized that there is a high

likelihood of bolt slip even in very frequent earthquake events (50% in 5 year event).

While the occurrence of slip is not detrimental to the performance of the splice or the

frame, it does produce a very loud and sharp noise which has been referred to as “bolt

banging”. With multiple splices throughout the building, this phenomenon can prove to

be a frightening experience for the building occupants and would likely lead to required

post-earthquake inspection. To postpone this phenomenon, the bolts could be designed

as slip critical according to the AISC-LRFD (2002) using the slip critical force of a bolt

(Equation J3.1,1.13 b sT Nμ ). In the test frame, this would have required approximately

50% more bolts than a typical bearing design.

6.3.3 Column Grouted Splice Design

Precast RC columns are spliced using grouted connections, which should be designed to

develop the full plastic moment of the section. It is recommended that the column splices

be located within the middle third of the column length for both the structural integrity of

the hinge and ease of construction. Placement of the splice within the column hinge zone

391

was investigated and found to provide sufficient strength but with more pronounced

stiffness and strength degradation at larger drifts.

6.3.4 Composite beams

Based on the results in the test frame (Chapter 3) and the calibration studies (Chapter 4),

it is recommended that the composite strength and stiffness of the beam be considered in

both in the design (i.e. strength, stiffness, and SCWB) and the analytical modeling stages.

It was shown that the plastic strength of a beam could easily be 30-40% stronger than a

bare steel section when considering the composite strength of the slab. Not accounting

for this strength could shift the hinging from the beams into the columns, leading to an

undesirable story mechanism. The stiffness of the composite beams can be handled

directly with the fiber beam-column element or by taking an average stiffness of the steel

and composite beam assuming that the member is in double curvature. This effect can

increase the stiffness of the bare steel beams between 50 to 100%. It is also

recommended that beams are designed as fully composite beams according to the AISC-

LRFD (2002) and shear studs are designed according to the AISC Seismic Provisions

(2002). For plastic strength purposes, the effective slab width can be taken as equal to

the width of the column with an effective stress of 1.3 . 'cf

6.3.5 Updated Joint Guidelines

Updated joint design guidelines (Chapter 2) are recommended for use in place of the

earlier 1994 ASCE guidelines. The updated model increased the accuracy of the original

joint bearing and shear strength models from a mean predicted-to-measured value of 0.76

and 0.80 to 0.92 and 0.96, respectively. This improvement is also reflected in the

consistency of the strength predictions as the coefficient of variation on these joint

bearing and shear mean values have decreased from the original (15% and 16%) to the

updated model (8% and 14%). In addition to the strength models, the resistance factors

(phi-factors) were also re-evaluated by processing the results of the calibration study with

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the beta-reliability method (Ravindra and Galambos, 1978) and are recommended as 0.75

and 0.85 for the joint bearing and shear strengths, respectively.

6.3.6 Bond-Slip in RC Columns

A simple elastic spring was proposed in Chapter 4 to model the bond slip deformations

that occur in reinforced concrete columns. Bond slip flexibility is not included in the

effective RC column stiffness calculations proposed in Equation 2.5. This effect was

shown to decrease the elastic stiffness of the frame by approximately 10%. It is

recommended that these springs are incorporated into analytical models of moment

frames with RC columns to account for the flexibility that bond slip adds to the response.

6.3.7 Analytical Modeling of Composite RCS Frames

This study has utilized the fiber beam-column elements and a 2-dimensional joint model

from the OpenSees simulation platform. A succinct set of modeling guidelines have been

proposed in Chapter 4 for these elements, which have been shown to accurately capture

the behavior of RC column, composite beam, and composite joint subassembly tests. As

described in Section 6.2.8, the simulated response of these frames begin to diverge from

the true response at drifts greater than 4% when the hinges in the steel beams begin to be

dominated by local buckling.

6.4 Future Work

Based on discussions with practicing structural engineers and contractors, there is clear

interest in use of composite RCS moment resisting frames for seismic design. The

advantages that these systems offer for seismic design been demonstrated in this research,

particularly, the inherent ductility and robustness of the systems. With many of the

questions of their seismic performance answered, a remaining practical challenge to

greater utilization of composite RCS systems lies with convincing the construction

industry of their economical advantages over conventional seismic resisting systems.

