Experimental and Analytical Dynamic Collapse Study of a Reinforced Concrete Frame with Light

Experimental and Analytical Dynamic Collapse Study of a

Reinforced Concrete Frame with Light Transverse Reinforcement

ByWassim Michael Ghannoum

B. Eng. (McGill University) 1997

M. Eng. (McGill University) 1999

A dissertation submitted in partial satisfaction o f the

requirements for the degree o f

Doctor o f Philosophy

in

Engineering - Civil and Environmental Engineering

in the

Graduate Division

o f the

University o f California, Berkeley

Committee in charge:

Professor Jack P. Moehle, Chair

Professor Stephen A. Mahin

Professor Douglas Dreger

Fall-2007

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Experimental and Analytical Dynamic Collapse Study o f a Reinforced Concrete Frame

with Light Transverse Reinforcement

Copyright © 2007

by

Wassim Michael Ghannoum

All rights reserved


Abstract

Experimental and Analytical Dynamic Collapse Study o f a Reinforced Concrete Frame

with Light Transverse Reinforcement

by

Wassim Michael Ghannoum

Doctor o f Philosophy in Engineering - Civil and Environmental Engineering

University o f California, Berkeley

Professor Jack P. Moehle, Chair

Post-earthquake investigations have shown that the primary cause o f collapse in cast-

in-place beam-column frames is failure o f columns, beam-column joints, or both. As

axial failure o f one or more member in a frame structure does not necessarily constitute

the collapse o f that structure, understanding frame-system behavior and frame member

interactions leading to collapse is essential in assessing the seismic collapse vulnerability

o f this type o f structure.

This study investigates, both experimentally and analytically, the seismic collapse

behavior o f non-seismically detailed reinforced concrete frames. To accomplish this task,

a 2D, three-bay, three-floor, third-scale reinforced concrete frame is built and

dynamically tested to collapse. The test frame contains non-seismically detailed columns

whose proportions and reinforcement details allow them to yield in flexure prior to

initiating shear strength degradation and ultimately reaching axial collapse (hereafter

referred to as flexure-shear critical columns). Experimental data is provided on the

dynamic behavior o f flexure-shear critical columns sustaining shear degradation and loss

1


o f axial load capacity and on load redistribution in a frame system after shear and axial

failure o f columns.

Analytical modeling o f the test frame is undertaken up to collapse. Good agreement

between analysis and experiment is achieved up to shear failure in columns. A new zero-

length fiber-section implementation o f bar-slip rotational effects is introduced. A new

shear failure model is introduced that determines column rotations at which shear

strength degradation in flexure-shear critical columns is initiated.

An analytical model o f the test frame is subjected to several near-fault ground

motions recorded during the 1994 Northridge earthquake. Variability o f ground motions

from site to site (so called intra-event variability) and directivity effects are found to play

an important role in analytical prediction o f structural collapse. A new ground motion

intensity measure that relates well to frame damage is proposed.

Approved:___________________________________________Professor Jack P. Moehle, Chair

2


Acknowledgements

I would like to express my sincerest gratitude to my advisor Professor Jack Moehle.

His patient guidance and continued support made my doctoral endeavor a rewarding and

pleasant experience. I am particularly grateful for his sound council in both academic and

professional matters. I enjoyed our discussions and always being greeted with a smile.

My thanks to all SEMM faculty members from whom I have learned much.

Particularly, I would like to thank members o f my qualifying exam and dissertation

committees, namely, Dr. Douglas Dreger, Dr. Haiyan Huang, Dr. Stephen Mahin, Dr.

Khalid Mosalam, and Dr. Raymond Seed for giving me guidance and being generous

with their valuable time.

I would like to thank the laboratory personnel at the Richmond field station for their

assistance in the experimental portion o f this dissertation. The dedication, knowledge,

and professionalism o f Don Clyde, David Maclam, Wes Neighbour, Donald Patterson,

Jose Robles, and Shakhzod Takhirov made ambitious laboratory work possible.

The research presented here was conducted under the umbrella o f the Pacific

Earthquake Engineering Research Center (PEER) through generous funding from the

National Science Foundation (NSF) and the State o f California. I would like to

acknowledge the positive impact that PEER had on this research work and particularly on

my academic formation. I learned much from PEER members and affiliates.

My friends and colleagues in the Department o f Civil and Environmental

Engineering, namely, Matthew Dry den, Tarek El-Khoraibi, Gabriel Hurtado, Colleen

McQuoid, Andreas Schellenberg, Yoon Boon Shin, Mohamed Talaat and Tony Yang

provided encouragement and assistance for which I am grateful. I would like to

i


acknowledge the PEER Intern Matthew Lackows for conducting beam-column joint

subassembly tests mentioned in this dissertation. Special thanks to Dr. Kenneth Elwood

for providing valuable feedback on this research topic.

I extend my deepest gratitude to my fiancee Mariah Hopkins for her love, patience,

and support that got me through the trials o f this daunting enterprise.

I am eternally grateful to my parents. Their sacrifices and encouragements made this

degree and all my achievements a reality for me.


Table of Contents

1 INTRODUCTION.............................................................................................................................. 1

1.1 M o t iv a t io n .........................................................................................................................................................................1

1.2 O b je c t iv e s a n d S c o p e ................................................................................................................................................... 2

1.3 O r g a n iz a t io n .....................................................................................................................................................................4

2 LITERATURE REVIEW...................................................................................................................6

2.1 C o l u m n s ................................................................................................................................................................................. 6

2.1.1 Flexure-shear critical Columns - Shear Behavior..............................................................6

2.1.2 Flexure-shear critical Columns - Axial Behavior.............................................................10

2.1.3 Analytical Implementation o f Shear and Axial Failure Models...................................... 11

2 .2 B e a m -C o l u m n Jo i n t s .................................................................................................................................................. 14

2.2.1 Behavioral Aspects............................................................................................................... 14

2.2.2 Joint Shear Strength.............................................................................................................16

2.2.3 Joint Models..........................................................................................................................17

2 .3 B a r S lip M o d e l s ............................................................................................................................................................19

2.3.1 Bond-Slip Models................................................................................................................. 20

2.3.2 Bar Slip Induced Frame-Element Rotations..................................................................... 23

2 .4 F r a m e T e s t s ......................................................................................................................................................................27

3 DESIGN AND DETAILS OF TEST FRAME............................................................................. 30

3.1 O b je c t iv e s a n d C o n s id e r a t io n s o f Ex p e r im e n t a l P r o g r a m ........................................................30

3 .2 D e s ig n P r o c e s s ............................................................................................................................................................... 31

3 .3 T e s t F r a m e D e t a il s ...................................................................................................................................................32

3.3.1 Dimensions and Reinforcing Details.................................................................................32

3.3.2 Gravity Loads........................................................................................................................37

3.3.3 Scaling Considerations........................................................................................................38

iii


3 .4 T e s t F r a m e A n a l y t ic a l M o d e l .......................................................................................................................38

3.4.1 Column Elements..................................................................................................................39

3.4.2 Beam Elements..................................................................................................................... 39

3.4.3 Joints..................................................................................................................................... 40

3.4.4 General Model Parameters................................................................................................. 40

3.4.5 Zero-Length Column and Beam Elements........................................................................ 41

3.4.5.1 Z ero-L ength R otational Spring E lem ents M odeling B ar Slip E ffec ts ...........................................41

3.4.5.2 Z ero-L ength Shear and Axial Failure Spring E lem en ts .....................................................................41

3 .5 F r a m e A n a l y t ic a l M o d e l B e h a v io r .............................................................................................................41

3 .6 NORTHRIDGE EARTHQUAKE CASE ST U D Y ........................................................................................................4 4

3.6.1 Selected Earthquake Ground Motions...............................................................................44

3.6.2 Analysis Results................................................................................................................... 47

3.6.3 Observations and Conclusions............................................................................................51

4 EXPERIMENTAL PROGRAM...................................................................................................51

4 .1 C o n s t r u c t io n a n d C a s t i n g ...................................................................................................................................51

4 .2 T e s t S e t u p .......................................................................................................................................................................... 53

4 .3 In s t r u m e n t a t i o n ..........................................................................................................................................................57

4 .4 G r o u n d M o t io n S e l e c t io n .................................................................................................................................... 60

4 .5 T e s t P r o t o c o l ................................................................................................................................................................ 62

5 EXPERIMENTAL RESULTS...................................................................................................... 65

5.1 F r a m e D y n a m ic P r o p e r t ie s ...................................................................................................................................65

5 .2 In it ia l G r a v it y -L o a d S t a t e ................................................................................................................................. 68

5 .3 H a l f -Y ie l d D y n a m ic T e s t R e s u l t s .................................................................................................................70

5 .3.1 Global Behavior....................................................................................................................70

5.3.2 Flexure-Shear-Critical Column Behavior..........................................................................75

5.3.3 Ductile Column Behavior.....................................................................................................79

iv


5.3.4 Bar slip..................................................................................................................................81

5 .4 D y n a m ic T e s t 1 R e s u l t s .........................................................................................................................................83

5.4.1 Global Behavior....................................................................................................................83

5.4.2 Flexure-Shear-Critical Column Behavior......................................................................... 93

5.4.3 Ductile Column Behavior..................................................................................................110

5.4.4 Bar slip................................................................................................................................112

5 .5 D y n a m ic T e s t 2 ...........................................................................................................................................................114

5.5.1 Global Behavior................................................................................................................. 114

5.5.2 Flexure-Shear-Critical Column Behavior........................................................................121

5.5.3 Ductile Column Behavior.................................................................................................. 131

5.5.4 Bar slip................................................................................................................................ 134

5 .6 D y n a m ic T e s t 3 ...........................................................................................................................................................135

5.6.1 Global Behavior..................................................................................................................135

5.6.2 Flexure-Shear-Critical Column Behavior........................................................................143

5.6.3 Ductile Column Behavior.................................................................................................. 147

5.6.4 Bar slip..................................................................................... 149

6 EVALUATION OF ANALYTICAL MODELS...................................................................... 150

6.1 Im p r o v e d A n a l y t ic a l M o d e l o f T e s t F r a m e ........................................................................................ 150

6.1.1 Column and Beam Discretizations................................................................................... 150

6.1.2 LimitState Materials...........................................................................................................152

6.1.3 Shear Deformations...........................................................................................................152

6.1.4 Bar Slip Model................................................................................................................... 153

6.1.5 Material Properties and Strain-Rate Effects...................................................................157

6 .2 C o m p a r is o n b e t w e e n A n a l y t ic a l M o d e l a n d E x p e r im e n t a l R e s u l t s ............................... 158

6.2.1 Half-Yield Level Test......................................................................................................... 158

6.2.1.1 G lobal B ehav ior............................................................................................................................................. 158

6.2.1.2 Flexure-Shear-C ritical Colum n B e h av io r............................................................................................. 163

V


6.2.1.3 Ductile Colum n B eh av io r .............................................................................................................................165

6.2.2 Dynamic Test 1 ................................................................................................................. 168

6.2.2.1 G lobal B ehav io r............................................................................................................................................... 168

6.2.2.2 Flexure-Shear-C ritical C olum n B e h av io r...............................................................................................174

6.2.2.3 Ductile Colum n B eh av io r .............................................................................................................................179

6 .3 E q u iv a l e n t E l a s t ic C o l u m n F l e x u r a l St if f n e s s e s ........................................................................ 181

7 FLEXURE-SHEAR-CRITICAL COLUMN SHEAR FAILURE MODELS......................183

7.1 C o l u m n D a t a b a s e .....................................................................................................................................................184

7 .2 A n a l y t ic a l R e p r e s e n t a t io n o f D a t a b a s e C o l u m n s .......................................................................190

7.2.1 Analytical Model Description......................................................................................190

7.2.2 Analytical Model Results.............................................................................................. 192

1 3 S h e a r F a i l u r e I n i t i a t i o n M o d e l .................................................................................................................... 198

7 .4 S h e a r S t r e n g t h D e g r a d a t io n M o d e l ....................................................................................................... 2 0 5

8 CONCLUSIONS AND FUTURE WORK..................................................................................211

8.1 S u m m a r y .......................................................................................................................................................................... 211

8.1.1 Experimental Phase........................................................................................................... 211

8.1.2 Analytical Phase.................................................................................................................213

8 .2 C o n c l u s i o n s ..................................................................................................................................................................2 15

8.2.1 Experimental Phase........................................................................................................... 215

8.2.2 Analytical Phase.................................................................................................................215

8.2.2.1 Collapse V ulnerability S tu d y ......................................................................................................................215

8.2.2.2 A nalytical W ork .............................................................................................................................................. 216

8.3 F u t u r e W o r k ................................................................................................................................................................ 21 7

REFERENCES..........................................................................................................................................253

vi


APPENDIX A: TEST FRAME DETAILS AND EXPERIMENTAL SETUP...............................231

A . 1 M a t e r ia l P r o p e r t ie s ........................................................................................................................................231

A.1.1 Concrete Properties............................................................................................................231

A. 1.1.1 M ix D e s ig n ......................................................................................................................................................231

A. 1. 1.2 Physical Properties........................................................................................................................................ 2 3 1

A .1.2 Reinforcing Steel Properties............................................................................................. 234

A .2 T e s t F r a m e A s -B u il t D r a w in g s ............................................................................................................... 2 3 7

A .3 F r a m e a n d T e s t S e t u p W e i g h t s ...............................................................................................................2 4 0

A .4 O u t -o f -P l a n e B r a c in g M e c h a n i s m .......................................................................................................241

A . 5 In s t r u m e n t a t i o n ................................................................................................................................................2 4 3

A.5.1 Shaking Table Instruments.................................................................................................249

A.5.2 Load Cells........................................................................................................................... 250

A.5.3 Strain Gauges......................................................................................................................250

A. 5.4 Accelerometers....................................................................................................................252

A. 5.5 Displacement Transducers................................................................................................ 253

A .5 .5 .1 Jo int-Location Instru m en ts ....................................................................................................................... 253

A .5.5.2 C olum n and Joint D eform ation In stru m en ts........................................................................................ 256

A .5 .5 .3 B ar Slip In stru m en ts .................................................................................................................................... 263

APPENDIX B: JOINT SUBASSEMBLY TEST DETAILS AND RESULTS...............................264

APPENDIX C: DATA REDUCTION AND VERIFICATION........................................................ 268

C. 1 S h a k in g T a b l e In p u t v s . O u t p u t G r o u n d M o t io n C o m p a r i s o n ............................................ 2 6 8

C .2 D a t a R e d u c t io n ........................................................................................................................................................2 6 9

C.2.1 Data Filtering.................................................................................................................... 269

C.2.2 Modal Property Calculations............................................................................................273

C .2.2 .1 C alculation M eth o d s.................................................................................................................................... 273

C .2 .2 .1.1 T im e D om ain M e th o d s..................................................................................................................... 275

vii


C.2.2.1.2 Frequency Domain M ethods........................................................................................................... 278

C.2.2.2 Initial “Undamaged” State Snap-Back Tests......................................................................................... 278

C.2.2.3 End o f Half-Yield Test Free-Vibration................................................................................................... 283

C.2.2.4 W hite-Noise Dynamic T est.........................................................................................................................283

C.2.2.5 End o f Dynamic Test 1 Free-Vibration...................................................................................................285

C.2.2.6 Damaged-State Snap-Back T ests.............................................................................................................. 285

C.2.2.7 End o f Dynamic Test 2 Free-Vibration...................................................................................................287

C.2.3 Initial Assumed Gravity-Load-State o f the Frame......................................................... 287

C. 2.4 First Story Column Force Calculations.......................................................................... 291

C. 2.5 Story Shear Force Calculations....................................................................................... 294

C.2.6 Joint Displacement Calculations..................................................................................... 295

C.2.6.1 On-Table Joint Triangulation Displacement Calculations................................................................295

C.2.6.2 Off-Table Joint Triangulation Displacement Calculations................................................................298

C.2.7 Column Critical-Section Rotations.................................................................................. 301

C .3 R e s u l t C h e c k s a n d B a l a n c e s .........................................................................................................................3 03

C.3.1 Base Shear Checks.............................................................................................................303

C.3.2 Overturning Moment Checks............................................................................................304

C.3.3 Lead-Weight Accelerometer Check..................................................................................307

C.3.4 On-Table versus off-Table Instrument Displacement Comparison...............................308

C.3.5 Out-of-Plane Displacements o f Frame............................................................................312

C .4 S t r a in -G a u g e R e a d in g s ...................................................................................................................................... 3 13

C.4.1 Half-Yield Dynamic Test...................................................................................................313

C.4.2 Dynamic Test 1 ..................................................................................................................319

APPENDIX D: OPENSEES MODELING...........................................................................................324

D . 1 M a t e r ia l P r o p e r t ie s ....................................................................................................................................... 3 2 4

D .2 M o m e n t -C u r v a t u r e S e c t io n a l A n a l y s e s ...................................................................................... 3 2 6

D .3 S h e a r a n d A x ia l L im it S t a t e M a t e r ia l P r o p e r t ie s .................................................................. 3 2 7

viii


E APPENDIX E: FRAME COMPONENT PICTURES AT VARIOUS DAMAGE STATES.

...................................................................................................................................................................................................... 3 3 2

E . l C o l u m n A 1 B a s e ........................................................................................................................................................3 3 2

E .2 Jo in t A 1 ............................................................................................................................................................................ 3 3 7

E .3 JOINT A 2 ............................................................................................................................................................................ 3 3 8

E .4 Jo in t A 3 ............................................................................................................................................................................ 3 4 0

E. 5 C o l u m n B 1 B a s e ......................................................................................................................................................... 3 4 2

E .6 Jo in t B 1 ............................................................................................................................................................................3 4 4

E .7 Jo in t B 2 ............................................................................................................................................................................3 4 6

E .8 JOINT B 3 ............................................................................................................................................................................3 4 7

E .9 C o l u m n C l B a s e .........................................................................................................................................................3 4 9

E .1 0 Jo in t C l .......................................................................................................................................................................351

E . l l Jo in t C 2 .......................................................................................................................................................................3 5 2

E .1 2 Jo in t C 3 .......................................................................................................................................................................3 5 4

E .13 C o l u m n D I B a s e ...................................................................................................................................................3 5 6

E .1 4 Jo i n t D I ......................................................................................................................................................................3 5 8

E .l 5 Jo in t D 2 ..................................................................................................................................................................... 3 5 9

E .1 6 Jo in t D 3 ..................................................................................................................................................................... 361

ix


List of Figure

F ig u r e 2 - 1 : I m p r o p e r u s e o f s t r e n g t h m o d e l t o e s t im a t e d is p l a c e m e n t s [ f r o m S e z e n (2 0 0 2 )]

(V=SHEAR RESISTANCE OF COLUMN SECTION, Vc=CONCRETE CONTRIBUTION TO SHEAR STRENGTH,

Vs=TRANSVERSE REINFORCEMENT CONTRIBUTION TO SHEAR STRENGTH, M,=COLUMN DRIFT,

AMa=CHANGE IN DRIFT AT FAILURE, M=MEAN RESPONSE,, X —STANDARD DEVI A TION, M=SLOPE)............... 7

F ig u r e 2 -2: E q u iv a l e n t a x ia l l o a d r a t io f r o m K a t o a n d O h n is h i (2 0 0 2 ) ( t = m in . a x ia l

LOAD/MAX. AXIAL LOAD; HP=MAX. AXIAL LOAD/AgFc ) ...........................................................................................................9

F ig u r e 2 -3 : E l w o o d a n d M o e h l e (2 0 0 5 b) s h e a r -d r i f t m o d e l c o m p a r is o n ..................................................10

F ig u r e 2 -4 : Z e r o -l e n g t h L im it S t a t e s p r in g e l e m e n t s [E l w o o d ( 2 0 0 2 ) ] ....................................................... 12

F ig u r e 2 -5 : S h e a r a n d a x ia l L im it S ta t e e l e m e n t r e s p o n s e s a n d l i m it c u r v e s [ E l w o o d (2 0 0 2 )] 14

F ig u r e 2 -6 : J o in t e l e m e n t d e v e l o p e d b y L o w e s e t a l . (2 0 0 4 ) ............................................................................... 19

F ig u r e 2 -7: B a r s l ip il l u s t r a t i o n ........................................................................................................................................... 19

F ig u r e 2 -8 : B o n d s t r e s s vs. s l ip (f r o m E l i g e h a u s e n e t a l . ( 1 9 8 3 ) ) .................................................................. 2 0

F ig u r e 2 - 9 : B o n d s t r e s s vs. s l ip (f r o m L e h m a n a n d M o e h l e ( 2 0 0 0 ) ) ...............................................................21

F ig u r e 2 - 1 0 : L o n g it u d in a l b a r b o n d s t r e s s , s t e e l s t r e s s a n d s t e e l s t r a i n p r o f il e s (f r o m S e z e n

(2 0 0 2 )), ( F c=CONCRETE u l t im a t e c o m p r e s s iv e s t r e s s , Fy=BAR y ie l d s t r e s s , f s= b a r s t r e s s a t

INTERFACE, Er=BAR YIELD STRAIN, ES=BAR STRAIN A T INTERFACE, A s=BARAREA)............................................... 21

F ig u r e 2 -1 1 : B a r s t r e s s vs . s l ip (f r o m B e r r y ( 2 0 0 6 ) ) .................................................................................................... 22

F ig u r e 2 - 1 2 : B a r s l ip r o t a t io n c e n t e r (f r o m S e z e n ( 2 0 0 2 ) ) ....................................................................................25

F ig u r e 2 -1 3 : B a r s l ip z e r o -l e n g t h f ib e r -s e c t io n e l e m e n t s (f r o m Z h a o a n d S r it h a r a n (2 0 0 7 )) ...2 5

F ig u r e 2 -1 4 : E f f e c t iv e c o n c r e t e d e p t h (f r o m B e r r y (2 0 0 6 ) ) ................................................................................26

F ig u r e 3-1: Te s t f r a m e d im e n s io n s a n d r e in f o r c e m e n t d e t a i l s .........................................................................33

F ig u r e 3 -2 : O p e n S E E S t e s t f r a m e a n a l y t ic a l m o d e l .................................................................................................39

F ig u r e 3 -3 : F i r s t -s t o r y d r if t r a t io v e r s u s b a s e s h e a r r e s p o n s e .......................................................................43

x


F ig u r e 3 -4: Th e 1 9 9 4 N o r t h r id g e , Ca l if o r n ia , e a r t h q u a k e : E p ic e n t e r (S t a r sy m b o l ) , s u r f a c e

PROJECTION OF THE FA UL T PLANE, AND LOCA TIONS OF THE SELECTED RECORDING ST A TIONS (SOLID

CIRCLES) ARE MARKED .......................................................................................................................................................................45

F ig u r e 3 -5: L in e a r l y e l a s t ic r e s p o n s e s p e c t r a f o r 5 % d a m p in g f o r b o t h h o r iz o n t a l

COMPONENTS OF THE SELECTED 1 9 9 4 NORTHRIDGE RECORDS ..................................................................................... 4 6

F ig u r e 3-6: F ir s t -s t o r y d r i f t r a t io h is t o r ie s ...................................................................................................................48

F ig u r e 3-7: F i r s t -s t o r y a b s o l u t e d r i f t r a t io s v s . g r o u n d m o t io n IM s . C i r c l e s m a r k t h e

HORIZONTAL COMPONENT 1 MOTIONS AND DIAMONDS THE HORIZONTAL COMPONENT 2 MOTIONS 50

F ig u r e 4 -1 : S p e c im e n c o n s t r u c t i o n ....................................................................................................................................... 52

F ig u r e 4 -2 : S p e c im e n c a s t in g ...................................................................................................................................................... 53

F ig u r e 4 -3 : S p e c im e n e r e c t i o n ..................................................................................................................................................54

F ig u r e 4 -4 : Te s t f r a m e s e t u p p i c t u r e ................................................................................................................................... 55

F ig u r e 4 -5 : Te s t f r a m e s e t u p d r a w i n g .................................................................................................................................. 56

F ig u r e 4 -6 : L e a d w e ig h t l o c a t io n ( t y p ic a l f o r a l l b e a m s ) .....................................................................................56

F ig u r e 4 -7 : F r a m e in s t r u m e n t a t io n s c h e m a t ic d r a w in g .......................................................................................... 58

F ig u r e 4 -8: B a r -s l ip in s t r u m e n t a t io n p i c t u r e ................................................................................................................59

F ig u r e 4 -9 : D y n a m ic T e s t 1 g r o u n d m o t io n d is p l a c e m e n t , v e l o c it y , a n d a c c e l e r a t io n

h is t o r ie s , p l u s a c c e l e r a t io n F o u r ie r t r a n s f o r m o f a c c e l e r a t io n h is t o r y .............................................61

F ig u r e 4 -1 0 : D y n a m ic T e s t 1 g r o u n d m o t io n r e s p o n s e s p e c t r a .......................................................................... 62

F ig u r e 5 - 1 : M o d a l f r e q u e n c ie s vs. m a x im u m a b s o l u t e v a l u e s o f r o o f a n d f ir s t -f l o o r d r i f t

RA TIOS FOR ALL TESTS........................................................................................................................................................................ 68

F ig u r e 5-2: F o o t in g a n d f l o o r - l e v e l a c c e l e r a t io n r e c o r d s - H a l f - y ie l d t e s t .....................................71

F ig u r e 5-3: S t o r y s h e a r r e c o r d s - H a l f - y ie l d t e s t .....................................................................................................71

F ig u r e 5 -4: I n t e r -s t o r y h o r iz o n t a l d r i f t r a t io r e c o r d s - H a l f -Y ie l d Te s t .............................................. 72

F ig u r e 5-5: M i n im u m a n d m a x im u m in t e r - s t o r y h o r iz o n t a l d r i f t r a t io p r o f il e s - H a l f -Y i e l d

Te s t ........................................................................................................................................................................................... 72

F ig u r e 5-6: I n t e r -s t o r y h o r iz o n t a l d r if t r a t i o s v s . s h e a r s - H a l f -Y ie l d T e s t .........................................73

xi


F ig u r e 5-7: F i r s t - s t o r y c o l u m n i n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o s vs. s h e a r s - H a l f - Y i e ld

Te s t 7 4

F ig u r e 5 -8: F ir s t -s t o r y c o l u m n in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . a x ia l l o a d s - H a l f -

Yie l d Te s t ..................................................................................................................................................................................... 75

F ig u r e 5 -9: C o l u m n s A1 &B1 TOP AND BOTTOM MOMENTS VS. DRIFT R ATIO S-H A LF -YlE LD TEST 7 6

F ig u r e 5 -10 : C o l u m n s A 1 &B1 b o t t o m vs. t o p m o m e n t s - H a l f - Y i e l d T e s t ......................................... 77

F ig u r e 5 -11: C o l u m n s A1 & B1 t o t a l r o t a t i o n s vs. m o m e n t s - H a l f - Y i e l d T e s t ............................... 78

F ig u r e 5 -12 : C o l u m n s A & B b o t t o m v s . t o p t o t a l r o t a t i o n s - H a l f - Y i e l d T e s t .............................. 79

F ig u r e 5 -13 : C o l u m n s Cl & D1 i n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o s vs. b o t t o m a n d t o p

m o m e n t s - H a l f -Y ie l d Te s t .................................................................................................................................................. 8 0

F ig u r e 5 -14 : C o l u m n s C l &D1 b o t t o m v s . t o p m o m e n t s - H a l f - Y i e l d T e s t ......................................... 81

F ig u r e 5 -15 : B a r s l ip v s . e n d m o m e n t s - H a l f -Y i e l d Te s t .................................................................................. 82

F ig u r e 5 -16: B a s e SHEAR COMPARISON b e t w e e n l o a d c e l l r e a d in g s a n d f l o o r in e r t ia c a l c u l a t io n

(FROMACCELEROMETERS) - DYNAMIC TEST 1 ................................................................................................................. 84

F ig u r e 5 -17: F o o t i n g a n d f l o o r - l e v e l a c c e l e r a t i o n r e c o r d s - D y n a m ic T e s t 1 .............................. 85

F ig u r e 5 -18 : S t o r y s h e a r r e c o r d s - D y n a m ic T e s t 1 .............................................................................................. 86

F ig u r e 5 -19 : I n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o r e c o r d s - D y n a m ic T e s t 1 ......................................... 86

F ig u r e 5 -20: M in im u m a n d m a x im u m in t e r -s t o r y h o r iz o n t a l d r if t r a t io p r o f il e s - D y n a m ic Te s t

1 87

F ig u r e 5 -21 : C o l u m n B1 d a m a g e d s t a t e - D y n a m i c T e s t 1 ................................................................................ 88

F ig u r e 5 -22 : C o l u m n in t e r -s t o r y h o r iz o n t a l v s . v e r t ic a l d r i f t r a t i o s - D y n a m ic T e s t 1 89

F ig u r e 5 -23 : I n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o s vs. s h e a r s - D y n a m i c T e s t 1 .................................... 90

F ig u r e 5 -24 : F ir s t -s t o r y c o l u m n in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs. s h e a r s - D y n a m ic Te s t

1 9 0

F ig u r e 5 -25 : F i r s t - s t o r y c o l u m n a x ia l l o a d h i s t o r i e s - D y n a m i c T e s t 1 ................................................. 91

F ig u r e 5 -26 : V e r t i c a l a c c e l e r a t i o n h i s t o r i e s o f F o o t i n g BO a n d J o i n t s B1 a n d B 2 a r o u n d t h e

t im e o f C o l u m n B1 s h e a r f a i l u r e - D y n a m i c T e s t 1 ........................................................................................... 91

F ig u r e 5 -2 7 : C o l u m n s A1 a n d B I d i l a t i o n h i s t o r y a t h = 6 in . f r o m b o t t o m - D y n a m i c T e s t I .... 96


F ig u r e 5 -28: C o l u m n s A1 & B1 i n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o s v e r s u s s h e a r s - D y n a m ic

Te s t I ...........................................................................................................................................................................................97

F ig u r e 5 -2 9 : C o l u m n B 1 b o t t o m s h e a r f a il u r e p h o t o g r a p h s - D y n a m ic T e s t I ......................................... 98

F ig u r e 5 -30: C o l u m n s A 1 & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v e r s u s a x ia l l o a d s (f u l l t e s t

AND 2 1 .9 5 < T < 2 3 .1 0 SEC.) - D YNAMIC TEST 1 ..................................................................................................................99

F ig u r e 5 - 3 1 : C o l u m n B I in t e r -s t o r y v e r t ic a l d r if t r a t io h is t o r y - D y n a m ic Te s t 1 ............................100

F ig u r e 5 -3 2 : C o l u m n B I in t e r -s t o r y h o r iz o n t a l vs. v e r t ic a l d r i f t r a t io s - D y n a m ic Te s t l . . . . \ 0 \

F ig u r e 5 -3 3 : C o l u m n B I a x ia l l o a d v s . in t e r -s t o r y v e r t ic a l d r i f t r a t io (f u l l t e s t a n d 2 1 .9 5 < t

< 2 3 .1 0 s e c .) - D y n a m ic Te s t 1 ...............................................................................................................................................102

F ig u r e 5 -34: C o l u m n s A l & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . t o p a n d b o t t o m m o m e n t s

- D y n a m ic T e s t 1 ........................................................................................................................................................................... 103

F ig u r e 5 -3 5 : C o l u m n s A l & B 1 c r it ic a l s e c t io n r o t a t io n s v s . t o p & b o t t o m m o m e n t s - D y n a m ic

Te s t I .........................................................................................................................................................................................103

F ig u r e 5 -3 6 : C o l u m n s A I & B 1 r e l a t iv e h o r iz o n t a l d r if t s vs . t o p a n d b o t t o m c r it ic a l s e c t io n

r o t a t io n s - D y n a m ic Te s t 1 .................................................................................................................................................... 104

F ig u r e 5 - 3 7 : C o l u m n s A I & B 1 c r it ic a l s e c t io n r o t a t io n s v s . s h e a r s - D y n a m ic Te s t 1 .....................104

F ig u r e 5 - 3 8 : C o l u m n s A I & B 1 b o t t o m v s . t o p c r it ic a l s e c t io n r o t a t io n s - D y n a m ic Te s t I .. .A Q 5

F ig u r e 5 - 3 9 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . s h e a r s - D y n a m i c Te s t I .

.........................................................................................................................................................................................I l l

F ig u r e 5 -4 0 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . a x ia l l o a d s - D y n a m ic

Te s t I .........................................................................................................................................................................................I l l

F ig u r e 5 -41: C o l u m n s C l a n d D 1 h o r iz o n t a l d r if t vs. t o p & b o t t o m m o m e n t s - D y n a m ic Te s t 1 .

112

F ig u r e 5 -4 2 : B a r s l i p vs. e n d m o m e n t s - D y n a m ic T e s t 1 ........................................................................................113

F ig u r e 5 -43: B a r s l i p vs. e n d r o t a t i o n s - D y n a m ic T e s t 1 .......................................................................................113

F ig u r e 5 -44: F o o t in g a n d f l o o r -l e v e l a c c e l e r a t io n r e c o r d s - D y n a m ic T e s t 2 ................................... 114

F ig u r e 5 -4 5 : S t o r y s h e a r r e c o r d s - D y n a m ic T e s t 2 ................................................................................................... 115

F ig u r e 5 -46: I n t e r -s t o r y h o r iz o n t a l d r i f t r a t io r e c o r d s - D y n a m ic T e s t 2 ..............................................115

xiii


F ig u r e 5-47: M in i m u m a n d m a x im u m h o r iz o n t a l r e l a t iv e f l o o r d r i f t p r o f il e s - D y n a m ic T e s t 2

116

F ig u r e 5 -4 8 : C o l u m n A l d a m a g e d s t a t e - D y n a m ic Te s t 2 ........................................................................................117

F ig u r e 5 -4 9 : C o l u m n in t e r -s t o r y h o r iz o n t a l vs . v e r t ic a l d r if t r a t i o s - D y n a m ic Te s t 2 .......... 117

F ig u r e 5 -5 0 : I n t e r -s t o r y h o r iz o n t a l d r i f t r a t i o s v s . s h e a r s - D y n a m ic Te s t 2 ...................................... 118

F ig u r e 5 -5 1 : F i r s t -s t o r y c o l u m n in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs. s h e a r s - D y n a m i c Te s t

2 118

F ig u r e 5 -5 2 : F i r s t -s t o r y c o l u m n a x ia l l o a d h i s t o r i e s - D y n a m ic Te s t 2 ..................................................... 119

F ig u r e 5 -5 3 : Ve r t ic a l a c c e l e r a t io n s o f F o o t in g BO a n d J o in t s B 1 a n d B 2 d u r in g s t r o n g

s h a k in g - D y n a m ic Te s t 2 ..........................................................................................................................................................119

F ig u r e 5 -5 4 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . s h e a r s - D y n a m ic Te s t 2 .

122

F ig u r e 5 -55: C o l u m n A l b o t t o m s h e a r f a il u r e p h o t o g r a p h s - D y n a m ic T e s t 2 .......................................123

F ig u r e 5 -56: C o l u m n A l d il a t io n h is t o r y a t h = 6 i n . f r o m b o t t o m - D y n a m ic Te s t 2 ............................. 124

F ig u r e 5 -5 7 : C o l u m n s A I in t e r -s t o r y h o r iz o n t a l d r i f t r a t io v s . d il a t io n a t h = 6 i n . f r o m b o t t o m

- D y n a m ic Te s t 2 .............................................................................................................................................................................125

F ig u r e 5 -5 8 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . a x ia l l o a d s - D y n a m ic

Te s t 2 125

F ig u r e 5 -5 9 : C o l u m n s A I & B 1 in t e r - s t o r y v e r t ic a l d r i f t r a t io h is t o r y - D y n a m ic T e s t 2 ........... 126

F ig u r e 5 - 6 0 : C o l u m n B 1 a x ia l l o a d vs . in t e r -s t o r y v e r t ic a l d r if t r a t io - D y n a m ic Te s t s I & 2 ....

......................................................................................................................................................................................... 127

F ig u r e 5 - 6 1 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . t o p a n d b o t t o m m o m e n t s

- D y n a m ic Te s t 2 .............................................................................................................................................................................127

F ig u r e 5 -6 2 : C o l u m n A l b o t t o m c r it ic a l s e c t i o n t o t a l r o t a t io n vs . b o t t o m m o m e n t (f u l l t e s t

a n d 21 s e c . < t < 31 s e c . ) - D y n a m ic Te s t 2 ....................................................................................................................128

F ig u r e 5 -63: C o l u m n A l in t e r -s t o r y h o r iz o n t a l d r i f t r a t io v s . b o t t o m t o t a l c r it ic a l s e c t io n

r o t a t io n - D y n a m ic Te s t 2 ....................................................................................................................................................... 129

F ig u r e 5 -6 4 : C o l u m n A l b o t t o m t o t a l c r it ic a l s e c t io n r o t a t io n vs . s h e a r - D y n a m ic T e s t 2 ... 129

xiv


F ig u r e 5-65: C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . s h e a r s - D y n a m ic T e s t 2 .

.........................................................................................................................................................................................132

F ig u r e 5 -6 6 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . a x ia l l o a d s - D y n a m ic

Te s t 2 .........................................................................................................................................................................................133

F ig u r e 5 -6 7 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . t o p & b o t t o m m o m e n t s -

D y n a m ic Te s t 2 .................................................................................................................................................................................133

F ig u r e 5 -6 8 : C o l u m n C l b a r s l ip v s . e n d m o m e n t s - D y n a m ic Te s t 2 ............................................................... 134

F ig u r e 5 -6 9 : F o o t in g a n d f l o o r -l e v e l a c c e l e r a t io n r e c o r d s - D y n a m ic Te s t 3 ....................................136

F ig u r e 5 -7 0 : S t o r y s h e a r r e c o r d s - D y n a m ic Te s t 3 ....................................................................................................136

F ig u r e 5 -7 1 : I n t e r -s t o r y h o r iz o n t a l d r i f t r a t io r e c o r d s - D y n a m ic Te s t 3 ...............................................137

F ig u r e 5 -7 2 : .M i n i m u m a n d m a x im u m h o r iz o n t a l r e l a t iv e f l o o r d r i f t p r o f il e s - D y n a m ic Te s t

3 137

F ig u r e 5 -73: C o l u m n s B 1 (l e f t ) a n d A 1 (r ig h t ) d a m a g e d s t a t e s - D y n a m ic Te s t 3 .................................... 138

F ig u r e 5 -74: F r a m e c o l l a p s e s t a t e - D y n a m ic Te s t 3 .................................................................................................. 139

F ig u r e 5 -7 5 : C o l u m n in t e r -s t o r y h o r iz o n t a l vs. v e r t ic a l d r if t r a t i o s - D y n a m ic T e s t 3 ................139

F ig u r e 5 -7 6 : F l o o r in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . s h e a r s - D y n a m ic T e s t 3 .........................140

F ig u r e 5 -7 7 : F ir s t -s t o r y c o l u m n s in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . s h e a r s - D y n a m ic T e s t

3 140

F ig u r e 5 -7 8 : F ir s t -s t o r y c o l u m n s a x ia l l o a d h is t o r ie s - D y n a m ic Te s t 3 ....................................................141

F ig u r e 5 -7 9 : F ir s t -s t o r y c o l u m n s in t e r - s t o r y h o r iz o n t a l d r i f t r a t io s vs . a x ia l l o a d s - D y n a m ic

Te s t 3 141

F ig u r e 5 -8 0 : Ve r t ic a l a c c e l e r a t io n s o f F o o t in g BO a n d J o in t s A l a n d A 2 a r o u n d a x ia l f a il u r e -

d y n a m i c T e s t 3 .................................................................................................................................................................................142

F ig u r e 5 -8 1 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . s h e a r s - D y n a m ic Te s t 3 . .