393

Discussions with construction firms and industry engineers have pointed to the

development of the precast system as being the key to making composite RCS frames

competitive in the current market. While some constructability issues were addressed in

this research, a more thorough handling of this topic is required to highlight the benefits

of composite RCS frames compared to the more traditional moment frames and other

systems. This could consist of construction engineering and cost analysis that would

compare the construction of RCS frames versus other competitive systems.

6.4.1 Calibration of Deteriorating Models

Limitations in the fiber beam-column elements prevents the ability to simulate large drifts

(>4%) and perform collapse studies. It is for these reasons that models that include more

significant strength and stiffness deterioration capabilities, such as the nonlinear (moment

versus rotation) hinge models proposed by Ibarra (2003), should be calibrated to use with

the RC columns and composite steel beams. These models are most important for the

composite steel beams since they will be able to capture the strength and stiffness

deterioration that occurs in these hinges due to local buckling in the flange and web of the

steel beam. This effect was shown to be an important effect in the response of the test

frame to the large earthquake intensities when interstory drifts exceeded 3-4%. These

models will provide the tools to more accurately simulate large drifts in these composite

RCS frames and allow the study of the collapse capacity of the system.

6.4.2 Investigation of Subassembly Boundary Conditions

Both of these boundary condition effects have proven to be a key difference between the

performance of steel beams and composite slabs in continuous moment frame systems

compared to a typical subassembly test. While no recommendations are made directly in

this study, this does leave some work to determine how these subassembly tests should be

interpreted given that these boundary conditions are not accurately captured. One idea is

to create a subassembly setup that will be able to accurately capture the realistic boundary

conditions of a continuous moment frame. While this would be a more complicated

394

setup than what is done for typical beam-column tests, the main intention would be

obtain a direct comparison between this and the traditional setup. This would give some

insight as to how much of the strength and stiffness deterioration in the composite beam

is due to the boundary conditions and perhaps provide a way to reinterpret the traditional

subassembly tests.

6.4.3 Alternative Energy-Based Damage Models

While the deformation-based damage model used in this study was shown to work in

capturing the physical damage of the test frame, there are some problems stemming from

the general assumptions used to compute plastic deformation. As described in Chapter 4,

these are due to (1) the overestimation of plastic rotations in OpenSees for unsymmetrical

sections (i.e. composite beams) and (2) the general problem of defining plastic rotations

for a highly pinched response. Alternatively, the use of an energy-based damage model

(i.e., Kratzig et al. 1989, Mehanny 1999) could help avoid some of the problems

observed in this study given that the calculation of hysteretic energy is less sensitive to

the issues described here. Measured and simulated results from this study could be

reinterpreted using these alternative damage measures and validated against the

performance of the test frame.

395

Bibliography ACI (2002). Building Code Requirements for Structural Concrete, ACI-318-02,

American Concrete Institute, Farmington Hills, MI. ACI-ASCE Committee 352 (1985). “Building Code Requirements for Structural

Concrete,” Report No. ACI 318-99, American Concrete Institute, Farmington Hills, Michigan.

Altoontash, A. (2004). Simulation and Damage Models for Performance Assessment of

Reinforced Concrete Beam-Column Joints, PhD. Thesis, Department of Civil and Environmental Engineering, Stanford University, CA.

AISC (1997). American Institute of Steel Construction, Inc., “Seismic Provisions for

Structural Steel Buildings, Load and Resistance Factor Design,” 2nd Edition, Chicago, Illinois, 1997.

AISC (1999). Load and Resistance Design Specification for Structural Steel Buildings,

2nd Ed., American Institute of Steel Construction, Chicago, IL, 1999, 2001 and 2005.

AISC (2002). Seismic Provisions for Structural Steel Buildings, American Institute of

Steel Construction, Chicago, IL, 2002 and 2005. ASCE Guidelines (1994). “Guidelines for Design of Joints Between Steel Beams and

Reinforced Concrete Columns,” Journal of Structural Division, ASCE, Vol. 120(8), pp. 2330-2357.