.........................................................................................................................................................................................143

F ig u r e 5 -8 2 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . a x ia l l o a d s - D y n a m ic

Te s t 3 144

F ig u r e 5 -83: C o l u m n s A l & B 1 in t e r -s t o r y v e r t ic a l d r i f t r a t io h i s t o r i e s - D y n a m ic Te s t 3 . . .A A A

XV


F ig u r e 5 -8 4 : C o l u m n A l in t e r -s t o r y h o r iz o n t a l vs . v e r t ic a l d r i f t r a t i o s - D y n a m ic Te s t 3 . . . . 145

F ig u r e 5 -8 5 : C o l u m n A l a x ia l l o a d vs. in t e r -s t o r y v e r t ic a l d r if t r a t i o - D y n a m ic Te s t 3 ...........145

F ig u r e 5 -86: C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . t o p a n d b o t t o m m o m e n t s

- D y n a m i c T e s t 3 .............................................................................................................................................................................146

F ig u r e 5 -8 7 : C o l u m n s C l & D 1 i n t e r - s t o r y h o r i z o n t a l d r i f t r a t i o s vs. s h e a r s - D y n a m ic T e s t 3 .

.........................................................................................................................................................................................147

F ig u r e 5 -88: C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs. a x ia l l o a d s - D y n a m ic

T e s t 3 148

F ig u r e 5 -8 9 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . t o p & b o t t o m m o m e n t s -

D y n a m ic T e s t 3.................................................................................................................................................................................148

F ig u r e 6 -1: S h e a r c r it ic a l c o l u m n a n a l y t ic a l r e p r e s e n t a t i o n ...................................................................... 152

F ig u r e 6 -2: B a r s l ip f ib e r -s e c t io n e q u il ib r iu m , s t r a i n p r o f il e s a n d m a t e r ia l s .................................... 154

F ig u r e 6-3: S t o r y s h e a r h i s t o r i e s - H a l f -Y ie l d Te s t ...............................................................................................159

F ig u r e 6 -4: F l o o r -l e v e l a c c e l e r a t io n h i s t o r i e s - H a l f -Y ie l d Te s t .............................................................160

F ig u r e 6 -5: I n t e r -s t o r y h o r iz o n t a l d r i f t r a t io h i s t o r i e s - H a l f -Y ie l d Te s t ........................................ 161

F ig u r e 6 -6: I n t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . s h e a r s - H a l f -Y ie l d Te s t ......................................161

F ig u r e 6 -7: F ir s t -s t o r y c o l u m n in t e r -s t o r y h o r iz o n t a l d r if t r a t io s vs . a x ia l l o a d s - H a l f -

Yie l d Te s t .........................................................................................................................................................................................162

F ig u r e 6 -8: C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s vs . s h e a r s - H a l f - Yie l d Te s t

.........................................................................................................................................................................................163

F ig u r e 6 -9: C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . t o p & b o t t o m m o m e n t s -

H a l f -Y ie l d T e s t .............................................................................................................................................................................164

F ig u r e 6 -1 0 : C o l u m n s A I & B 1 t o t a l e n d r o t a t io n s vs . m o m e n t s - H a l f -Y ie l d T e s t ...........................165

F ig u r e 6 -1 1 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs . s h e a r s - H a l f - Yie l d T e s t

166

F ig u r e 6 -1 2 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s vs. t o p a n d b o t t o m

m o m e n t s - H a l f -Y ie l d Te s t ......................................................................................................................................................167

F ig u r e 6 -1 3 : S t o r y s h e a r h i s t o r i e s - D y n a m ic T e s t 1 ................................................................................................168

xvi


F ig u r e 6 -1 4 : F l o o r -l e v e l a c c e l e r a t io n h i s t o r i e s - D y n a m ic T e s t I .................................................................169

F ig u r e 6 -1 5 : I n t e r -s t o r y h o r iz o n t a l d r i f t r a t i o h is t o r ie s - D y n a m ic Te s t 1 ............................................170

F ig u r e 6 -1 6 : I n t e r -s t o r y h o r iz o n t a l d r if t r a t io s v s . s h e a r s - D y n a m ic Te s t I ......................................... 170

F ig u r e 6 -1 7 : C o l u m n s A I & B 1 in t e r -s t o r y v e r t ic a l d r i f t r a t io h i s t o r y - D y n a m ic T e s t I 171

F ig u r e 6 -1 8 : C o l u m n A l a x ia l l o a d h is t o r ie s - D y n a m ic Te s t 1 .......................................................................... 171

F ig u r e 6 - 1 9 : C o l u m n B 1 a x ia l l o a d h i s t o r i e s - D y n a m ic Te s t 1 .........................................................................172

F ig u r e 6 -2 0 : C o l u m n s C l & D 1 a x ia l l o a d h i s t o r ie s - D y n a m ic Te s t I ........................................................... 172

F ig u r e 6 - 2 1 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v e r s u s s h e a r s - D y n a m ic

Te s t I ......................................................................................................................................................................................... 174

F ig u r e 6 -2 2 : C o l u m n s A I & B 1 in t e r - s t o r y h o r iz o n t a l d r i f t r a t io s v e r s u s a x ia l l o a d s -

D y n a m ic Te s t I .................................................................................................................................................................................175

F ig u r e 6 -2 3 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l vs. v e r t ic a l d r i f t r a t i o s - D y n a m ic Te s t

1 175

F ig u r e 6 - 2 4 : C o l u m n B 1 a x ia l l o a d vs . in t e r -s t o r y v e r t ic a l d r i f t r a t i o - D y n a m ic Te s t I 176

F ig u r e 6 -2 5 : C o l u m n s A I & B 1 c r it ic a l s e c t io n r o t a t io n s v s . t o p & b o t t o m m o m e n t s - D y n a m ic

Te s t I ......................................................................................................................................................................................... 176

F ig u r e 6 -2 6 : C o l u m n s A I & B 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . t o p a n d b o t t o m m o m e n t s

- D y n a m ic T e s t 1 ............................................................................................................................................................................177

F ig u r e 6 -2 7 : C o l u m n s C l a n d D I in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . t o p a n d b o t t o m

m o m e n t s - D y n a m ic Te s t 1 ......................................................................................................................................................180

F ig u r e 6 -2 8 : C o l u m n s C l & D 1 in t e r -s t o r y h o r iz o n t a l d r i f t r a t io s v s . s h e a r s - D y n a m ic Te s t 1 .

181

F ig u r e 7 -1 : C o l u m n s h e a r v e r s u s d r i f t r a t io e n v e l o p e - il l u st r a t io n o f n o t a t i o n ........................ 187

F ig u r e 7 -2: I l l u s t r a t io n o f y ie l d d is p l a c e m e n t a n d s h e a r f o r c e e s t im a t io n (a d a p t e d f r o m

S e z e n (2 0 0 2 ) ) ..................................................................................................................................................................................... 189

F ig u r e 7 -3: S a m p l e p u s h o v e r c u r v e o v e r l a id o n e x p e r im e n t a l s h e a r -d r i f t r e l a t io n (f o r

COLUMN S E 2 C L D 1 2 ) ....................................................................................................................................................................191

F ig u r e 7 -4: Va r ia t io n s i n o Totmax w it h c h a n g e s i n b o n d - s t r e s s a s s u m p t i o n ................................................ 195

xvii


F ig u r e 7 -5: &TOtmax/ d r i f t r a t io (a ^ f o r a l l c o l u m n s ...........................................................................................195

F ig u r e 7 -6: P r o p o r t i o n o f c o l u m n f l e x u r a l r o t a t io n s o v e r L p ( 0 ,TOtma>) a n d b a r -s l ip r o t a t io n s

(®BSTotmax) COMPRISING QtotmaxFOR DIFFERENT BOND-SLIP PARAMETERS...............................................................197

F ig u r e 7 -7 : I l l u s t r a t io n o f c o l u m n s h e a r s t r e n g t h c o m p o n e n t s .................................................................198

F ig u r e 7 -8: P r e d ic t o r v a r ia b l e s v e r s u s 0 TOtmax.......................................................................................................... 201

F ig u r e 7 -9: S h e a r f a il u r e in it ia t io n m o d e l e s t im a t e s o f r o t a t io n s v e r s u s d a t a b a s e c o l u m n

ROTATIONS ........................................................................................................................................................................................ 2 0 5

F ig u r e 7 -1 0 : P r e d ic t o r v a r ia b l e s v e r s u s 4 wearJ h ...................................................................................................... 2 0 8

F ig u r e 7 -1 1 : E s t im a t e d v e r s u s o b s e r v e d P /( A g f 'c) v e r s u s A %„eakJ h ................................................................ 2 1 0

F ig u r e A - l : C o n c r e t e c o m p r e s s iv e s t r e n g t h h is t o r y ............................................................................................. 2 3 2

F ig u r e A -2 : C o n c r e t e m e a s u r e d s t r e s s -s t r a in c u r v e s .......................................................................................... 233

F ig u r e A - 3 : #3 r e in f o r c in g s t e e l b a r s t r e s s -s t r a in c u r v e s .................................................................................2 3 4

F ig u r e A - 4 : #2 r e i n f o r c i n g s t e e l b a r s t r e s s - s t r a i n c u r v e s .................................................................................235

F ig u r e A -5 : 3 /1 6 i n . d ia m e t e r s t e e l w ir e s t r e s s -s t r a in c u r v e s ..........................................................................2 3 5

F ig u r e A -6 : 2/16 in . d i a m e te r s t e e l w i r e s t r e s s - s t r a i n c u r v e s ..........................................................................2 3 6

F ig u r e A -7 : F r a m e r e in f o r c in g d e t a il s - A s - B u i l t ..................................................................................................2 3 7

F ig u r e A - 8 : F r a m e r e in f o r c in g d e t a il s - A s - B u il t D e t a il s ................................................................................ 2 3 8

F ig u r e A -9 : F r a m e r e in f o r c in g d e t a i l s - A s - B u il t S e c t i o n s ..............................................................................2 3 9

F ig u r e A - 10: O u t - o f -p l a n e b r a c in g p ic t u r e .................................................................................................................... 2 4 2

F ig u r e A - 11: O u t - o f -p l a n e b r a c in g d e t a i l s .................................................................................................................... 243

F ig u r e A - 12: S h a k in g t a b l e in s t r u m e n t a t io n p l a n .....................................................................................................2 4 9

F ig u r e A -1 3 : L o a d c e l l c o n n e c t io n d e t a i l ...................................................................................................................... 2 5 0

F ig u r e A - 14: S t r a in g a u g e l o c a t i o n s ...................................................................................................................................251

F ig u r e A -1 5 : A c c e l e r o m e t e r s a t J o i n t A 1 ........................................................................................................................2 5 2

F ig u r e A - 16: A c c e l e r o m e t e r l o c a t io n d r a w i n g .......................................................................................................... 253

F ig u r e A - 17: T y p ic a l c o n n e c t io n d e t a il s f o r d is p l a c e m e n t t r a n s d u c e r s .........................................................2 5 4

F ig u r e A - 18: J o in t -l o c a t io n in s t r u m e n t l a y o u t .......................................................................................................... 255

F i g u r e A - 19: C o l u m n a n d j o i n t d e f o r m a t io n in s t r u m e n t l a y o u t .....................................................................2 5 6

xviii


F ig u r e A -2 0 : C o l u m n in s t r u m e n t b r a c k e t d e t a i l - A t f o o t in g A O ................................................................... 2 5 7

F ig u r e A - 2 1: T y p ic a l c o l u m n in s t r u m e n t c o n n e c t io n d e t a i l s - A t f o o t in g A O ........................................2 5 8

F ig u r e A -2 2 : T y p ic a l j o i n t in s t r u m e n t c o n n e c t io n d e t a i l s - A t j o i n t A 2 .................................................... 2 5 9

F ig u r e A -2 3 : T y p ic a l j o i n t i n s t r u m e n t c o n n e c t i o n d e t a i l s - A t j o i n t B 1......................................................2 5 9

F ig u r e A - 2 4 : C o l u m n a n d j o i n t i n s t r u m e n t l o c a t io n d r a w in g s w i t h n o d e n u m b e r in g s c h e m e

2 6 2

F ig u r e A -2 5 : B a r s l ip in s t r u m e n t s - d e t a il p i c t u r e s ................................................................................................... 263

F ig u r e B - l : J o i n t s u b a s s e m b l y t e s t s e t u p p i c t u r e .................................................................................................... 2 6 5

F ig u r e B -2 : J o i n t s u b a s s e m b l y c o n c r e t e c y l in d e r s t r e s s -s t r a i n r e s u l t s .................................................. 2 6 5

F ig u r e B -3 : J o i n t s u b a s s e m b ly a p p l i e d b e a m f o r c e vs. d i s p l a c e m e n t - T e s t s 1 & 2 ...........................2 6 6

F ig u r e B -4 : J o in t s u b a s s e m b l y n o r m a l iz e d j o i n t s h e a r s t r e s s vs. b e a m d is p l a c e m e n t (p s i u n its)

- T e s t s 1 & 2 ......................................................................................................................................................................................2 6 6

F ig u r e B -5 : J o i n t s u b a s s e m b l y f a il u r e p i c t u r e - T e s t 2 ........................................................................................ 2 6 7

F ig u r e C - l: S h a k in g t a b l e i n p u t v s . o u t p u t m o t io n a c c e l e r a t io n r e s p o n s e s p e c t r a ........................ 2 6 8

F ig u r e C -2: F il t e r e d v s . n o n - f il t e r e d F T p l o t s f o r v e r t ic a l a c c e l e r o m e t e r a t J o in t A 1 -

H a l f -Y ie l d Te s t ..............................................................................................................................................................................2 7 0

F ig u r e C -3: Ra t i o o f f il t e r e d t o n o n -f il t e r e d F T f o r h o r iz o n t a l a c c e l e r o m e t e r a t J o i n t D 1 -

H a l f -Y ie l d Te s t ............................................................................................................................................................................. 271

F ig u r e C -4: F il t e r e d v s . n o n -f il t e r e d F T p l o t s f o r h o r iz o n t a l a c c e l e r o m e t e r s a t J o in t s D ] ,

D 2 , a n d D 3 - H a l f -Y ie l d Te s t ................................................................................................................................................2 7 2

F ig u r e C -5: T y p ic a l h o r iz o n t a l a c c e l e r a t io n r e s p o n s e f il t e r in g a r o u n d t h e f i r s t t h r e e

MODES. A ) F T PLOT ILLUSTRATING THE FREQUENCY FILTERING AROUND THE FIRST THREE MODES, B ) THE

CORRESPONDING HISTORY PLOTS OF THE FILTERED RESPONSE FOR ALL THREE MODES - (JOINT B 2 , F IRST

F l o o r E l a s t ic S n a p -B a c k T e st ) ............................................................................................................................................2 7 7

F ig u r e C -6: S n a p -b a c k s e t u p a t t h ir d f l o o r ..................................................................................................................2 7 9

F ig u r e C -7: F o u r ie r t r a n s f o r m p l o t s f o r t h e e l a s t ic s n a p -b a c k t e s t s - A c c e l e r o m e t e r s .......... 2 8 0

F ig u r e C -8: F i r s t f l o o r s n a p -b a c k : t y p ic a l d is p l a c e m e n t h is t o r ie s o f a l l t h r e e f l o o r s ............. 281

F ig u r e C - 9 : Th ir d F l o o r s n a p -b a c k : t y p ic a l d is p l a c e m e n t h is t o r ie s o f a l l t h r e e f l o o r s 281

xix


F ig u r e C -10: T y p ic a l t r a n s f e r f u n c t io n (a c c e l e r o m e t e r a t J o in t A l ) ...........................................................2 8 4

F ig u r e C - l l : D i s p l a c e m e n t h is t o r ie s o f a l l f l o o r s a t c o l u m n a x is A - F i r s t 1 k i p s n a p - b a c k t e s t

a f t e r D y n a m ic T e s t 1 ................................................................................................................................................................. 2 8 6

F ig u r e C -1 2 : F r a m e in it ia l g r a v it y -l o a d -s t a t e - B e a m b e n d in g m o m e n t d i a g r a m s ...............................2 8 9

F ig u r e C - 13: F r a m e in it ia l g r a v it y -l o a d -s t a t e - B e a m s h e a r f o r c e d ia g r a m s ..........................................2 8 9

F ig u r e C -14: F r a m e in it ia l g r a v it y -l o a d -s t a t e - C o l u m n b e n d in g m o m e n t d ia g r a m s ......................... 2 9 0

F ig u r e C -15: F r a m e in it ia l g r a v it y -l o a d -s t a t e - C o l u m n s h e a r f o r c e d i a g r a m s ...................................2 9 0

F ig u r e C - 16: F r a m e in it ia l g r a v it y -l o a d -s t a t e - F r a m e d e f o r m e d s h a p e ................................................... 291

F ig u r e C - 17: T y p ic a l f i r s t s t o r y c o l u m n s c h e m a t ic f o r c e s a n d s i g n c o n v e n t i o n s ............................... 2 9 3

F ig u r e C -1 8: J o in t d is p l a c e m e n t t r ia n g u l a t io n s u b - s y s t e m s ..............................................................................2 9 6

F ig u r e C -1 9 : O f f -T a b l e t r ia n g u l a t io n a d j u s t m e n t s ..................................................................................................3 0 0

F ig u r e C -20: C o l u m n r o t a t io n s ................................................................................................................................................ 3 0 2

F ig u r e C -21: B a s e s h e a r c o m p a r is o n b e t w e e n l o a d c e l l s a n d a c c e l e r o m e t e r s - T y p ic a l e l a s t ic

s n a p -b a c k , H a l f -Y ie l d Te s t , t y p ic a l d a m a g e d -s t a t e s n a p -b a c k t e s t a n d D y n a m ic Te s t 2 .............3 0 4

F ig u r e C -22: O v e r t u r n in g m o m e n t a b o u t c e n t e r l in e o f f r a m e : c o m p a r is o n b e t w e e n lo a d c e l l s

a n d a c c e l e r o m e t e r s - T y p ic a l e l a s t ic s n a p -b a c k t e s t ........................................................................................305

F ig u r e C -23: O v e r t u r n in g m o m e n t a b o u t c e n t e r l in e o f f r a m e : c o m p a r is o n b e t w e e n l o a d c e l l s

a n d a c c e l e r o m e t e r s - D y n a m ic Te s t I ........................................................................................................................... 3 0 6

F ig u r e C -24: O v e r t u r n in g m o m e n t a b o u t c e n t e r l in e o f f r a m e : c o m p a r is o n b e t w e e n l o a d c e l l s

a n d a c c e l e r o m e t e r s - D y n a m ic Te s t 2 ........................................................................................................................... 3 0 6

F ig u r e C -25: L e a d w e ig h t h o r iz o n t a l a c c e l e r a t io n s , v s . f r a m e a c c e l e r a t io n s - D y n a m ic Te s t 2 .

.........................................................................................................................................................................................30 7

F ig u r e C -26: L e a d w e ig h t h o r iz o n t a l a c c e l e r a t io n s , vs . f r a m e a c c e l e r a t i o n s - D y n a m ic Te s t 3 .

.........................................................................................................................................................................................3 0 8

F ig u r e C -27: F i r s t f l o o r h o r iz o n t a l d r i f t h is t o r y c o m p a r is o n b e t w e e n o n - t a b l e a n d o f f - t a b l e

in s t r u m e n t m e a s u r e m e n t s - H a l f - Yie l d Te s t ............................................................................................................ 3 1 0

F ig u r e C -2 8 : Th ir d f l o o r h o r iz o n t a l d r i f t h is t o r y c o m p a r is o n b e t w e e n o n - t a b l e a n d o f f - t a b l e

in s t r u m e n t m e a s u r e m e n t s - H a l f - Y ie l d T e s t ............................................................................................................ 3 1 0

XX


F ig u r e C -29: F i r s t f l o o r h o r iz o n t a l d r i f t h is t o r y c o m p a r is o n b e t w e e n o n - t a b l e a n d o f f - t a b l e

in s t r u m e n t m e a s u r e m e n t s - D y n a m ic Te s t I ...............................................................................................................311

F ig u r e C -30: Th ir d f l o o r h o r iz o n t a l d r if t h i s t o r y c o m p a r is o n b e t w e e n o n - t a b l e a n d o f f - t a b l e

INSTRUMENTMEASUREMENTS - DYNAMIC TEST 1 ...............................................................................................................311

F ig u r e C -3 1: J o in t A 3 o u t - o f -p l a n e h o r iz o n t a l d r i f t r a t io - D y n a m ic Te s t s 1 ,2 , a n d 3 ...................313

F ig u r e C -32: C o l u m n A 1 l o n g it u d in a l b a r s t r a in s vs. m o m e n t s - H a l f -Y ie l d T e s t ................................3 1 4

F ig u r e C -33: C o l u m n B 1 l o n g it u d in a l b a r s t r a in s vs. m o m e n t s - H a l f -Y i e l d Te s t ............................... 3 1 5

F ig u r e C -34: C o l u m n s A 1 & A 2 l o n g it u d in a l b a r s t r a in h is t o r ie s - H a l f -Y ie l d Te s t ..........................3 1 6

F ig u r e C -3 5: C o l u m n s B I & B 2 l o n g it u d in a l b a r s t r a in h is t o r ie s - H a l f - Y ie l d Te s t ..........................3 1 7

F ig u r e C -3 6: B e a m A B I l o n g it u d in a l b a r s t r a i n h i s t o r i e s - H a l f -Y ie l d Te s t ........................................... 3 1 8

F ig u r e C -37: B e a m A B I l o n g it u d in a l b a r s t r a i n vs. f i r s t s t o r y d r i f t r a t i o - H a l f -Y ie l d Te s t . 3 1 9

F ig u r e C -38: C o l u m n A 1 l o n g it u d in a l b a r s t r a in s vs . m o m e n t s - D y n a m ic T e s t 1 .................................. 3 2 0

F ig u r e C -39: C o l u m n B 1 l o n g it u d in a l b a r s t r a in s v s . m o m e n t s - D y n a m ic Te s t I .................................. 3 2 0

F ig u r e C -40: C o l u m n s A 1 & A 2 l o n g it u d in a l b a r s t r a in h is t o r ie s - D y n a m ic Te s t 1 .............................321

F ig u r e C -4 1 : C o l u m n s B 1 & B 2 l o n g it u d in a l b a r s t r a i n h i s t o r ie s - D y n a m ic Te s t 1 .............................3 2 2

F ig u r e C -42: B e a m A B I l o n g it u d in a l b a r s t r a in h is t o r ie s - D y n a m ic T e s t I ..............................................323

F ig u r e C -43: B e a m A B I l o n g it u d in a l b a r s t r a i n v s . f i s t s t o r y d r i f t r a t i o - D y n a m ic T e s t I 323

F ig u r e D - l : D u c t il e a n d n o n -d u c t il e c o l u m n m o m e n t c u r v a t u r e a n a l y s e s ...........................................3 2 7

F ig u r e E - l: C o l u m n A 1 B a s e - P o s t H a l f -Y ie l d T e s t ...............................................................................................3 3 2

F ig u r e E -2: C o l u m n A 1 B a s e , w id e v i e w - P o s t D y n a m ic T e s t I ........................................................................333

F ig u r e E -3: C o l u m n A 1 B a s e , w id e v ie w - P o s t D y n a m ic Te s t 2 ........................................................................3 3 4

F ig u r e E -4: C o l u m n A 1 B a s e , S o u t h d e t a i l - P o s t D y n a m ic Te s t 2 ................................................................335

F ig u r e E -5: C o l u m n A 1 B a s e , N o r t h d e t a i l - P o s t D y n a m ic Te s t 2 ................................................................335

F ig u r e E - 6 : C o l u m n A 1 B a s e , w id e v i e w - P o s t D y n a m ic Te s t 3 ........................................................................3 3 6

F ig u r e E -7: J o i n t A 1 - P o s t H a l f -Y ie l d Te s t ................................................................................................................3 3 7

F ig u r e E -8: J o in t A 1 - P o s t D y n a m ic Te s t 1 ...................................................................................................................337

F ig u r e E -9: J o i n t A 1 - P o s t D y n a m ic T e s t 2 ...................................................................................................................3 3 8

F ig u r e E -10: J o in t A 2 - P o s t H a l f -Y ie l d Te s t ................................................................................................................ 3 3 8

xxi


F ig u r e E - l 1: J o in t A 2 - P o s t D y n a m ic T e s t I ................................................................................................................... 3 3 9

F ig u r e E -12: J o in t A 2 - P o s t D y n a m ic Te s t 2 ................................................................................................................... 3 3 9

F ig u r e E - 13: J o in t A 2 - P o s t D y n a m ic T e s t 3 ................................................................................................................... 3 4 0

F ig u r e E -14: J o in t A 3 - P o s t H a l f -Y ie l d Te s t ................................................................................................................ 3 4 0

F ig u r e E -15: J o in t A 3 - P o s t D y n a m ic T e s t I ................................................................................................................... 341

F ig u r e E -16: J o in t A 3 - P o s t D y n a m ic T e s t 3 ................................................................................................................... 341

F ig u r e E -17: C o l u m n B 1 B a s e - P o s t H a l f -Y ie l d Te s t ............................................................................................... 3 4 2

F ig u r e E - 1 8 : C o l u m n B I B a s e , w id e v ie w - P o s t D y n a m ic T e s t 1 ........................................................................3 4 2

F ig u r e E -1 9 : C o l u m n B I B a s e - P o s t D y n a m ic T e s t 2 .................................................................................................343

F ig u r e E -2 0 : C o l u m n B I B a s e - P o s t D y n a m ic Te s t 3 .................................................................................................343

F ig u r e E - 2 1: J o i n t B 1 - P o s t H a l f -Y i e l d Te s t .................................................................................................................3 4 4

F ig u r e E -22: J o i n t B 1 - P o s t D y n a m ic Te s t 1 ................................................................................................................... 3 4 4

F ig u r e E -23: J o i n t B 1 - P o s t D y n a m ic T e s t 2 ................................................................................................................... 345

F ig u r e E -24: J o in t B 1 - P o s t D y n a m ic Te s t 3 ................................................................................................................... 345

F ig u r e E -25: J o in t B 2 - P o s t H a l f -Y i e l d Te s t .................................................................................................................3 4 6

F ig u r e E -26: J o i n t B 2 - P o s t D y n a m ic T e s t 1 ................................................................................................................... 3 4 6

F ig u r e E -27: J o in t B 2 - P o s t D y n a m ic T e s t 3 ................................................................................................................... 3 4 7

F ig u r e E -28: J o in t B 3 - P o s t H a l f -Y i e l d Te s t .................................................................................................................3 4 7

F ig u r e E -29: J o in t B 3 - P o s t D y n a m ic T e s t 1 ................................................................................................................... 3 4 8

F ig u r e E -30: J o in t B 3 - P o s t D y n a m ic Te s t 3 ................................................................................................................... 348

F ig u r e E - 3 1: C o l u m n C l B a s e - P o s t H a l f -Y ie l d Te s t .............................................................................................3 4 9

F ig u r e E -32: C o l u m n C l B a s e - P o s t D y n a m ic T e s t 1 ............................................................................................... 3 4 9

F ig u r e E -33: C o l u m n C l B a s e - P o s t D y n a m ic Te s t 2 ................................................................................................3 5 0

F ig u r e E -34: C o l u m n C l B a s e - P o s t D y n a m ic Te s t 3 ................................................................................................3 5 0

F ig u r e E -35: J o i n t C l - P o s t H a l f -Y ie l d Te s t .................................................................................................................351

F ig u r e E -36: J o in t C l - P o s t D y n a m ic Te s t 1 ....................................................................................................................351

F ig u r e E -37: J o i n t C I - P o s t D y n a m ic Te s t 3 ................................................................................................................... 3 5 2

F ig u r e E - 3 8 : J o in t C 2 - P o s t H a l f -Y ie l d Te s t .................................................................................................................352

xxii


F ig u r e E -39: J o in t C 2 - P o s t D y n a m ic Te s t I ................................................................................................................... 353

F ig u r e E -40: J o in t C 2 - P o s t D y n a m ic Te s t 3 ................................................................................................................... 353

F ig u r e E -4 1 : J o in t C 3 - P o s t H a l f -Y i e l d T e s t ................................................................................................................ 3 5 4

F ig u r e E -42: J o in t C 3 - P o s t D y n a m ic Te s t 1 ................................................................................................................... 3 5 4

F ig u r e E -43: J o in t C 3 - P o s t D y n a m ic Te s t 3 ................................................................................................................... 355

F ig u r e E - 4 4 : J o i n t C 3, t o p v ie w - P o s t D y n a m ic T e s t 3 ............................................................................................355

F ig u r e E -45: C o l u m n D l B a s e - P o s t H a l f -Y ie l d Te s t ..............................................................................................3 5 6

F ig u r e E -46: C o l u m n D l B a s e - P o s t D y n a m ic Te s t I .................................................................................................3 5 6

F ig u r e E -47: C o l u m n D l B a s e - P o s t D y n a m ic T e s t 2 .................................................................................................3 5 7

F ig u r e E -48: C o l u m n D l B a s e , b a r f r a c t u r e - P o s t D y n a m ic T e s t 3 ................................................................3 5 7

F ig u r e E -49: J o in t D l - P o s t H a l f -Y ie l d Te s t ................................................................................................................ 3 5 8

F ig u r e E -50: J o i n t D I - P o s t D y n a m ic Te s t I ..................................................................................................................3 5 8

F ig u r e E -5 1: J o in t D l - P o s t D y n a m ic Te s t 3 ..................................................................................................................3 5 9

F ig u r e E -5 2 : J o in t D 2 - P o s t H a l f -Y ie l d Te s t ................................................................................................................ 3 5 9

F ig u r e E -5 3 : J o in t D 2 - P o s t D y n a m ic Te s t 1 ..................................................................................................................3 6 0

F ig u r e E -54: J o in t D 2 - P o s t D y n a m ic Te s t 3 ..................................................................................................................3 6 0

F ig u r e E -55: J o in t D 3 - P o s t H a l f -Y ie l d T e s t . ............................................................................................................... 361

F ig u r e E -5 6: J o in t D 3 - P o s t D y n a m ic Te s t 1 ..................................................................................................................361

F ig u r e E -57: J o in t D 3 - P o s t D y n a m ic Te s t 3 ..................................................................................................................362

xxiii


List of Tables

T a b l e 3 -1 : F r a m e e l e m e n t f l e x u r a l a n d s h e a r s t r e n g t h s ...................................................................................36

T a b l e 3 -2 : Jo in t s h e a r r e s is t a n c e v e r s u s m a x im u m p r o b a b l e a p p l ie d s h e a r s t r e s s f a c t o r s .3 7

T a b l e 3 -3 : St r o n g m o t io n r e c o r d s .......................................................................................................................................... 45

T a b l e 3 -4 : Su m m a r y t a b l e o f f ir s t - s t o r y m a x im u m d r if t r a t io s a n d g r o u n d m o t io n

in t e n s it y m e a s u r e s ...................................................................................................................................................................... 4 7

T a b l e 4 -1 : T e s t in g p r o t o c o l .........................................................................................................................................................6 3

T a b l e 5 -1 : Su m m a r y o f f r a m e m o d a l p r o p e r t ie s ..........................................................................................................67

T a b l e 5 -2 : C o l u m n B I s h e a r f a il u r e p h o t o g r a p h d e s c r ip t io n s - D y n a m i c T e s t 1 ..............................97

T a b l e 5 -3 : C o l u m n s A 1 & B 1 s t a t e s a t in it ia t io n o f C o l u m n B 1 s h e a r f a il u r e .................................. 105

T a b l e 5 -4 : C o l u m n A 1 s h e a r f a il u r e p h o t o g r a p h d e s c r ip t io n s - D y n a m ic T e s t 2 ..........................122

T a b l e 5 -5 : C o l u m n A 1 s t a t e a t in it ia t io n o f s h e a r f a il u r e (D y n a m ic T e s t 2 ) a n d C o l u m n B 1

s t a t e a t in it ia t io n o f s h e a r f a il u r e (D y n a m ic T e s t 1 ) ...................................................................................130

T a b l e 5 -6 : C o l u m n s A 1 s t a t e a t in it ia t io n o f its a x ia l f a il u r e - D y n a m ic T e s t 3 ............................... 146

T a b l e 6 -1 : A n a l y t ic a l v s . e x p e r im e n t a l f r a m e d y n a m ic p r o p e r t ie s - H a l f -Y ie l d T e s t ........... 158

T a b l e 7 -1 : C o l u m n d a t a b a s e p r o p e r t ie s ...........................................................................................................................185

T a b l e 7 -2 : C o l u m n d a t a b a s e e x t r a c t e d r e s p o n s e v a l u e s ..................................................................................187

T a b l e 7 -3 : C o l u m n d a t a b a s e a n a l y t ic a l r o t a t io n v a l u e s ...............................................................................193

T a b l e 7 -4 : C o l u m n -r o t a t io n r o b u s t r e g r e s s io n p a r a m e t e r s .......................................................................... 2 0 3

T a b l e 7 -5 : C o l u m n d r if t s a n d s h e a r d e f o r m a t io n s a t r e s id u a l s h e a r s t r e n g t h ............................ 2 0 7

T a b l e A - l : C o n c r e t e m ix d e s i g n ........................................................................................................................................ 231

T a b l e A -2 : C o n c r e t e c o m p r e s s iv e s t r e n g t h h i s t o r y .........................................................................................2 3 2

T a b l e A - 3 : C o n c r e t e sp l it t in g t e s t r e s u l t s ............................................................................................................. 233

T a b l e A -4 : C o n c r e t e m e a s u r e d m e a n m a t e r ia l p r o p e r t ie s ...........................................................................2 3 3

T a b l e A -5 : R e in f o r c in g s t e e l m e a n m e a s u r e d m a t e r ia l p r o p e r t ie s .......................................................2 3 6

T a b l e A -6 : F r a m e c o m p o n e n t w e ig h t s .......................................................................................................................... 2 4 0

xxiv


T a b l e A -7 : F r a m e g r o u p w e ig h t s ......................................................................................................................................2 4 0

T a b l e A -8 : In s t r u m e n t a t io n l i s t ......................................................................................................................................2 4 4

T a b l e A -9 : C o l u m n a n d jo in t in s t r u m e n t c o o r d in a t e s .................................................................................. 2 6 0

T a b l e C - l : D y n a m ic m o d a l p r o p e r t y e x t r a c t io n o v e r v i e w .......................................................................2 7 4

T a b l e C -2 : F r a m e m o d a l p r o p e r t ie s - in it ia l “u n d a m a g e d ” s t a t e s n a p -b a c k t e s t s .................2 8 2

T a b l e C -3 : F r a m e m o d a l pr o p e r t ie s - f r e e -v ib r a t io n p o s t H a l f -Y ie l d T e s t ................................. 2 8 3

T a b l e C -4 : F r a m e m o d a l p r o p e r t ie s - w h it e -n o is e t e s t .................................................................................. 2 8 4

T a b l e C -5 : F r a m e m o d a l p r o p e r t ie s - f r e e -v ib r a t io n p o s t D y n a m ic T e s t 1 ....................................2 8 5

T a b l e C -6 : F r a m e m o d a l p r o p e r t ie s - d a m a g e d - st a t e s n a p - b a c k t e s t s ............................................2 8 6

T a b l e C -7 : F r a m e m o d a l p r o p e r t ie s - f r e e -v ib r a t io n p o s t D y n a m ic T e s t 2 ....................................2 8 7

T a b l e C -8 : S u m m a r y o f in it ia l g r a v it y -l o a d -s t a t e f o r c e s a n d d e f o r m a t i o n s .......................... 2 8 8

T a b l e D - l : U n i- a x ia l m a t e r ia l m o d e l s ........................................................................................................................ 325

T a b l e D -2 : L im itS t a t e m a t e r ia l s - in p u t p a r a m e t e r s ...................................................................................... 3 2 8

T a b l e D - 3 : S h e a r L im it C u r v e (f r o m E l w o o d ( 2 0 0 2 ) ) ........................................................................................3 2 9

T a b l e D -4 : A x ia l L im it C u r v e (f r o m E l w o o d (2 0 0 2 ) ) .........................................................................................3 3 0

T a b l e D -5 : T r i- l in e a r h y s t e r e t ic m a t e r ia l f o r s h e a r a n d a x ia l s p r in g s (f r o m E l w o o d

(2 0 0 2 )) 331

xxv


1 Introduction

1.1 Motivation

In areas o f high seismicity around the world, including the west coast o f the United

States, a major risk to life safety lies in the collapse vulnerability o f older reinforced

concrete structures built prior to the advent o f more effective seismic design codes in the

1970s. The large number o f these older structures coupled with the overwhelming

proportion o f them that would require retrofit i f assessed according to current practices is

hindering region-wide mitigation efforts.

Seemingly in direct contradiction with region-wide seismic collapse forecasts based

on current codes o f practice, post earthquake reconnaissance studies show a relatively

low rate o f collapse amongst older non-seismically detailed concrete structures even in

major earthquakes [Otani (1999)]. This observation suggests that current practices for

assessing collapse are overconservative, and that more refined engineering tools might be

useful to identify the small portion o f buildings that are most collapse prone so that

resources can be focused on the seismic mitigation o f only those most critical buildings.

Through better understanding o f mechanisms that cause collapse, improved

engineering tools for use by practicing engineers may be developed to better assess the

collapse vulnerability o f non-seismically detailed reinforced concrete frame structures.

This has been the aim o f several recent studies and continues to be a high priority for

improving seismic safety worldwide.

1


1.2 Objectives and Scope

The broad objective o f this study is to investigate, both experimentally and

analytically, the seismic collapse behavior o f non-seismically detailed reinforced concrete

frames. Collapse is defined in this study as the loss o f axial load carrying capacity o f one

or more elements leading to partial or complete vertical subsiding o f a structure.

Particularly, this study is aimed at investigating structural framing effects on column

shear and axial failures and conversely the effects o f localized column failures on frame-

system collapse vulnerability. As failure o f one or more columns in a frame system does

not necessarily constitute the collapse o f that structure, understanding these interactions is

essential in assessing the collapse vulnerability o f this type o f structure.