ASCE (2002). “Minimum Design Loads for Buildings and Other Structures,” SEI/ASCE

7-02, ASCE, Reston, VA, 2002 and 2005. Aslani, H. (2005). Probabilistic Earthquake Loss Estimation and Loss Disaggregation in

Buildings, Ph.D. Dissertation, Department of Civil and Environmental Engineering, Stanford University.

Aktan, A.E., M. ASCE, and Bertero, V.V. (1987). “Evaluation of Seismic Response of

RC Buildings Loaded to Failure,” Journal of Structural Engineering, Vol. 113, No. 5, May 1987.

Baba, N., Nishimura, Y. (2000). “Seismic Behavior of RC Column to S Beam Moment

Frames,” Proc.12WCEE. Baker, J. and Cornell, A.C.(2005) “A Vector-Valued Ground Motion Intensity Measure

Consisting of Spectral Acceleration and Epsilon,” Earthquake Engineering and Structural Dynamics, Vol. 34, No. 10, pp. 1193-1217.

396

Bernal, D. (1994). “Viscous Damping in Inelastic Structural Response,” Journal of

Structural Engineering, Vol 120, No. 4. pp 1241-1254. Building Seismic Safety Council (BSSC), 1995, 1994 Edition NEHRP Recommended

Provisions for the Development of Seismic Regulations for New Buildings, Part 1: Provisions, part II: Commentary, developed for Federal Emergency Management Agency, FEMA 222 and 223, Washington DC.

Bugeja, M., Bracci, J.M., and Moore, W.P. (1999). “Seismic Behavior of Composite

Moment Resisting Frame Systems,” Technical Report CBDC-99-01, Dept. of Civil Engrg., Texas A & M University.

Bugeja, M., Bracci, J.M., and Moore, W.P. (2000). “Seismic Behavior of Composite RCS

Frame Systems.” Journal of Structural Engineering, 126(4), 429-436. Bursi, O.S., and Ballerini, M. (1996). “Behavior of Steel-Concrete Composite

Substructure with Full and Partial Shear Connection,” Proceedings of 11th World Conference on Earthquake Engineering, Paper No. 771, Acapulco, Mexico, 1996.

Carrasquillo, R.L., Nilson, A.H., and Slate, F.O. (1981). “Properties of High Strength Concrete Subjected to Short Term Loads,” ACI Structural Journal, V.78, No. 3, May-June 1981, pp. 171-178.

Chen, C.C. and Lin, N.J. (2002), Seismic Behavior of Steel Beam-to-RC Column Joint,

Technical Report, National Center for Research on Earthquake Engineering. (in Chinese)

Cheng, C.T. and Cian, P.H. (2002), Composite Behavior of Slab and Steel Beam-to-RC

Column, Technical Report, National Center for Research on Earthquake Engineering. (in Chinese)

Civjan, S.A., Engelhardt, M.D., and Gross, J.L. (2000). “Retrofit of Pre-Northridge

Moment-Resisting Connections,” Journal of Structural Engineering, V. 126, No.4, April 2000.

Civjan, S.A., M.ASCE, and Singh, P. (2003). “Behavior of Shear Studs Subjected to

Fully Reversed Cyclic Loading,” Journal of Structural Engineering, V.129, No. 11, November 2003.

Chopra, A.K. (1995). “Dynamics of Structures”. Theory and Applications to Earthquake

Engineering, Prentice-Hall. Committee on Design of Steel Building Structures of the Committee on Metals,

Structural Division. “Compendium of Design Office Problems,” Journal of Structural Engineering, Vol 118, No. 12, December, 1992.

397

Cordova, P.P., Deierlein, G. G., Mehanny, S.S.F. and Cornell, C. A. (2001). Development of a Two-Parameter Seismic Intensity Measure and Probabilistic Assessment Procedure, The Second U.S.-Japan Workshop on Performance-Based Earthquake Engineering Methodology for Reinforced Concrete Building Structures, Sapporo, Hokkaido, March 2001.

Cordova, P.P., Chen, C.H., Lai, W.C., Deierlein, G.G., and Tsai, K.C. (2006). Pseudo-

Dynamic Test of Full-Scale Composite RCS Frame,” John A. Blume Earthquake Engineering Center, Department of Civil Engineering, Stanford University, CA (in press).