To date, there have been relatively few tests on lightly confined reinforced concrete

frame systems in the literature In an attempt to fill some o f this gap, a main component o f

this study involved building and dynamically testing to collapse a 2D, three-bay, three-

story, third-scale reinforced concrete frame. This frame contained non-seismically

detailed columns whose proportions and reinforcement details allow them to yield in

flexure prior to initiating shear strength degradation and ultimately reaching axial

collapse (these columns are hereafter referred to as flexure-shear-critical columns). The

interest in this class o f column stems not only from their ability to withstand moderate to

large deformations prior to axial collapse [Moehle et al. (2000)] but from the fact that

current codes o f practice and design guidelines under-estimate their deformation

capabilities, often leading to overly conservative predictions o f structural collapse. The

scope o f this study does not encompass bi-directional column loading, joint failures, or

2


lap-splice failures, but focuses on shear failure leading to loss o f axial carrying capacity

o f flexure-shear critical columns due to uni-directional seismic loading.

The analytical emphasis o f this study is on assessing and improving the accuracy o f

beam-column element formulations for modeling frame-system and frame-element force-

deformation relations. Analytical formulations are evaluated in terms o f matching test

frame results, obtained from the experimental portion o f this study, over the full range o f

frame deformations. The investigated range o f deformations covered concrete flexural

cracking, flexural yielding, and shear and axial degradation in flexure-shear-critical

column elements. Particular attention is given to attain fiber-section element formulations

that reasonably accurately reproduce beam-column behavior not only at the global

element level but also at the local plastic hinge level. Improvements are proposed for

modeling longitudinal-bar anchorage slip, a mechanism that results in frame element

rigid-body rotations and increased flexibility relative to models that consider only flexure

and shear.

This study also aims to improve modeling capabilities o f recently developed shear

and axial failure analytical elements, labeled LimitState elements [Elwood (2002)]. These

elements in their current formulation are capable o f modeling flexure-shear-critical

column behavior up to complete collapse. Deficiencies in these elements are discussed

based on test frame experimental data and a new shear failure model for flexure-shear-

critical columns is proposed. This model relates shear failure to local deformations and

stresses within element critical sections, in contrast with existing models based on global

deformation or lateral drift [Pujol et al. (1999), Kato and Ohnishi (2002), Elwood and

3


Moehle (2005)]. It is anticipated that a model based on local deformations may be more

accurate and may be more suitable for implementation in available software.

1.3 Organization

Chapter 2 presents a review o f previous research relevant to this study. Experimental

investigations conducted on flexure-shear-critical columns are presented along with

various analytical approaches used to model shear and axial failure in this type o f

column. A brief summary on behavior and modeling o f beam-column joints is also

presented. Analytical representations o f bar-slip induced frame-element rotations are also

discussed. Finally, an overview o f past experimental studies on non-seismically detailed

reinforced concrete frames is presented with emphasis on column behavior.

Chapter 3 presents the design process that produced the final test frame dimensions

and details. An analytical model that was developed to design the test frame is described.

Test frame final dimensions and details are given and an analytical case study aimed at

estimating the collapse vulnerability o f this type o f frame structure to a near-fault

earthquake scenario is presented.

Chapter 4 describes the construction process, test setup, loading, and instrumentation

o f the test frame. This chapter also describes the ground motion record from the 1985

Chile earthquake that was used as the input table motion at various scaling factors for the

various dynamic tests imposed on the test frame.

Chapter 5 presents and discusses experimental results obtained from the main

dynamic tests that were imposed on the test frame up to initiation o f partial collapse.

Recorded response values for the test frame included first-story column forces and

4


deformations, relative in-plane motion o f all frame joints, in-plane accelerations o f key

joints in the frame, and longitudinal bar strains in select flexure-shear critical columns.

Chapter 6 introduces a revised analytical model o f the test frame that is based on

non-linear fiber-section beam-column elements, improved fiber-section representation o f

bar-slip induced rotations, and rigid joints. Analytical results are compared with

experimental ones for various dynamic tests. Deficiencies in LimitState shear and axial

failure models are discussed.

Chapter 7 introduces a new shear failure model that determines column rotations at

which shear strength degradation (or shear failure) in flexure-shear critical columns is

initiated. A database o f 56 column tests is used in a parametric regression analysis to

determine factors that most significantly affect the rotation capacity o f this type o f

column. Factors affecting the rate o f shear strength degradation are also investigated.

Chapter 8 presents conclusions and provides recommendations for future work.

5


2 Literature Review

Surveys o f past collapses o f lightly reinforced concrete frames reveal that it is

usually the failure o f columns and joints that cause collapse [Otani (1999)]. This chapter

provides a summary o f past experimental work on these components as well as on

complete frame systems, and looks into current approaches for modeling their behavior.

2.1 Columns

Lightly confined reinforced concrete columns can be subdivided into two main

categories: shear-critical and flexure-shear-critical columns. A shear-critical column is

one that fails in shear before yielding in flexure. This type o f column has a brittle mode

o f failure when loaded past the column shear strength. A flexure-shear-critical column is

one that fails in shear after yielding in flexure. This type o f column is the subject o f this

research and will be discussed in more depth in the following section.

2.1.1 Flexure-shear critical Columns - Shear Behavior

Flexure-shear critical columns, which are typically more slender columns, have

higher shear strength than flexural strength, which allows them to yield in flexure prior to

shear failure. Shear failure in these columns will only occur after the plastic hinge region

deteriorates sufficiently, resulting in degradation in shear strength. Several models for

shear strength have been proposed [Watanabe and Ichinose (1992); Aschheim and

Moehle (1992); Priestley et al. (1994); Sezen (2002)] to model this shear degradation

with respect to increasing deformation demands. While these adequately model shear

strength as function o f drift demand, they produce poor results when used in reverse to

6


estimate deformation capacity given a shear force demand. This behavior can be

explained by observing that the relationship between shear resistance and drift demand

has a relatively shallow slope (Figure 2-1), such that any small change in shear or flexural

strength could result in a large change in calculated drift.

m = 3 /40

0.7H-<T

Figure 2-1: Improper use o f strength model to estimate displacements [fromSezen (2002)] (V=shear resistance o f column section, Vc=concrete contribution to shear strength, Vs=transverse reinforcement contribution to shear strength, gd=column drift, A ft change in drift at failure, /u=mean response,, o=standard deviation, m= slope)

Given the aforementioned limitation, several displacement-based models have been

developed to estimate deformation capacity o f flexure-shear-critical columns given a

shear force demand [Pujol et al. (1999); Kato and Ohnishi (2002); Elwood and Moehle

(2005b); Mostafaei and Kabeyasawa (2007)]. Pujol et al. (1999) proposed a lower-bound

empirical estimate o f the drift at shear failure based on a database o f 92 columns. Pujol et

al. (1999) observed that the maximum drift ratio (AMax/L, AMAx=column drift at shear

failure, L=column length) tended to increase with increasing aspect ratio (a/d, a=column

half-span, d=column section depth from center o f tension reinforcement to extreme

compression fiber) and increasing transverse reinforcement index (r*fy/vMAx,

7


r=transverse reinforcement ratio, fy=yield stress o f transverse reinforcement,

VMAx=column shear stress at shear failure). The proposed equation is:

*MAX 100 =rf y

\ V MAX J

(2- 1)

This equation shows a large scatter between observed and calculated values

indicating that a more refined relation taking into account more parameters might provide

a better estimate. Also, this equation provides a lower-bound estimate o f drift capacity,

making it less useful within a performance-based engineering framework that requires a

mean estimate prediction.

Kato and Ohnishi (2002) proposed an approach whereby the plastic drift capacity

can be estimated based on the maximum edge strain in the core concrete, the axial load

ratio, and the cross section dimensions. The total drift ratio is defined by summing the

drift ratio at yield o f longitudinal reinforcement (Ay/L) and the calculated plastic drift

ratio (Ap/L):

L L L

(2-2)

A„Where , =

L

Dms,.cp

3e_

D

V J e J

ms V If /AAcp 2/3/V. Je JK / V

(2-3)

where D is the depth o f the gross cross section, j e is the depth o f the core, £cp is the strain

at the maximum stress for the core, m is the ratio o f the concrete strain at the edge o f the

core concrete to scp at shear or axial failure (determined empirically for shear (m=2.3)

and axial (m=3.6) failures), and en is an equivalent axial load ratio as defined in Figure

2 - 2 .

8


Maximum axial load ratio tj p

Figure 2-2: Equivalent axial load ratio from Kato and Ohnishi (2002)( y=min. axial load/max. axial load; t]p=max. axial load/A f ’)

While this model generates a reasonably accurate estimate o f the drift at shear

failure, it relies on obtaining an accurate estimate o f the yield drift which might be

difficult in design and analysis applications [Elwood and Eberhard (2006)]

Elwood and Moehle (2005b) proposed an empirical, regression-based, shear-drift

model that utilized a database o f 50 columns focusing only on flexure-shear critical,

lightly-confined concrete columns. This model is based on observations that the drift

ratio at shear failure (As/L) is positively correlated with transverse reinforcement ratio p”

and negatively correlated with shear stress ratio (u/Vfc’) and axial load ratio (P/Agfc’).

The proposed equation is:

Figure 2-3 compares drifts at shear failure from database columns with those

calculated using Equation (2-4) and shows an adequate fit with moderate variability

between the two. This model is based on column pseudo-static cyclic tests, in most cases

(psi units)(2-4)

9


with constant axial loads. As well, all column tests in this database have almost fixed-

fixed end conditions, which is generally not the case for frame structures.

0.06

0.05

° 0.03

m£ 0.02 w TJ v/

0.01

0.01 0.02 0.03 0.04 0.0S 0.06 drift ratio m easu red

V 0.0 > p"> 0.00 (10 0.001 J > p r> 0.0020A 0.0020 > p"> 0.00400 0.0040 > p*> 0.0055Q 0.0055 > p”> 0.0070

Figure 2-3: Elwood and Moehle (2005b) shear-drift model comparison

2.1.2 Flexure-shear critical Columns - Axial Behavior

Previous experimental work on collapse o f lightly confined reinforced concrete

columns has shown that loss o f axial load capacity does not necessarily follow

immediately after loss o f lateral load capacity [Lynn (2001); Sezen (2002); Elwood

(2002)]. These results suggest that the drift at which axial failure occurs is mainly

dependent on the axial stress and the amount and spacing o f transverse reinforcement.

Other tests have illustrated that axial failure occurred when the shear resistance had

degraded to approximately zero and that the drift at axial failure decreased with

increasing axial stress [Yoshimura and Yamanaka (2000); Yoshimura and Nakamura

(2002)]. Tasai (2000) reports results from five pseudo-dynamic tests in which shear

damaged columns were returned to a plumb vertical position and loaded axially until

vertical collapse. From these experiments, Tasai (2000) observed that the residual axial

10


capacity decreased with increasing maximum lateral drift demand and with increasing

shear degradation. It was also noted from these tests that the deterioration o f residual

axial capacity with increasing lateral drifts was related to the deterioration o f a concrete

compressive strut within the shear-damaged zone.

Few axial-drift failure models [Elwood and Moehle (2005a); Mostafaei and

Kabeyasawa (2007)] have been presented to date for flexure-shear type columns. The

model o f interest was developed by Elwood and Moehle (2005a) and is based on the

shear-friction model [Mattock and Hawkins (1972)] calibrated to test data from the

previously mentioned 50-column database. From the database, Elwood and Moehle

(2005a) observed that contribution o f longitudinal reinforcement to axial capacity was

minimal. Thus the shear-friction equations were modified to only account for transverse

reinforcement ratio and axial load. The relation for the drift ratio at axial failure is

presented as follows:

A _ _4 1 + tan2 0 (2-5)L ~ 100

tan 6 + PV A J y , d c t a n ^

where 0 is the angle o f the shear failure surface from horizontal and is assumed to be 65°,

P is the axial load, Ast is the transverse reinforcement area at spacing 5 and with yield

strength fyt, and dc is the depth o f the column core between centerlines o f the ties.

One should note that this axial-drift model was calibrated to a relatively small

number o f column tests, all o f which were conducted pseudo statically.

2.1.3 Analytical Implementation of Shear and Axial Failure Models

Elwood (2002) provides an overview o f analytical models that allow the simulation

o f flexure-shear-critical column behavior. O f interest in the work presented here are the

11


LimitState models that were developed by Elwood (2002) and implemented in

OpenSEES [McKenna et al. (2000)], which allow the complete simulation o f flexure-

shear-critical column behavior to collapse.

The implementation o f shear and axial failures was done through the addition o f

zero-length LimitState spring elements at the ends o f line column elements (as illustrated

in Figure 2-4). These elements have differing backbone curves before and after failures

are detected by the drift capacity Equations (2-4) and (2-5). Prior to shear failure, the

shear springs are linear-elastic with stiffness corresponding to the equivalent elastic shear

stiffness o f the column. Once the column element reaches the limit curve defined by the

empirical shear-drift relation [Equation (2-4)] the shear spring backbone curve is

modified to a degrading hysteretic curve (Figure 2-5). The shear degrading slope K jeg is

calibrated based on observations from previous tests [Yoshimura and Nakamura (2002)],

which have shown that axial failure is initiated when shear strength degrades to about

zero. Thus the shear degrading slope is set to achieve the residual shear strength at the

projected axial failure drift as defined by Equation (2-5).

L im it S ta te i= -> u n ia x ia l m a ter ia l 1 w ith a x ia l l im it c u r v e

khor<

Figure 2-4: Zero-length LimitState spring elements [Elwood (2002)]

12


Similarly, the zero-length axial springs have a “rigid” backbone prior to reaching the

axial load-drift limit curve [Equation (2-5)] (illustrated in Figure 2-5). It is important to

note here that this limit curve can only be defined after shear failure as it relies on the

shear friction model, which assumes a shear slip surface. Once the column element

reaches that drift limit curve its axial-load to vertical-deformation backbone is modified

to a degrading material model. Because the shear-friction model only describes

compression failures, the backbone is only redefined for compressive axial loads. Beyond

the initiation o f axial failure, a coupling effect exists between the horizontal and vertical

deformations where an increase in horizontal drift causes an increase in vertical

deformation. This effect is modeled in the vertical spring element with an iterative

procedure that keeps the column response on the horizontal-drift to axial-load curve

defined by the shear-friction model. When the column motion reverses direction, the

vertical spring backbone is redefined to an elastic response with a reduced elastic

stiffness to account for the damage in the column. This modification also halts the axial

degradation in the column as it is assumed that the sliding shear crack surface closes,

thereby preventing any further sliding along that crack.

These LimitState shear and axial models will be used throughout the analysis phase

o f this project as they provide a comprehensive basis for modeling the behavior o f

flexure-shear-critical columns while offering ease o f use and recalibration potential under

OpenSEES.

13


Shear spring response

Beam-Coliinmresponse

Totalresponse

(A = AS + Af)

V V Vshear

\ .— limit curve

K r~~~T1 J

4 Af A

axial limit cum*

displacement at axial failure for P = PS

axiallim it cu rve

Stii ter re sponse if .iv loud ing co lum n

/ after de lec tion o f / axial failure-

Figure 2-5: Shear and axial LimitState element responses and limit curves [Elwood (2002)]

2.2 Beam-Column Joints

2.2.1 Behavioral Aspects

Beam-column joints have been observed to sustain severe damage and degradation

during strong seismic loading. In structures containing joints with little or no transverse

14


reinforcement, significant joint deterioration leading to structural collapse have even been

observed [Comartin (1995); Hall (1995); Sezen (2000)].

Numerous experimental investigations on beam-column joint sub-assemblies have

investigated factors influencing joint strength and deformation capacities. The amount

and detailing o f transverse reinforcement in joints has been shown to substantially

increase the shear strength and ductility o f beam-column joints [Kitayama et al. (1985)].

Bonacci and Pantazopoulou (1993) conducted a parametric study on test results o f 86

interior-joint connections possessing a wide range o f axial loads, concrete strengths,

transverse reinforcement ratios, bond demands and transverse beam arrangements. In this

study, joint transverse hoops were found to increase shear resistance o f joints. No

discemable effect o f axial load on shear strength was found, and joints with transverse

beams on both sides were found to have higher shear strength than joints with only one

transverse beam or none.

Park (2002) tested interior beam-column joints with no transverse reinforcement and

exterior joints with very little transverse reinforcement. Results from these tests showed

poor seismic performance for joints with little transverse reinforcement due to early

concrete diagonal cracking. Exterior joints were found to have lower shear strength than

interior joints. Contrary to Bonacci and Pantazopoulou (1993), Park (2002) observed that

a column axial load ratio o f about 0.25 resulted in a large increase in joint stiffness and

strength.

French and Moehle (1991) conducted beam-column-slab sub-assembly tests. From

these tests, they observed significant increases in beam ultimate moment strength when

the slab was on the flexural tension side. This increase in beam moment strength was

15


found to increase joint shear stress demands. Cheung et al. (1991) observed similar beam

strengthening due to slab participation and added that while slabs increased shear

demands in joints they did not contribute much to joint shear strength.

The joint shear transfer mechanism is affected by bond stresses developed between

the joint longitudinal reinforcing bars and the surrounding joint concrete [Zhu (1983);

Park (2002)]. Viawanthanatepa et al. (1979) and Eligehausen et al. (1983) observed that

the stress state o f concrete in the embedment region and the stress state o f the embedded

longitudinal bars affect the maximum bond stress that can be developed.

Viawanthanatepa et al. (1979) and Eligehausen et al. (1983) have shown that embedment

zones in which concrete is in tension or is damaged are not able to accommodate as much

bond stress as zones in which concrete is in compression or is confined. As well, they

observed that in regions where reinforcing bars are yielded, bond stresses are lower than

in region where reinforcing bars remain elastic.

2.2.2 Joint Shear Strength

Joint shear demand and capacity commonly is expressed in terms o f an average shear

stress across a horizontal cross section o f the joint. A widely used equation for joint shear

strength is:

V, = r V T T w (psi) <2-6>

with Vr = joint shear resistance, y = strength factor, f c = concrete compressive strength,

b= joint effective width, and d = joint depth.

ACI-ASCE Committee 352 (2001) estimates the shear strength factor y for joints

containing a specified amount o f transverse reinforcement, varying the value o f y as a

function o f joint geometry and whether joints are expected to undergo relatively small or

16


large plastic deformations. Recommended values o f y range from 24 to 8 (in psi units).

The highest value o f y is assigned to joints expected to sustain mild plastic deformations

and that have four beams and a continuous column framing into them. The lowest value

o f y is given to joints expected to undergo large plastic deformations and that have fewer

than three beams and a discontinuous column framing into them.

FEMA 356 [FEMA (2000)] provides y values for joints o f existing buildings. Values

o f y vary with joint geometry and with amount o f transverse reinforcement. The range o f

y values in FEMA 356 are 20 to 4 (in psi units).

2.2.3 Joint Models

Some o f the earliest work on joint modeling accounted for joint deformations

through calibration o f the flexural stiffness o f beam and column framing elements [Otani

(1974); Anderson and Townsend (1977)]. While this modeling approach is

computationally efficient, the inability to distinguish separately between frame member

and joint deformations and strengths is a limitation.

Lumped-plasticity rotational hinge models to directly model joint deformations have

also been proposed [Alath and Kunnath (1995); El-Metwally and Chen (1988)]. These

models account for joint deformations though calibration o f zero-length rotational spring

elements placed at ends o f beams and columns. The main advantages o f these models are

computational efficiency and the separation o f joint responses from those o f beams and

columns. This allows for easier model calibration and more transparent interpretation o f

results. These models did not account for axial load variations during response and only

modeled rotational and not shear deformations in joints. Shear deformations have been

shown to be substantial at high shear demands particularly for joints with substandard

17


transverse reinforcement [Park (2002), Cheung et al. (1993); Pantelides et al. (2002);

Walker et al. (2002)].