Deierlein, G.G., Yura, J.A., and Jirsa, J.O. (1988). “Design of Moment Connections

forcomposite Framed Structures,” PMFSEL Report No. 88-1, University of Texas at Austin, Texas.

Deierlein, G.G., Sheikh, T.M., Yura, J.A., and Jirsa, J.O. (1989). “Beam-Column

Moment Connections for Composite Frames: Part 2”, Journal of Structural Engineering ASCE, Vol. 115, November 1989, pp. 2877-2896.

Deierlein, G.G. (2000). “New Provisions for the Seismic Design of Composite and

Hybrid Structures” Earthquake Spectra, EERI, 16(1), pp. 163-178. Deierlein, G.G. and Noguchi, H. (2004). “Overview of US-Japan Research on the

Seismic Design of Composite Reinforced Concrete and Steel Moment Frame Structures,” Journal of Structural Engineering, ASCE, 130(2), pp. 361-367.

Dooley, K.L. and Bracci, J.M. (2001). “Seismic Evaluation of Column-to-Beam Strength

Ratios in Reinforced Concrete Frames,” ACI Structural Journal, V.98, No.6, Nov.-Dec. 2001.

Du Plessis, D.P. and Daniels, J.H. (1972). “Strength of Composite Beam to Column

Connections.” Report No. 374.3, Fritz Engineering Lab., Lehigh University, Bethlehem, Pa.

Fardis, M. N. and Biskinis, D. E. (2003). “Deformation Capacity of RC Members, as

Controlled by Flexure or Shear,” Otani Symposium, 2003, pp. 511-530. FEMA-273 (1997). “NEHRP Commentary on the Guidelines for the Seismic

Rehabilitation of Buildings,” American Society of Civil Engineers (funded by Federal Emergency Management Agency), 1997.

FEMA-350 (2000). “Recommended Seismic Design Criteria for New Steel Moment-

Frame Buildings,” SAC Joint Venture (funded by Federal Emergency Management Agency), June 2000

398

FEMA-351 (2000). “Recommended Seismic Evaluation and Upgrade Criteria for Existing Welded Steel Moment-Frame Buildings,” SAC Joint Venture (funded by Federal Emergency Management Agency), July 2000.

FEMA-356 (2000). “Prestandard and Commentary for the Seismic Rehabilitation of

Buildings,” ASCE (funded by Federal Emergency Management Agency), November 2000.

Filippou, F.C. (1986). “A Simple Model for Reinforcing Bar Anchorages Under Cyclic

Excitations”, ASCE, Journal of Structural Engineering, Vol. 112, No. 7, July 1986.

Filippou, F.C., Popov E.P., and Bertero V.V. (1986). "Modeling of R/C joints under

cyclic excitations," Journal of Structural Engineering, Vol. 109, No. 11, pp. 2666-2684.

Foutch, D.A., Goel, S.C., Roeder, C.W. (1987). “Seismic Testing of Full-Scale Steel

Building – Part 1”, Journal of Structural Engineering, Vol. 113, No. 11, November 1987.

Goel, S.C. (2004). “United States-Japan Cooperative Earthquake Engineering Research

Program on Composite and Hybrid Structures,” Journal of Structural Engineering, Vol. 130, No. 2, February 2004.

Griffis, L.G. (1986). “Some Design Considerations for Composite-Frame Structures,”

AISC Engineering Journal, Second Quarter, pp. 59-64. Griffis, L.G. (1992). “Composite Frame Construction,” Constructional Steel Design, Ed.

P.J. Dowling, J.E. Harding, R. Bjorhovde, Elsevier Applied Sciences, NY, pp. 523-554.

Gupta, A. and Krawinkler, H. (1999). “Seismic Demands for Performance Evaluation of

Steel Moment Resisting Frame Structures,” John A. Blume Earthquake Engineering Center, Report No. 132, Department of Civil Engineering, Stanford University.

Ibarra, L. (2003). Global Collapse of Frame Structures Under Seismic Excitations, PhD.

Thesis, Department of Civil and Environmental Engineering, Stanford University, CA.