Continuum type models, which represent joints with 3D or 2D continuum finite-

element models that are linked to beam-column line elements through transition

elements, have also been proposed [Fleury et al. (2000); Elmorsi et al. (2000)]. These

methods are computationally intensive and not likely to be robust in large ffame-system

applications, especially at high deformation demands. A variation on this type o f model

[Coronelli and Mulas (2001)] makes use o f refined joint finite-element models to

calibrate hysteretic behaviors o f lumped-plasticity rotational spring elements. While this

method permits the calibration o f lumped-plasticity springs to any joint geometry it is

computationally intensive and requires large user involvement in the analysis process.

Lowes and Altoontash (2003) proposed the joint analytical model illustrated in

Figure 2-6. This element formulation is compatible with beam-column line elements and

is able to model joint rotational and shear deformations independently. This model uses

an objective calibration process whereby users are not required to enter arbitrary

calibration parameters, but only enter joint details. To achieve this, the element uses self-

calibrating bond-slip springs and shear deformation panel, with behaviors pre-calibrated

to a broad range o f experimental results.

18


external node

internal node

zero-length, bar-slip spring j—■

I p < , p O shear panelzero-length - * [ J

interfaoe-shear spring 111“W

zero-width region shown with finite width y to fascilitate discussion

m rigid internal interface plane

rigid external interface plane

Figure 2-6: Joint element developed by Lowes et al. (2004)

2.3 Bar Slip Models

Longitudinal reinforcement o f frame members must be anchored into adjacent beam-

column joints and footings. Under tensile stress, the reinforcing bars require a finite

length over which to transfer stress into the anchorage zone. The resulting bar strain

within the anchorage zone leads to bar elongation that manifests itself in slip from the

anchorage zone. This so-called bar slip is illustrated in Figure 2-7. Bar slip generates

rigid-body rotations at the ends o f frame elements that can influence significantly their

lateral stiffness. These rotations have been reported in some cases to account for up to

40% o f lateral deformations in columns, particularly at low axial loads [Sezen and

Moehle (2006)].

r Bar Slip

F ootin g or Joint

Figure 2-7: Bar slip illustration

19


2.3.1 Bond-Slip Models

Several researchers have experimentally investigated the anchorage behavior o f

reinforcing bars, and several analytical models o f the relation between bond stress and

slip (that is, bond-slip models) have been developed. Among the first such relations is

one developed by Otani and Sozen (1972) in which a constant bond stress is assumed

over the embedment length o f reinforcing bars. More elaborate bond-slip models such as

the one attributed to Eligehausen et al. (1983) and Ciampi et al. (1982) define a multi

linear constitutive law (Figure 2-8) that describes the hysteretic bond-slip relationship in

an anchored bar as a function o f the concrete strength, confinement, and interface

geometry. Several researchers implemented similar multi-linear bond-slip relations

[Filippou et al. (1986); Pochanart and Harmon (1989); Soroushian and Choi (1989);

Saatcioglu et al. (1992)].

T[N/mm*]

— — -

- EXPERIMENTAL” ANA -YTICA L

..........

8 12 16 s [mm]

Figure 2-8: Bond stress vs. slip (from Eligehausen et al. (1983))

Based on cyclic tests o f highly confined circular cross-section columns, Lehman and

Moehle (2000) presented the simpler form o f the bond stress versus slip relation

illustrated in Figure 2-9. In this relation, bond stress is related to steel stress and is

assumed to be constant prior to yielding at 1 2 f ' c (psi) and constant past yielding at

20


6yjf 'c (psi). Using this relation, the variation o f the steel stresses and strains over the

embedment length can be determined as illustrated in Figure 2-10. The total bar slip at

the edge o f the anchorage zone is then obtained by integrating the steel strains over the

embedment length.

-0.1 0.4 0.9 1.3 1.8 Z2 - 2.7 3.1 3.0

Measured Model

•0412 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14Slip (in.)

Figure 2-9: Bond stress vs. slip (from Lehman and Moehle (2000))

Reinforcingbar

Column base

Ull^l3 I

! i

TTTVtV

Ay

Figure 2-10: Longitudinal bar bond stress, steel stress and steel strain profiles (fromSezen (2002)), ( fc=concrete ultimate compressive stress, f y=bar yield stress, f s=bar stress at interface, ey=bar yield strain, es=bar strain at interface, As=bar area)

21


Sezen (2002) used the bond model developed by Lehman and Moehle (2000) to

obtain a monotonic relation for bar slip versus bar stress at a column base. For a bar with

sufficient anchorage length this approach gives:

s ,ip = £ i r ’s - - s ’

slip = £ y f y d b [ (g , + £ y l f s ~ f y ) d .

8 u„y r*b

8 u,

(2-7)

(2-8)

(see Figure 2-10 for illustration o f terminology)

with, db = bar diameter, ue = elastic bond stress = (psi), and up = plastic bond

stress = 6tJf ' c (psi).

For a bi-linear steel stress-strain relation, this bar slip relation is parabolic with

respect to steel stress in both the elastic and plastic regions. Berry (2006) linearized these

relations for simplicity as illustrated in Figure 2-11.

1.5

0.5

Figure 2-11: Bar stress vs. slip (from Berry (2006))

22


Zhao and Sritharan (2007) use a direct bar slip versus bar stress relation derived from

experiments, thereby circumventing the intermediate step o f estimating the relation

between bond and steel stresses. The bar slip versus bar stress relation is taken to be

linear with an empirically derived slope to yielding, and to be a power curve that is

asymptotic to an empirically determined steel ultimate stress at large slip values. Zhao

and Sritharan (2007) also determine the hysteretic properties o f the bar slip versus bar

stress empirically.

2.3.2 Bar Slip Induced Frame-Element Rotations

Numerous methods have been proposed to estimate the increased structural

flexibility due to bar slip at beam or column interfaces with joints and footings. These

methods include simplified approaches that use reduced beam and column flexural

rigidities [Priestley et al. (1996a); FEMA (2000); Elwood et al. (2007)], 3D finite

elements methods, and methods that use various stress-slip relations for anchored bars in

conjunction with techniques that locate the center o f bar slip induced rigid-body

rotations.

Finite element models have been proposed to evaluate bar slip effects on frame

element deformations [Lowes (1999); Girard and Bastien (2002)]. These require a fine

mesh to model the bond behavior between deformed longitudinal steel bars and

surrounding concrete. They are computationally intensive and not compatible with beam-

column line elements.

Another category o f models lumps the effects o f bar slip in non-linear rotational

spring elements that are attached to the ends o f frame elements [Otani (1974); Priestley et

al. (1996b); Sezen (2002)]. This approach is suitable for lumped plasticity frame models.

23


These models do not actively account for variations o f member axial loads during

analysis.

Certain methods such as the one developed by Monti and Spacone (2000) introduce

bar slip effects directly into the frame-element fiber-section representation. In this

fashion, bar slip induced rotations are distributed across frame elements and effectively

reduce frame-element flexural rigidity. This approach has been shown to adequately

model force-displacement responses o f flexural members and has the advantage o f being

easily implemented for any column or beam cross-section. The ability o f this method to

estimate local column responses such as section curvatures, plastic rotations, or material

strains has not been demonstrated.

Otani and Sozen (1972) estimated bar slip induced rigid-body rotations by

combining a bar slip versus bar stress model with a radius o f rotation equal to the

distance between the outermost tension and compression longitudinal bars in column

sections. Sezen (2002) assumed that the center o f rotation coincided with the flexural

neutral axis o f the column section as illustrated in Figure 2-12 and used the bi-uniform

bond-stress model described in Equations (2-7) and (2-8).

Using the same assumption as Sezen (2002) for the center o f rotation, Berry (2006)

and Zhao and Sritharan (2007) implemented bar slip rotation effects through a zero-

length fiber-section element placed in series with columns and beams as illustrated in

Figure 2-13. This implementation by virtue o f its formulation produces bar slip rotations

about the flexural neutral axis o f the section and has the advantage o f adapting to varying

levels o f axial loads.

24


iTffTnI-----------c ------------1

I I I I

i:

* « * * * . *

Figure 2-12: Bar slip rotation center (from Sezen (2002))

NodekSec. n

beam-cohttnnelement

Sec. 2

zero-length ’ cc 1 t f section Node j

element Node i

Figure 2-13: Bar slip zero-length fiber-section elements (from Zhao and Sritharan(2007))

The difference between the methods by Berry (2006) and Zhao and Sritharan (2007)

lies in the choice o f material properties for the steel and concrete fibers o f the bar slip

element. Berry (2006) defines the bar slip steel fibers as a bi-linear material with

hysteretic properties defined by the uni-axial material steelOl in OpenSEES [McKenna et

al. (2000)]. These properties are calibrated to the stress-slip model developed by Lehman

and Moehle (2000) as defined by Equations (2-7) and (2-8). These relations are linearized

by Berry (2006) as illustrated in Figure 2-11. Because the steel properties in this fiber

25


section define a stress-deformation rather than a stress-strain relation, achieving force

equilibrium though strain compatibility across the bar slip fiber-section (plane section

assumption) pushes the concrete material to very high levels o f strain. To remedy this

issue, Berry (2006) modifies the concrete properties in the bar slip element from a stress-

strain to a stress-deformation relation by integrating the concrete material properties over

an “effective” depth in the anchorage zone (Figure 2-14). The optimal depth was

determined empirically to be 0.5c, with c being the depth o f the compression zone in the

section.

Figure 2-14: Effective concrete depth (from Berry (2006))

Zhao and Sritharan (2007) use an empirically derived stress-deformation relation for

the bar slip steel-fiber material. The material properties o f the concrete fibers are the

same as those in the adjacent column element except the residual stress at large strains is

taken as 0 .8f c. This effectively creates a uniform concrete compression stress block in the

bar slip section at the strain levels expected in this formulation.

Both approaches by Berry (2006) and Zhao and Sritharan (2007) have a drawback.

These methods alter the stiffness ratio between the steel and concrete fibers in the bar slip

fiber-section from the ratio present in the adjacent frame-element fiber-section. This

26


results in discontinuities in steel stresses and neutral axis locations at the bar slip interface

between adjacent fiber-sections.

2.4 Frame Tests

To date, there have been relatively few tests on lightly confined reinforced concrete

frame systems in the- literature and none conducted dynamically to collapse. The

following review considers tests that have some parameters in common with the current

study.

Otani and Sozen (1972) conducted a series o f dynamic shaking-table tests on three

1/8 scale reinforced concrete planar frames with one bay and three floor levels. The joints

contained transverse reinforcement and the remaining reinforcement details conformed to

ductile detailing practices o f that time. The frames were subjected to increasing levels o f

the El-Centro and Taft ground motions. The observed failure sequence began with

formation o f beam plastic hinges in the first two levels followed by hinging at the base o f

the first-story columns. None o f these frames collapsed even though the maximum first

story drift recorded was about 12%. Otani and Sozen (1972) presented a lumped

plasticity model to analyze the structures.

Shahrooz and Moehle (1987) conducted a shaking-table test on a quarter-scale

reinforced concrete frame structure with set-back. The test specimen was a two-bay by

two-bay, six-story reinforced concrete frame with a 50% (of floor area) set back at mid

height. The structure was designed for construction in seismic zone 4 according to the

1982 Uniform Building Code [Uniform Building Code (1982)] and detailed as a special

moment-resisting frame according to ACI-318-83 standard [ACI (1983)]. It was

subjected to uni-directional simulated earthquake loading both parallel and skew the

27


principal axes o f the framing, sustaining a maximum inter-story drift ratio o f about 3% in

the first story without collapse. The slab contributed significantly to beam negative

moment strength and overall frame stiffness, especially at larger deformations. Analytical

modeling o f the frame was done using elastic line elements with equivalent stiffnesses

and rotational springs at their ends that followed a bi-linear hysteretic model. Shahrooz

and Moehle (1987) noted that the choice o f initial stiffness o f elements had a strong

effect on the computed dynamic response.

Bracci et al. (1992a) conducted shaking-table testing on a third-scale, one-bay by

four-bay by three-story reinforced concrete frame structure designed for gravity loads

only. This structure was subjected to low, moderate, and high levels o f uni-directional

seismic excitation and reached a maximum drift ratio o f 2.24% without collapse. From

these tests Bracci et al. (1992b) observed that higher-mode effects were negligible for the

low and moderate shaking levels. Substantial second-mode contributions were observed

at severe shaking level. Large decreases in story stiffness and frame natural frequencies

were noted at the end o f testing. A large increase in equivalent viscous damping ratio due

to hysteretic damping was also noted. Slab effect on beam flexural strength and stiffness

was found to be significant. An analytical model was developed consisting o f elastic

beam and column elements with equivalent elastic stiffnesses calibrated to match test

data. Inelastic rotational springs were added at the ends o f beam and column elements.

Calvi et al. (2002) conducted a quasi-static cyclic test on a 2/3 scale three-bay, three-

story, 2D, reinforced concrete frame with “poor” seismic detailing. Beam-column joints

had no transverse reinforcement. Damage concentrated in the first-floor edge joints,

which exhibited relatively brittle failures. This behavior was found to reduce the

28


rotational demand on exterior first-story columns, which increased the demands on the

interior columns whose joints showed no notable cracking. Also, the damage in the

exterior joints was observed to spread the inter-story drift demand between the first and

second story columns at those joints, which delayed a soft-story failure mechanism. The

modeling o f this frame was done through elastic line elements with lumped-plasticity

rotational springs at their ends. Explicit modeling o f joint deformations was implemented

through calibration o f the rotational springs at the joint-element interface.

Pinto et al. (2002) performed pseudo-dynamic experiments on two full-scale, two-

bays by one-bay by four-story reinforced concrete frames with detailing following

predominant practices in Europe from around the 1960s (i.e., with low confinement,

smooth longitudinal bars, no joint reinforcement, and short lap splices at column bases).

This study concluded that this type o f frame is very vulnerable to seismic loading. The

structure reached imminent collapse o f the third story due to longitudinal bar slippage in

columns at an inter-story drift ratio o f 2.4%.

None o f the frame specimens cited previously were tested to severe shear

degradation in columns or axial collapse. Notable observations from these tests were: (1)

lightly confined and poorly detailed reinforced concrete frame structures were highly

vulnerable to critical damage due to intense seismic loading; (2) joint deformations and

bar slip within joints had a large effect on global frame stiffness; (3) higher-mode effects

were found to contribute more to structural response after structural damage; and (4) slab

participation affected the column-to-beam strength ratio significantly.

29


3 Design and Details of Test Frame

This chapter presents details o f the reinforced concrete test frame used in the

experimental portion o f this work. Also presented are details o f the analytical model that

was u.sed during the design phase as an analysis tool to explore different design and test

options.

3.1 Objectives and Considerations of Experimental Program

To study the behavior, up to collapse, o f reinforced concrete frames with light

transverse reinforcement, a multi-bay, multi-story frame was built and dynamically tested

on the University o f California, Berkeley shaking table. Final dimensions and

reinforcement details o f this frame were influenced by the following main considerations:

laboratory and shaking table limitations, replication o f column details from previous

tests, analytical capabilities, desired failure mode, and cost. The target failure mode was

partial collapse that would enable examination o f load redistribution during collapse.

As the scope o f this study does not encompass bi-directional column loading, the test

frame was chosen to be 2D rather than 3D. This choice resulted in considerable cost

savings. The overall dimensions o f the 2D frame were determined by the shaking table

size and weight limits. A scaling factor o f one-third was chosen as the largest scale

possible that would permit floor heights and spans typical o f 1960s and 1970s California

office buildings, while allowing for three floors and three bays. The choice o f three floors

stemmed from practical construction considerations while still allowing for higher-mode

dynamic effects to be observed during testing.

30


Non-seismically detailed flexure-shear-critical columns in the test frame were

intended to have dimensions and details similar to those tested previously [Elwood

(2002), Sezen (2002)]. These details were chosen to be typical o f 1960s and 1970s office

building construction in California, with widely spaced ties formed with 90 degree hooks.

Beam dimensions and details were also chosen as representative o f that construction era.

Beam transverse reinforcement provided sufficient shear strength to develop full flexural

strength, while longitudinal reinforcement was chosen to create a weak-column strong-

beam mechanism typical o f the construction era. Neither beams nor columns had lap

splices, thus removing splicing effects from the scope o f this study. Initially, joints were

intended be constructed without transverse reinforcement as was typical o f earlier non-

seismically detailed construction practices. However, owing to concerns that these joints

might fail during testing, and that these failures would not be representative because of

the planar geometry o f the frame, transverse reinforcement was provided.

Concrete was chosen to be normal-weight density with a target cylinder compressive

strength o f 3 ksi. Reinforcing steel was chosen to be A615 Grade 60.

3.2 Design Process

Given the complexity o f desired test frame behavior and failure mechanisms, a

detailed analytical model, rather than classical design methods, was used to design the

test frame. An extensive parametric study was performed using the analytical model to

determine optimal test frame final dimensions and details. Effects o f varying the

following parameters were investigated: 1) concrete and steel material properties, 2)

beam spans, depths and longitudinal reinforcement ratios, 3) number, location, and

longitudinal reinforcement ratios o f ductile columns, 4) number o f floors in frame, 5)

31


number o f bays in frame, and 6) ground motion input (to insure that the shaking table had

sufficient capacity reserve to fail the test specimen). Throughout the parametric study,

dimensions and reinforcing details o f flexure-shear-critical columns were fixed but their

numbers and layout in the test frame were varied.

This analytical exercise also served the purpose o f evaluating the reliability and

accuracy o f current analytical models and methods, within the analysis platform

OpenSEES [McKenna et al. (2000)], in modeling the behavior o f the test frame.

Resulting test frame details and dimensions are presented in the next section and

details o f the analytical model used in the design process are presented in the subsequent

section.

3.3 Test Frame Details

3.3.1 Dimensions and Reinforcing Details

With the considerations and limitations discussed in the previous section in mind, the

test frame dimensions and details were chosen as reproduced in Figure 3-1. More detailed

as-built drawings are in Appendix A .2. Based on Figure 3-1 and for ease o f reference

throughout this document, columns, beams, and joints o f the test frame will be referred to

using the following nomenclature. Columns will be referred to by their axis letter (Figure

3-1) and story number; thus Column A l is the one at the first-story level o f column axis

A. Joints will follow a similar nomenclature with the number indicating the floor number

they are on; thus Joint A l is the joint above Column A l. Beams will be referenced with

two letters corresponding to the column axes that bound them and with the number o f the

floor they are on; Beam A B 1 is the beam West o f Joint A l .

32


m 4 4 4 M + H 4 4+ll4 *11444

m

* I- 1 4 4 1 - 1 4 4 4 m - r mBffl44-i-H 4"h:bl~

ffl0) mCO "6 2

I f f l

Figure 3-1: Test frame dimensions and reinforcement details

33


■2'-

8'

The test frame is a three-story, three-bay frame, which was built to one-third o f full

scale. Beam spans, measured to column centerlines, are 70 in. and clear floor heights are

39 in.. Columns all had gross-section dimensions o f 6x6 in. while beams were 6x9 in..

The two East columns (column axes A and B) were nominally identical over all floors

and matched the dimensions and details o f previously tested columns [Sezen (2002),

Elwood (2002)]. These columns are intended to be o f the flexure-shear-critical type (see

Chapter 2), having ties with 90 degree hooks spaced at 4 in. on centers over the column

height. The resulting transverse reinforcement ratio was p’ -0.0015 (p’ - A st/bs, Ast=area

o f transverse reinforcement with spacing s, b=column width). The longitudinal steel ratio,

defined as total cross-sectional area o f longitudinal reinforcement divided by the gross

area, was pi=0.0245. The two West columns (column axes C and D) had detailing as

required by ACI 318-2005 [American Concrete Institute (ACI) Committee 318 (2005)]

for special moment-resisting frames. These columns had a maximum transverse

reinforcement ratio p”=0.011 and a longitudinal reinforcement ratio pi=0.0109.