International Code Council (2003). International Code Council, Falls Church, VA, 2000, 2003, and 2005.

Kannan, A.E., and Powell, G.H. (1973). “Drain-2D, a general purpose computer program

for dynamic analysis of inelastic plane structures,” Report No. UCB/EERC 73-6, Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.

399

Kanno, R. (1993). “Strength, Deformation, and Seismic Resistance of Joints Between

Steel Beams and Reinforced Concrete Columns,” PhD. Thesis, Cornell University, Ithaca, NY

Kanno, R. and Deierlein, G.G. (1994). “Cyclic Behavior of Joints Between Steel Beams

and Reinforced Concrete Columns,” ASCE Structures Congress Proceedings. Kanno, R. and Deierlein, G.G. (1997). “Seismic Behavior of Composite (RCS) Beam-

Column Joint Subassemblies,” Composite Construction in Steel and Concrete III, American Society of Civil Engineers, Reston, VA, 1997, pp. 236-249.

Kanno, R. and Deierlein, G.G. (2000). “Design Model of Joints for RCS Frames”

Composite Construction IV, ASCE, (in press). Kanno, R. and Deierlein, G.G. (2002). “Design Model of Joints for RCS Frames.”

Composite Construction in Steel and Concrete IV, ASCE Reston, VA., 947-958. Kaul, R. (2004). “Object Oriented Development of Strength and Stiffness Degrading

Models for Reinforced Concrete Structures,” Ph.D. Thesis, Department of Civil and Environmental Engineering, Stanford University, CA.

Kemp, A.R. and Dekker, N.W. (1991). “Available Rotation Capacity in Steel and

Composite Beams,” The Structural Engineer, Vol. 69, No. 5, March, 1991, pp. 88-97.

Kratzig, W.B., Meyer, I.F., and Meskouris, K. (1989). “Damage Evolution in

ReinforcedConcrete Members under Cyclic Loading,” 5th International Conference on Structural Safety and Reliability, San Francisco, CA, Vol. II, pp. 795-802.

Krawinkler, H., Miranda E., Bozorgnia, Y. and Bertero, V. V. (2004). Chapter 9:

Performance Based Earthquake Engineering,, Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, CRC Press, Florida.

Kuramoto, H. (1996). “Seismic Resistance of Through Column Type Connections for

Composite RCS Systems.” Proc., 11 WCEE, Paper No. 1755, Elsevier Science. Kuramoto, H. and Nishiyama, I. (2004). “Seismic Performance and Stress Transferring

Mechanism of Through-Column-Type Joints for Composite Reinforced concrete and Steel Frames.” Journal of Structural Engineering, 130(2), 352-360.

Lee, K. and Foutch, D.A. (2002). “Seismic Performance Evaluation of Pre-Northridge

Steel Frame Buildings with Brittle Connections,” Journal of Structural Engineering, Vol. 128. No. 4, April 2002.

400

Lee, S.J. (1987). “Seismic Behavior of Steel Building Structures with Composite Slabs,” Ph.D. Thesis, Department of Civil Engineering, Lehigh University, Bethlehem, 1987

Lee, S.J. and Lu, L.W. (1989). “Cyclic Tests of Full-Scale Composite Joint

Subassemblages,” Journal of Structural Division, ASCE, Vol. 115, No. 8, Aug. 1989, pp. 1977-1998.

Leon, R.T. and Deierlein, G.G. (1995). “An Overview of Codes, Standards, and

Guidelines for Composite Construction,” ASCE Conference Proceedings, Boston, May 1995, pp. 1297-1300

Leon, R.T. and Flemming, D.J. (1997). “The Shear Resistance of Headed Studs Used

with Profiled Steel Sheeting,” Composite construction in Steel and Concrete III, 325-338.

Leon, R.T., Hajjar, J.F., and Gustaafson, M.A., (1998). “Seismic Response of Composite

Moment-Resisting Connections. I: Performance,” Journal of Structural Engineering, ASCE 124(8), 868-876.

Liang, S. and Ding, D. (1994). “Comparative Experimental lStudies of Models of Self-

Controlled and Ordinary Frames on the Shaking Table,” Earthquake Engineering and Structural Dynamics, Vol. 24, 533-547 (1995).

Liang, X., Parra-Montesinos, G, and Wisght, J.K. (2003). Seismic Behavior of RCS

Beam-column Subassemblies and Frame Systems Designed Following a Joint Deformation-Based Capacity Design Approach, Report Number UMCEE 03-10, University of Michigan, MI.

Liang, X. and Parra-Montesinos, G.J. (2004). “Seismic behavior of reinforced concrete

column-steel beam subassemblies and frame systems.” Journal of Structural Engineering, 130(2), 310-319.

Maffei, J., Stanton, J., Nigel, P., and Park, R. (2004). "Design Approaches,"Seismic

Design of Precast Building Structures, State of the Art Report [Robert Park editor], Commission 7, Federation International du Beton, Lausanne, Switzerland, Chapter 4, January 2004.

Mahin, S.A. and Shing, P.B. (1985). "Pseudodynamic Method for Seismic Testing,"

Journal of Structural Engineering, Vol. 111, No. 7, pp. 1482-1503. Mann, A.P. and Morris, L.J. (1984). “Lack of Fit in High Strength Connections,” Journal

of Structural Engineering, ASCE, Vol. 110, No. 6, June, 1984, pp 1235-1252.

401

Mazzoni, S. and Moehle, J.P. (2001). “Seismic Response of Beam-Column Joints in Double-Deck Reinforced Concrete Bridge Frames.” ACI Structural Journal 98 (3): 259-269.

McKenna, F. and G. L. Fenves (1999). “G3 Class Interface Specification Version 0.1 –

Preliminary Draft,” Pacific Earthquake Engineering Research Center, University of California at Berkeley, CA

Medina, R. and Krawinkler, H. (2003), “Seismic Demands for Non-Deteriorating Frame Structures and Their Dependence on Ground Motions”, Report PEER 2003/13, Pacific Earthquake Engineering Center, October 2003. Mehanny, S.S., Cordova, P.P., and Deierlein, G.G. (2000). Seismic Design of Composite

Moment Frame Buildings – Case Studies and Code Implications, Composite Construction IV, ASCE, in press.

Mehanny, S.S.F. and Deierlein, G.G. (2001). “Seismic Damage and Collapse Assessment

of Composite Moment Frames.” Journal of Structural Engineering, ASCE, 127(9), 1045-1053.

Noguchi, H. and Kim, K. (1998). “Shear Strength of Beam-to-Column Connections in

RCS System,” Proceedings of Structural Engineers World Congress, Paper No.T177-3, Elsevier Science, Ltd.

Noguchi, H. and Uchida, K. (2004). “Finite Element Method Analysis of Hybrid

Structural Frames with Reinforced concrete Columns and Steel Beams.” Journal of Structural Engineering, 130(2), 328-335.

Neuenhofer, A. and Filippou, F.C. (1997). "Evaluation of Nonlinear Frame Finite

Element Models", Journal of Structural Engineering, American Society of Civil Engineers, Vol. 123, No. 7, July 1997, pp. 958-966.

Ollgaard, Slutter, R. G., and Fisher, J. W. (1971). "Shear strength of stud connectors in

lightweight and normal-weight concrete." Engineering Journal, 8(2), pp. 55–64. Panagiotakos, T. B. and Fardis, M. N. (2001). “Deformations of Reinforced Concrete at

Yielding and Ultimate,” ACI Structural Journal, Vol. 98, No. 2, March-April 2001, pp. 135-147.

Parra-Montesinos, G. and Wight, J.K., (2000). Seismic Behavior, Strength and Retrofit

of Exterior RC Column-to-Steel Beam Connections, Report No. UMCEE 00-09, University of Michigan, MI.

Parra-Montesinos, G. and Wight, J.K. (2001). “Modeling Shear Behavior of Hybrid RCS

Beam-Column Connections,” Journal of Structural Engineering, ASCE, 127(1), pp. 3-11.

402

Parra-Montesinos, G., Liang, X., and Wight, J.K., (2003). “Towards Deformation-Based

Capacity Design of RCS Beam-Column Connections,” Engineering Structures, 25(5), 681-690.