The two ductile columns on the West side o f the frame, while not representative o f

older non-seismically detailed reinforced concrete construction, were introduced for the

following reasons. First, these columns were introduced to control the collapse

mechanism for the test frame, which was chosen to be a partial, rather than a complete,

collapse mechanism. In this mechanism, only the non-seismically detailed columns were

designed to collapse, while the ductile columns were detailed to retain axial load-carrying

capacity. Second, these columns were added to simulate the more gradual lateral failure

mechanism that would be anticipated in a typical building during severe earthquake

excitation. As most concrete buildings contain columns o f varying dimensions,

34


reinforcement details, and axial loads, structural systems are commonly expected to

sustain a gradual loss o f lateral load-carrying capacity as columns fail in a staggered

manner at different deformation levels. This effect is partially simulated with the

inclusion o f the ductile columns in the test frame. Another advantage o f this column

arrangement is that it allowed different loading and end-fixity conditions to be applied to

the non-seismically detailed columns. In this arrangement, columns at axis A are

subjected to lighter average axial loads than those at axis B. These axial loads are also

substantially more variable in axis A columns due to framing effects, than in those at axis

B. In addition, columns at axis A have significantly lower end-fixity conditions in this

arrangement than those at axis B because they frame into beams on only one side.

Beam dimensions and longitudinal reinforcement were identical on all floors and

spans and were designed to support gravity loads (see Section 3.3.2) while creating a

strong-beam weak-column mechanism. Beams were chosen to be deeper (at 9 inches)

than required to resist gravity loads so that they would have ample torsional stiffness and

strength to resist accidental torsion that may be generated during strong shaking. This

deeper beam profile also reduced joint shear stresses. Beam transverse reinforcement was

designed to resist shears corresponding to development o f beam flexural strengths at

opposite ends, and was in the form o f closed stirrups with 135 degrees to increase

torsional resistance.

Table 3-1 lists beam and column element flexural and shear strengths as evaluated

based on ACI 318-05 [American Concrete Institute (ACI) Committee 318 (2005)]

recommendations.

35


T able 3-1: Frame element flexural and shear strengthsElement P M v m d Vy Vo V c vs Vr

kips kip-in. kip-in. kips kips kips kips kipsBeams 0 220 275 10.0 11.7 5.4 9.1 14.5Flexure-shear-criticalcolumns

0 121 151 6.2 7.7 3.4 3.2 6.6-10 140 175 7.2 9.0 3.9 3.2 7.1-20 157 197 8.1 10.1 4.3 3.2 7.6-30 174 217 8.9 11.1 4.8 3.2 8.0

Ductilecolumns

0 60 75 3.1 3.9 3.4 13.5 16.9-10 82 102 4.2 5.3 3.9 13.5 17.4-20 101 127 5.2 6.5 4.3 13.5 17.9-30 119 148 6.1 7.6 4.8 13.5 18.3

Notes: P=axial load (compression is negative), My=yield moment obtained from moment-curvature analysis, Mp=probable moment=1.25My, Vy=shear corresponding to My (includes gravity loads for beams), Vp=shear corresponding to Mp (includes gravity loads for beams), V0=concrete contribution to shear resistance calculated according to ACI 318-05 recommendations for members with axial load [American Concrete Institute (ACI) Committee 318 (2005)], Vs=transverse reinforcement contribution to shear strength calculated according to ACI 318-05, Vr=Vc+Vs.In all calculations f c=concrete compressive stress=3 ksi, fy,=transverse reinforcement yield stress=70 ksi, fyi=longitudinal reinforcement yield stress=69 ksi.

Joints in the test frame were originally designed to have no transverse reinforcement.

Preliminary analyses, however, determined that joints might experience large shear

stresses during testing that could result in joint failure prior to shear failure o f the flexure-

shear-critical columns. To better understand behavior, reversed cyclic tests were

conducted on two subassemblies replicating exterior joints o f the test frame without

transverse steel. Appendix B presents details and key results o f these joint tests. The tests

confirmed the vulnerability o f the test frame joints, showing joint failure prior to

significant deterioration in the columns. These failures were deemed unrepresentative, as

the joints were not confined by slabs and transverse beams as is common in actual

buildings. Consequently, transverse reinforcement was installed in all frame joints. Table

3-2 compares joint resisting shear stress factors (y) given by FEMA 356 [American

36


Society o f Civil Engineers (ASCE) (2000)] with values obtained from joint maximum

probable design shear stresses (vj) evaluated according to FEMA 356 guidelines.

Table 3-2: Joint shear resistance versus maximum probable applied shear stressfactors

Joints YUnreinforced

YReinforced

v i

VFTKnee Joints 4 8 12.4Exterior Joints 6 12 12.5Interior Joints 10 15 5.4

N o te s : v r= y ( f c) ° 5, v r= jo in t sh e a r s tre s s re s is ta n c e , V j= joint m a x im u m p ro b a b le d e s ig n sh e a r s tre s s

Test frame footings were designed conservatively to provide a “rigid” connection for

the columns and to remain elastic during testing.

The planar test frame was cast in a horizontal position from a single batch o f

concrete, and subsequently lifted to the upright position. Thus, there was no attempt to

replicate typical construction practices.

3.3.2 Gravity Loads

Subsidiary mass was added to the test frame in the form o f lead weights attached to

the beams. Resulting at-rest axial load ratios were approximately 0.2 in Columns B1 and

C l and 0.1 in Columns A l and D l, based on concrete compressive strength o f 3 ksi.

Axial load ratio is defined as the ratio o f axial load to f cAg, in which f c = concrete

compressive strength and A g = gross-section area. In the as-built test frame, concrete

compressive strength was 3.57 ksi, resulting in axial load ratios o f 0.168 and 0.084.

Loads were distributed equally to all beams, approximately uniformly distributed

along beam spans. This layout simulated the loading effects o f one-way slabs framing

into the beams.

37


3.3.3 Scaling Considerations

In scaling the prototype frame to one-third o f its full model size, similitude

requirements similar to those detailed in Krawinkler and Moncarz (1982) were observed.

This reference mentions the inability to satisfy mass density similitude requirements

when scaling concrete structures if the same concrete material is used in both model and

prototype. In the case o f this frame, where 97.5% o f the frame mass is lumped at beam-

level, however, the error originating from the lack o f mass density similitude is

negligible.

Prototype test frame concrete-mix design was intended to be similar to that which

would be used in a full-scale model except the maximum nominal diameter o f aggregate

was limited to 3/8 in..

Longitudinal reinforcing bars in the test frame were deformed #2 and #3 (nominal

diameter o f 0.25 and 0.375 in., respectively) A615 Grade 60 bars. Bar deformations help

maintain bond conditions similar to those in full-scale construction using deformed bars,

though it is well established that bond does not scale perfectly. Transverse reinforcing

bars were smooth wires o f 1/8 in. and 3/16 in. diameters. These wires do not replicate

bond conditions o f the full-scale model. In the ductile columns and beams, transverse ties

and stirrups were given ample anchorage length to develop their full tensile capacity.

3.4 Test Frame Analytical Model

A model o f the test frame was developed in OpenSEES. Figure 3-2 shows a

schematic o f the model.

38


3.4.1 Column Elements

Displacement (or stiffness) formulation rather than the force (or flexibility)

formulation was used to model columns because o f numerical convergence issues with

the latter formulation. Twelve displacement-formulation sub-elements were used to

model each column.

'r r

II □ = Limit State Elements 11

- - • = EPP Rotational Springs - -

II 0 = Rotational Slip Springs 11

rrm?

-t-

-- -Displacement-formulation 11 fiber section column elementsl I 11-12 sub-elem ents per column 11 • ■ with 2 fiber sections each

rrm

YRigid Joints

I Linear elastic beam elements I ; with equivalent stiffness ;- obtained from moment- > curvature analysis (« 1 1 1 •

mm

-i h

I

Typica loading pattern j (all beams)

O

n m

Figure 3-2: OpenSEES test frame analytical model

3.4.2 Beam Elements

Beam discretization had little effect on the computed overall response o f the frame.

Beams were discretized into four elastic sub-elements for computational efficiency. The

equivalent flexural stiffness was derived from moment-curvature analysis, which

produced a flexural stiffness parameter, El = 380,000 kip-in.2, with E = concrete modulus

o f elasticity and I = section moment o f inertia (note: 0.35EIgrOss = 430,000 kip-in2, with

39


E=57000(f c)0'5 = 3370 ksi). At the ends o f the beams, elastic-perfectly-plastic (EPP)

rotational springs were added to model yielding o f longitudinal reinforcement. Beam

yield moment was estimated at 240 kip-in.

3.4.3 Joints

All joints in the test frame were well confined by transverse reinforcement. Tests

[Bonacci and Pantazopoulou (1993); Lowes and Altoontash (2003)] have shown that

even highly reinforced joints can undergo appreciable deformations, especially when

structures are pushed to high drifts. As such, an attempt was made to use the joint model

developed by Lowes and Altoontash (2003). Because o f numerical convergence problems

with this model, it was abandoned in favor o f using rigid elements in the joints. All

results presented here are for the rigid joint model.

3.4.4 General Model Parameters

Lead-weight gravity loads and corresponding masses were introduced in the

numerical model at beam nodes as illustrated in Figure 3-2. Frame self-weight masses

were distributed across all nodes in the model according to the tributary mass o f each

node. Care was taken to ensure that no node remained massless to avoid numerical

convergence issues related to massless nodes.

P-delta effects were included in the column-element formulation to account for non

linear geometric effects, which may be significant at anticipated maximum drift levels.

Damping was modeled with constant stiffness and mass proportional Rayleigh damping

based on the 1st and 2nd “initial” elastic modes o f vibration o f the structure. The damping

ratio was taken as 3% o f critical.

40


3.4.5 Zero-Length Column and Beam Elements

3.4.5.1 Zero-Length Rotational Spring Elements Modeling Bar Slip Effects

Elastic rotational springs were introduced at the ends o f columns and beams to

account for longitudinal bar slip within the footings and joints. The bond stresses

developed in the joints and footings were assumed to be identical in this analytical model.

All column and beam bar slip rotational springs were given a stiffness that was scaled

from column tests conducted by Elwood (2002). Based on Sezen (2002), bar slip induced

rotations at yield are assumed proportional to bar slip and neutral axis depth. Thus bar

slip rotational spring stiffnesses used in test frame elements were scaled from Elwood

(2002) estimates by the factor (dbf/dbe)*(hf/he) (with dbf=longitudinal bar diameter o f

frame element in test frame, dbe=longitudinal bar diameter o f flexure-shear-critical

column in Elwood (2002) tests, hf=test frame element height, hf=column height in

Elwood (2002) tests).

3.4.5.2 Zero-Length Shear and Axial Failure Spring Elements

To model the flexure-shear-critical column shear and axial failures, the LimitState

zero-length spring elements (developed by Elwood (2002) as described in Chapter 2)

were introduced at the top o f each o f the flexure-shear-critical columns. Because the

LimitState elements are calibrated to drift, whether the elements are placed at the top or

bottom o f column elements is inconsequential.

3.5 Frame Analytical Model Behavior

Dimensions and detailing o f the test frame were likely to result in concentrated

damage in the flexure-shear-critical columns in the first story, with relatively less damage

in upper-story columns prior to collapse. To get a sense o f the damage sequence o f the

41


frame up to collapse, the analytical model was subjected to a nonlinear static (pushover)

analysis driven by lateral forces with a first-mode vertical distribution that acted from

West to East. The observed response and damage sequence are summarized in Figure

3-3, which plots the base shear versus first-story drift ratio. This figure also marks the

various damage milestones, specifically:

1. Yielding o f longitudinal steel o f all first-story columns occurs at first-story

horizontal drifts between 0.7% and 1.0%.

2. At about 2.2% horizontal drift, shear failures initiate in the yielded regions o f

flexure-shear-critical columns A l and B l.

3. Between 2.2% and 5.5% horizontal drift, a gradual loss o f shear resistance is

observed in Columns A l and B l until residual strength is reached.

4. Axial failure is initiated at residual shear strength. It is important to note here that

these high drift levels at axial failure are mainly a function o f the low axial load

on the columns as well as the flexure-then-shear failure sequence o f the columns.

5. As the structure is pushed to even higher drifts, it collapses on the East side

dragging the ductile side with it. A first-story drift ratio o f 8% was assessed as the

collapse drift for this frame.

It should be noted from Figure 3-3 that the pushover curve terminated at a drift o f

about 5.5%. This is because numerical instability is encountered when axial load

degradation is initiated in a static analysis, which lacks dynamic equations o f equilibrium.

This problem is averted in dynamic analyses, and the value o f 8% drift for collapse o f the

structure is obtained from those analyses.

42


First Floor C olum nsSpad ing

Ductile O u te r Col.

Ductile Inner Col.

N on-D uctile In n e r Col.

N on-D uctile O u te r Col.

Q.S h e a r failure

initiationAxial failure

initiation P ro jec ted b eh av io rLong, s te e l

yieldingu.

- X

C o llap seOT 10 R esid u a l s h e a r s tre n g th s

FEM A 356 C o llap se P rev en tio n

Limit

0 1 2 3 4 6 85 7 9

Drift Ratio (%)

Figure 3-3: First-story drift ratio versus base shear response

The collapse limit state for this structure was compared with the FEMA 356

[American Society o f Civil Engineers (ASCE) (2000)] Collapse Prevention Performance

Level for a structure with shear-critical primary columns. FEMA 356 guidelines define

Collapse Prevention in this case as “the deformation at which shear strength is calculated

to be reached.” This state occurs at a first-floor drift o f about 2.2% for this frame whereas

the model estimates collapse to occur at a much higher drift o f 8%. It is clear that FEMA

356 guidelines can be too conservative for this type o f structure, particularly for low axial

loads.

The relatively large drift capacity o f this frame is not generally applicable to this

class o f buildings, but is a result o f the specific conditions o f the frame studied. Drift

capacity is sensitive to the amount o f axial load on the columns, which drives the axial

43


failure, as well as the amount o f longitudinal steel in the columns, which affects the

flexure-shear failure sequence (Elwood and Moehle, 2005b).

3.6 Northridge Earthquake Case Study

The previously defined analytical model was used in a case study to evaluate the

collapse vulnerability o f this type o f frame structure to a near-fault earthquake scenario.

The earthquake scenario chosen was the 1994 Northridge, California, earthquake.

3.6.1 Selected Earthquake Ground Motions

The test frame analytical model was subjected separately to both components o f

seven ground motions recorded during the 1994 Northridge, California, earthquake. By

choosing the records from a single earthquake, the earthquake-to-earthquake variability

o f ground motions is excluded from the analysis. Additionally, by selecting a set o f

recording sites located in the same general area, spatial variability o f the recorded ground

motion is relatively reduced. The selected strong motion recording stations are listed in

Table 3-3.

The locations o f the recording stations, the epicenter, and the surface projection o f

the fault rupture plane are mapped in Figure 3-4. As provided in Table 3-3, the selected

recording stations constitute a closely spaced cluster o f sites located between 5.2 and 6.5

km from the fault plane. The sites have either NEHRP [International Code Council (ICC)

(2003)] site class ‘C’ or ‘D .’ The shear-wave velocity in the top 30 meters o f soil is in the

range o f 251 to 441 m/s (see Table 3-3).

44


Table 3-3: Strong motion records

Station

Ground Motion Horizontal

Components 1

Ground Motion Horizontal

Components 2Rrup(km)

NEHRPsite

classVs30(m/s)

Rinaldi Receiving Sta RRS228 RRS318 6.5 D 282Sylmar - Converter Sta SCS142 SCS052 5.3 D 251Newhall - Fire Sta NWH360 NWH090 5.9 D 269Sylmar - Converter Sta East

SCE018 SCE2885.2 C 371

Sylmar - Olive View Med FF

SYL360 SYL0905.3 C 441

Jensen Filter Plant JEN292 JEN022 5.4 C 373Newhall - W Pico Canyon Rd.

WPI046 WPI3165.5 D 286

Notes:Rrup = Distance to fault rupture planeNEHRP = U.S. National Earthquake Hazard Reduction Program [International Code Council

(ICC) (2003)]Vs30 = Average shear-wave velocity in the top 30-meters o f soilGround motion horizontal components are presented in two sets, components 1 and 2 which

correspond to the components that produce higher and lower damage to the frame, respectively.

34.5

a>■c3

_l

34 -

-119 ■118.5 -118

Longitude

Figure 3-4: The 1994 Northridge, California, earthquake: Epicenter (Star symbol),surface projection o f the fault plane, and locations o f the selected recording stations (solid circles) are marked

Figure 3-5 shows 5% damped elastic response spectra o f the horizontal ground

motions at the selected sites. This figure shows the variability o f the ground motion in

terms o f a linearly elastic structural response intensity measure. The effects o f such

45


variability on nonlinear dynamic response o f the structural models will be discussed

the next section.

Ground Motion Horizontal Components 1

— RRS228 SCSI 42

— NWH360 SCE018 SYL360

*»JEN292 —-WPI046

Mean

T =0.62sec

T2=0.19seci i

1 1.5Period (sec)

Ground Motion Horizontal Components 2

— RRS318 SCS052

-NWH090 - SCE288 SYL090 JEN022 WPI316 Mean

T =0.62sec

T2=0.19sec

1 1.5Period (sec)

Figure 3-5: Linearly elastic response spectra for 5% damping for both horizontalcomponents o f the selected 1994 Northridge records

46


3.6.2 Analysis Results

The displacement-controlled behavior o f the test frame prompted the use o f the first-

story drift ratio as the damage parameter for comparison between the different ground

motion simulations. Figure 3-6 shows the first-floor drift ratio histories o f the frame when

subjected to each component o f the seven ground motion records individually. Table 3-4

summarizes the absolute value o f the maximum first-story drift ratios for each o f the

ground motions.

Table 3-4: Summary table o f first-story maximum drift ratios and ground motionintensity measures

Ground 1 Motion

Maximum Absolute First-Story Drift Ratio (%)

PGAGO

PGV(cm/sec)

Elastic SaT! (g)

SIVTi(cm)Ti-»1.5Ti

s iv t 2(cm)T2"M.5Ti

RRS 228 8.00* 0.83 160 1.96 5.17 18.0318 2.41 0.49 74 0.92 2.31 12.0

scs 142 5.78 0.61 117 1.37 4.04 11.7142neg 6.55 0.61 117 1.37 4.04 11.7052 4.89 0.90 102 1.48 3.55 13.6

NWH 360 4.36 0.59 97 2.00 4.36 16.4090 1.31 0.58 75 1.17 2.17 14.6

SCE 018 2.18 0.83 117 1.11 3.34 14.0288 1.55 0.49 75 0.76 2.11 9.2

SYL 090 2.20 0.60 78 1.14 2.58 10.6360 1.36 0.84 129 1.35 2.91 18.1

JEN 292 2.09 0.57 76 0.73 2.04 11.3022 1.66 1.02 67 1.17 2.98 19.2

WPI 046 0.93 0.45 93 0.65 2.02 7.2316 0.80 0.33 67 0.56 1.56 6.5 1

*: L im ited to 8% drift correspon d ing to c o lla p sePGA = Peak ground acceleration, PGV = Peak ground velocitySaT i = Elastic response spectrum value at l sl mode period Tj

H.57-1SI VTi = Modified Housner (Housner, 1959) Spectrum Intensity = ^ Sv (T,5%)dT

With Sv(T,n)=velocity response spectrum value corresponding to period T and 5% damping. SIVT2 = same as above with integration bounds ranging from T2 to 1.5T|.