Paulay, T. and Priestly, M.J.N. (1992). “Seismic Design of Reinforced Concrete and

Masonry Buildings,” John Wiley & Sons. PEER (2005). Pacific Earthquake Engineering Research Center: PEER Strong Motion

Database, University of California, Berkeley, http://peer.berkeley.edu/smcat/ (September 15, 2005).

Ravindra, M. K. and Galambos, T. V. (1978). “Load and Resistance Factor Design for Steel.” ASCE Journal of the Structural Division, 104, ST9, 1337-1353. RCSC Committee 15 (2000). “Specification for Structural Joints Using ASTM A325 or

A490 Bolts”. Research Council on Structural Connections, June 2000. Roeder, C.W., Foutch, D.A., and Goel, S.C. (1987). “Seismic Testing of Full-Scale Steel

Building – Part II,” Journal of Structural Engineering, Vol. 113, No. 11, November 1987.

Ruiz-Garcia, J. (2004). “Performance-Based Assessment of Existing Structures

Accounting for Residual Displacements,” PhD. Thesis, Department of Civil and Environmental Engineering, Stanford University, CA.

Saatcioglu, M. and Ozcebe, G. (1989). “Response of Reinforced Concrete columns to

Simulated Seismic Loading,” American Concrete Institute, ACI Structural Journal, January-February 1989, pp. 3-12.

Saatcioglu, M. and Grira, M. (1999). “Confinement of Reinforced Concrete Columns

with Welded Reinforcement Grids,” ACI Structural Journal, January-February 1999, pp 29-39.

Schwein, R.L. (1999). “The Banging Bolt Syndrome,” Modern Steel Construction,

November 1999. Scott, B. D., Park R., and Priestley, M. J. N. (1982). Stress-Strain Behavior of Concrete

Confined by Overlapping Hoops and Low and High Strain Rates, ACI Journal, January-February 1982, No. 1, pp. 13-27.

Sheikh, T.M., Yura, J.A., and Jirsa, J.O. (1987). “Moment Connections between

SteelBeams and Concrete Columns,” PMFSEL Report No. 87-4, University of Texas at Austin, Texas.

403

Sheikh, T.M., Deierlein, G.G., Yura, J.A., and Jirsa, J.O. (1989). “Beam-Column Moment Connections for Composite Frames: Part 1,” Journal of the Structural Division, ASCE, Vol. 115, No. 11, Nov. 1989, pp. 2858-2876.

Shome, N., (1999). “Probabilistic Seismic Demand Analysis of Nonlinear Structures,”

Ph.D. Thesis, Stanford University. Stevens, N. J., Uzumeri, S.M., Collins, M.P., and Will, G.T. (1991). “Constitutive Model

for Reinforced Concrete Finite Element Analysis,” ACI Structural Journal, V.88, No. 1, January-February 1991.

Tagawa, Y., Kato, B., and Aoki, H. (1989). “Behavior of Composite Beams in Steel

Frame Under Hysteretic Loading,” Journal of Structural Division, ASCE, Vol. 115, No. 8, Aug. 1989, pp. 2029-2045.

Tanaka, H., and Park, R. (1990). “Effect of Lateral Confining Reinforcement on Ductile

Behavior of Reinforced Concrete Columns,” Report No. 90-2, Department of Civil Engineering, University of Cantebury, Christchurch, New Zealand.

Tide, R.H.R. (1999). “Banging Bolts – Another Perspective,” Modern Steel Construction,

November 1999. Tsai, K.C. and Chen, P.C. (2002). A Study of RC Column-to-Foundation and Steel

Beam-to-RC Column Joints for an RCS Frame Specimen, Technical Report, National Center for Research on Earthquake Engineering. (in Chinese)

Uang C.M., and S. Kiggins (2003). “Reducing Residual Drift of Buckling-Restrained

Braced Frames as a Dual System,” Proceedings of the International Workshop on Steel and Concrete Composite Construction (IWSCCC), October 8-9, Taipei, Taiwan.

Vamvatsikos, D. and Cornell, C.A. (2002). Incremental Dynamic Analysis. Earthquake

Engineering and Structural Dynamics 31, 491-514.

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