47


Firs

t-Sto

ry

Drift

Rat

ios

(%)

Firs

t-Sto

ry

Drift

Ra

tios

(%)

Ground Motion Horizontal C om p on en ts 1

Initiation of axial loadloss at +5.5% drift

. Yielding at +1-0 .7% drift

Initiation of shear failure at +1-2 .2% drift

0

“T"

2~i-

4

T"

6I

8Time (sec)

RRS228- - SCS142- " SCS142neg- NWH360

SCE018- - - SYL360

JEN292 WPI046

12

6

4

2

0

Ground Motion Horizontal C om p on en ts 2

-2

-4 -

Initiation of axial load loss at +5.5% drift

Yielding at +/-0.7% drift

Initiation of shear failure at +1-2 .2% drift

0 6Time (sec)

8

-RRS318SCS052NWH090SCE228SYL090JEN022

-WPI31612

Figure 3-6: First-story drift ratio histories

48


As can be seen in Figure 3-6, there is high variability in the frame response when

subjected to ground motions obtained from the same earthquake at sites o f close

proximity with similar soil conditions. The responses range from complete collapse o f the

frame to almost no yielding o f the first-story column longitudinal steel. It is evident that

local geological and soil conditions have significant effects on the seismic response o f a

structure. As well, a high variability in response is observed in Figure 3-6 when

considering the frame response to either o f the two components o f each ground motion.

This suggests that orientation o f the structure can have a significant effect on its response.

While this might relate in part to differences in ground motion associated with fault-

normal and fault-parallel directions, this is not the sole source o f the difference. To

demonstrate this point, the frame was subjected to the SCS142 ground motion in both the

East-West direction, and rotated 180 degrees in the West-East direction. For the EW

direction, frame action resulted in increased axial load in flexure-shear-critical columns at

peak drift response, leading to loss o f axial load carrying capacity. For the rotated ground

motion, frame action resulted in uplift on flexure-shear-critical columns at peak drift in

which case axial failure did not occur.

To better understand why the frame sustained such a wide range o f damage due to

these ground motions, several ground motion intensity measures (IMs) are investigated

with relation to the frame maximum first-floor drift ratios (absolute values). These IMs

are the peak ground acceleration (PGA), the peak ground velocity (PGV), the spectral

acceleration at the first-mode elastic period (T t) o f the structure (SaTi), and two modified

Housner velocity spectrum intensity measures (Housner 1959). These measures are

derived by integrating the spectral velocity curve over a period range. In this work the

49


period ranges considered were Ti to 1.5 Tj and T2 to 1.5Ti (dubbed SIVTi and SIVT2).

These IMs are summarized in Table 3-4 along with the maximum absolute first-story

drift ratios. Figure 3-7 plots these data with a least-squares linear regression fit through

them and presents the coefficients o f determination (R2) for the fits. The results for PGA

were not reported in Figure 3-7 as PGA showed least correlation with frame drift with a

coefficient o f determination R2=0.08. Different relations can be expected between the

IMs presented here and the frame drift ratios in the elastic and inelastic drift ranges. As

all ground motions in this study pushed the frame into the inelastic range, it is the intent

o f this work to investigate these relations for inelastic drift ranges only. A simple linear

regression fit is used here for quantitative comparison between the different IMs.

co 2

iTO, lO 1 0 0PGV (cm/sec.)

1 5 0

° 8 -4—»roK 6 £□ 4

oCO 2

w \T 0.

00 1

/ 1 ♦ /

/ 0

0 >

R2= 0 .5 7•% ♦

-j -o-

SIVT, (cm)

0 1 2 3Spectral Acceleration at T (g)

9o

i i o , 20SIVT2 (cm)

Figure 3-7: First-story absolute drift ratios vs. ground motion IMs. Circles mark thehorizontal component 1 motions and diamonds the horizontal component 2 motions

50


As can be seen in Figure 3-7 the intensity measure SIVTi shows a strong linear

relation with respect to maximum first-story drift with an R2=0.81. This correlation level

is followed by that o f SaTl and PGV which showed more dispersion with several outliers

and R2 values o f 0.57 and 0.51, respectively. SIVT2 did not show much relation to the

first-story drift ratios as the response o f this frame is mostly dominated by the first mode.

3.6.3 Observations and Conclusions

Response o f the frame was found to be sensitive to ground motion input, with

responses to individual ground motions varying from almost no yielding o f longitudinal

steel to total collapse. The response o f the frame was sensitive to its orientation and the

component o f the ground motion to which it was subjected. Thus, the variability o f

ground motion from site to site (so called intra-event variability) was found to play an

important role in analytical prediction o f structural collapse.

In addition, the common site classification parameters: site soil classification, soil

shear wave velocity (first 30m), and distance from fault rupture plane, have little

correlation with the damage state induced in the structure. As for ground motion intensity

measures, a modified Housner spectrum intensity measure with integration bounds

between Ti and 1.5Ti was found to correlate well with damage o f the frame.

In conclusion, these results seem to suggest that the low-collapse statistics from

major earthquakes are more due to site variability than to the actual low number o f

collapse prone lightly-reinforced concrete frame structures. One should note at this stage,

however, that this study is still rather limited and its results cannot be generalized before

more analysis is conducted.

51


4 Experimental Program

4.1 Construction and Casting

The test frame was built lying down on a wood platform supported by a stiff steel

frame as shown in the pictures o f Figure 4-1. Longitudinal reinforcing bars were cut and

bent by a local supplier to ACI 318-05 [American Concrete Institute (ACI) Committee

318 (2005)] recommendations (i.e., bend diameter = 6 times the bar diameter db).

Transverse reinforcement was bent at the University o f California, Berkeley laboratories

using a bend diameter o f 6 times the bar diameter. Steel cages were constructed on the

wood platform and the forms were then built around them (Figure 4-1). The only

exception to this was the addition o f transverse reinforcement in the beam-column joints.

This reinforcement was added after the forms were constructed and thus had a

configuration different from typical joint details (see Appendix A.2 for as-built

drawings). This modification was decided late in the construction process; as described in

Chapter 3 it was intended to avoid unrealistic nonlinear joint behavior.

Threaded rods were imbedded at the center o f each joint and at the four

reinforcement comers o f Joints A l, B l, A2 and B2 (Figure 4-1). These rods were

provided as attachment points for instruments that monitored joint movements and

deformations during testing.

52


Figure 4-1: Specimen construction

The test frame was cast monolithically using gravity feed from a ready-mix concrete

truck (Figure 4-2). Concrete was vibrated, leveled, and troweled during casting and

afterwards. After final troweling, the specimen was covered with wet burlap and plastic

sheathing and cured for 14 days. The wet-curing duration was determined by monitoring

strength development from concrete cylinder tests (see Appendix A. 1 for frame material

testing results).

53


Figure 4-2: Specimen casting

4.2 Test Setup

Following concrete casting, the specimen was rolled into the shaking table laboratory

at the University o f California at Berkeley and tilted into an upright position (Figure 4-3).

The steel frame and wood platform backing the test frame were then removed and two

large S-section steel girders were prestressed on either side o f the frame footings. These

steel beams were used as stiffeners while the frame was lifted, by crane, onto the shaking

table where it was bolted to eight load cells (two per column), which were previously

bolted to the shaking table.

54


Figure 4-3: Specimen erection

Two steel frames were then bolted to the shaking table on either side o f the concrete

frame (Figure 4-4). These frames were used to brace the frame in the out-of-plane

direction. The concrete frame was connected to the steel frames though a bracing

mechanism that was designed to prevent out-of-plane motion but allow free in-plane

motion (both horizontal and vertical) o f the test frame (see Appendix A.4). The bracing

mechanism was attached to the test specimen at five locations (Figure 4-5) by

prestressing stiff C-sections on either side o f beams at their mid-span.

55


Figure 4-4: Test frame setup picture

Each beam was then loaded with twelve lead bundles o f 0.5 kips each, which were

arranged in packets o f three (Figure 4-5). Appendix A.3 summarizes test frame weights.

Lead-weights were prestressed onto beams with contact points being one neoprene pad

( 5 x !/2.x ‘/2 ) in. and one steel plate (5 x '/2 X % ) in. per packet (Figure 4-6). The flexible

neoprene pads were used to reduce the stiffening effects o f lead packets on beams. Steel

plates in this arrangement provided the lateral load transfer between lead packets and

concrete beams and were always placed towards the middle o f the span where flexural

deformations were smallest.

56


C-Section connecting Lead Weight Packetsout-of-plane bracing (1.5 kips top and 1.5 Out-of-Planemechnism to beam kips bottom) Bracing Mechanism ^

_18.-------------^ — \ ........................................ V t

West

C a tc h in g D e v ic e C a tc h in g D e v ic eLoad Cells

SHAKlI J TABLE

1 3 -10y2"

q — vo>

Figure 4-5: Test frame setup drawing

BEAM Steel PlatesNeoprene Pads

Figure 4-6: Lead weight location (typical for all beams)

57


For safety reasons, two steel catching devices were constructed on top o f the shaking

table and beneath Beams AB1 and CD1 (Figure 4-5). Under Beam AB1 the top surface o f

the catching device was positioned such that it allowed the test frame to fall by about 5

in. upon collapse. Below Beam CD1, only about 2 in. o f falling space was provided as no

collapse was anticipated on that side. In anticipation o f a possible second-story collapse

mechanism between column axes A and B, a smooth contact surface was placed on top o f

the lead weights o f Beam AB1 (Figure 4-5). For additional safety, four large C sections

were clamped onto the two steel bracing frames, thus bridging both frames at roughly the

first and second test frame levels (Figure 4-4). These sections were placed at least 12 in.

from the test frame and were meant to prevent the frame from falling onto or off the

shaking table.

4.3 Instrumentation

Test frame instrumentation used in this experiment consisted of: 1) force transducers

(or load cells) that measured shear, axial, and bending forces at the base o f the frame

footings; 2) strain gauges that measured longitudinal steel strain in columns and beams;

3) accelerometers that measured horizontal and vertical accelerations at various points on

the frame; and 4) displacement transducers that measured both local column and global

frame deformations. Details for all instruments can be found in Appendix A .5. Figure 4-7

shows a schematic instrumentation drawing for all frame instruments (except strain

gauges, which are only detailed in Appendix A.5).

The frame was attached to the shaking table through eight load cells (two per

column). These load cells are capable o f reading axial, shear, and bending forces in the

direction o f motion.

58


Strain gauges were placed on the longitudinal reinforcing steel at the ends of

Columns A l, A2, B l, B2, as well as the ends o f beam AB1 (one inch from the edge o f

joints or footings).

HorizontalA c cele ro m eter East

West O ff-T able Jo in t Location in strum en ts

O n-T able Jo in t L ocation Instrum en 5

Vertical an d ^H orizontalA ccele rom eters

V ertical an d XH orizontalA c cele ro m eters

H orizontalA ccele rom eter

Colum n an d Joint D eform ationInstrum ents

V ertical and H orizontal

i $ A ccele rom etersV ertical a n d XH orizontalA c cele ro m eters

HorizontalA c cele ro m eter

Load CellsO ut-of-P lane >ut-of-PlaneVertical andH orizontalA ccele rom eters—V*

SHAKi 3 TABLE

Figure 4-7: Frame instrumentation schematic drawing

Thirteen accelerometers were affixed using epoxy to the South side o f the specimen

at the following locations: footing BO (vertical and horizontal accelerometers); Joints A l,

A2, B l, and B2 (vertical and horizontal accelerometers); and Joints D l, D2, and D3 (only

horizontal accelerometers). In addition, following the first high-level dynamic test, four

accelerometers were affixed using epoxy onto bottom lead packets at beams AB1, AB3,

CD1, and CD3 to monitor slip o f these weights with respect to the test frame (see

Appendix C.3.3).

59


Horizontal (X axis) and vertical (Y axis) locations o f all frame joints were monitored

using displacement transducers attached to 3/8 in.-diameter threaded rods that were

imbedded into the center o f each joint (termed the on-table instruments). These

instruments varied from wire pots with a + 20 in. range to Direct Current Displacement

Transducers (DCDTs) with ranges o f +1 to 3 in.. For redundancy and increased accuracy,

column axis A was further instrumented from outside the shaking table in a pattern that

monitored the location o f each o f its joints independently from the on-table instruments.

These instruments were attached to a steel frame that was adjacent to the shaking table

and connected to the specimen through targets glued onto the faces o f joints.

Flexure-shear-critical Columns A l, A2, B l, and B2, as well Joints A l and B l, had

displacement transducers attached in the pattern illustrated in Figure 4-7. These

instruments allowed monitoring o f column and joint local deformations. As well, bar-slip

deformations were monitored through displacement transducers attached at various points

across the frame as illustrated in Figure 4-8.

Figure 4-8: Bar-slip instrumentation picture

60


4.4 Ground Motion Selection

A long-duration ground motion was preferred as it would allow for longer data

recording and more gradual failure. The ground motion chosen also needed to remain

within the shaking table capacities. For these reasons, various records from the 1985

Chile earthquake at Valparaiso (Valparaiso 1985-03-03 22:47:07 UTC) were explored

using the test frame analytical model described in Chapter 3, before a scaled version o f

the component 100 at the Llolleo station was chosen (Station Latitude & Longitude: -

32.6350, -71.6300). This station is located in the basement o f a one-story building built

on sandstone and volcanic rock. This motion was scaled up 4.06 or 5.8 times from its

original acceleration amplitudes for the main shaking table dynamic tests. To remain

within the shaking table frequency range, this motion was also filtered in the frequency

domain by multiplying its Fourier transform with the trapezoidal function U f(f):

0 . 0 when 0 . 0 < / < 0 . 2 Hz 0 .0 - > 1 . 0 when 0 . 2 < / < 0.25Hz

u f { f ) = < 1.0 when 0.25 < / < 12Hz1 .0 - > 0 . 0 when 1 2 < / < 15Hz

0.0 when f > \5H z

( f — frequency)

Due to the one-third scale o f the prototype structure, the ground motion time scale

was scaled down by a factor ofV3 to satisfy similitude requirements.

Figure 4-9 plots the displacement, velocity, and acceleration histories o f the motion

used in Dynamic Test 1 (see Section 4.5 for test definitions), as well as a plot o f the

motion acceleration Fourier transform. Figure 4-10 plots the response spectra o f the

motion for 2%, 3% and 5% critical damping. This figure also locates the analytically

estimated “elastic” first three mode periods o f the structure as well as the anticipated first

61


three mode periods evaluated just prior to the collapse o f the structure. Analytical periods

o f the test frame were obtained from eigenvalues recorded at the beginning and end o f

each dynamic simulation.

Acceleration

0.5

-0.5

seconds

.x 10 Acceleration Frequency

-Signal!...Scaled Llolled, dti*0-.00289-t Filter pts: 0.2:

Velocity

-17.28o<wtfi<D

.Coc

-10

-20,30 40seconds

Displacement

-1.820.5

in<p

. coc-0.5

seconds

Figure 4-9: Dynamic Test 1 ground motion displacement, velocity, and accelerationhistories, plus acceleration Fourier transform o f acceleration history

62


Response Spectra 2%, 3%, 5%

Second1 Mode Shift '

G round Motion: S ca led Llolleo, F ac to r = 4 .06Tim e s te p 0.()0289Filter P o in ts (j.2 0 .25 12

05

.2 6First Mode Shift

< 4

0.2 0.6 Period (sec)

0 .4 0.8

Figure 4-10: Dynamic Test 1 ground motion response spectra

4.5 Test Protocol

Table 4-1 lists the successive snap-back and dynamic tests applied to the test

specimen. The first tests performed on the structure were a series o f three snap-back tests

applied at the third floor and three snap-back tests applied at the first floor. Following

these tests, a low-level dynamic test was performed at a scaling factor o f 0.0725 o f the

original Llolleo, Chile ground motion. This test served as a check on all systems and

instruments o f the frame. The next test performed was a half-yield level dynamic test

with the Llolleo motion scaled by a factor o f 0.3625. Following this test, a low level

white-noise dynamic test was imparted to the frame to assess its new “cracked” state

dynamic properties. Subsequently, the frame was subjected to the Llolleo ground motion

63


scaled by a factor o f 4.06 times in Dynamic Test 1. Some lead weights decoupled from

the structure during this dynamic test and had to be repositioned and re-stressed to the

frame before a series o f third-floor snap-back tests were performed to assess the

damaged-state dynamic properties o f the frame. Following that, the frame was re-tested

in Dynamic Test 2 using the same ground motion as the one used in Dynamic Test 1.

This test did not prove sufficient to collapse the structure as its fundamental period had

shifted significantly due to the damage it incurred in Dynamic Test 1. In the end, a

ground motion scaling factor o f 5.8 was used in Dynamic Test 3 to bring Columns A l

and B l to collapse.

Table 4-1: Testing protocol

Test Description Date Earthquake Motion Amplitude Scaling Factor

Snap-Back at third floor level 02/07/06 - -

Snap-Back at first floor level 02/07/06 - -

Low-Level Dynamic Test 02/07/06 Llolleo, Chile Comp. 100 0.0725Half-Yield Dynamic Test 02/08/06 Llolleo, Chile Comp. 100 0.3625White Noise Test 02/08/06 - -

Dynamic Test 1 02/08/06 Llolleo, Chile Comp. 100 4.06Snap-Back at third floor level 02/16/06 - -

Dynamic Test 2 02/16/06 Llolleo, Chile Comp. 100 4.06Dynamic Test 3 02/16/06 Llolleo, Chile Comp. 100 5.8

64


5 Experimental Results

This chapter presents the results from the main dynamic tests performed on the test

frame (as enumerated in Chapter 4). It also presents frame dynamic properties at various

damage stages as the. frame went through increasing levels o f dynamic shaking.

Calculation details for these results can be found in Appendix C.

Throughout this chapter, frame elements will be referred to according to the axis

system defined previously (i.e., Column A l is the first-story column located on axis A).

5.1 Frame Dynamic Properties

Modal properties o f the test frame were extracted from snap-back tests, the end-of-

test free-vibration phase at the end o f each dynamic test, and a white-noise dynamic test.

Initially, the frame dynamic properties were extracted from two series o f snap-back tests

performed on the “undamaged” frame prior to any other testing. Following that, the

Half-Yield dynamic test was performed on the frame and its free-vibration phase

produced another set o f dynamic properties that reflected the additional cracking

sustained by the frame during the test. Immediately after that, a low-amplitude white-

noise test was performed on the frame to compare with dynamic properties obtained from

the free-vibration phase. Subsequently, the frame was subjected to Dynamic Test 1 from

which new dynamic frame properties were extracted during its end-of-test free-vibration

phase. Following that test, a series o f snap-back tests were performed on the frame to

produce additional free-vibration data. Finally, the frame dynamic properties were

extracted from the end-of-test free-vibration phase o f Dynamic Test 2. Dynamic Test 3

65


collapsed the frame and no useful free-vibration properties could be extracted from that

test.

The dynamic properties o f the frame as obtained from all the tests described above

are summarized in Table 5-1. This table contains the mean values o f the first three modal

periods, frequencies, and damping ratios o f the frame. Modal property extraction for the

test frame was performed using two basic methods: the frequency-domain method and

the time-domain method. The frequency-domain method consisted o f extracting modal

periods from peaks in the response Fourier Transforms or Transfer Functions, while the

time-domain method utilized bandpass filtered history responses (around each mode

period) to obtain modal periods, frequencies, and damping ratios. Damping ratios could

only be extracted from the time-domain method. Details o f the modal property extraction

calculations can be found in Appendix C.2.2 along with detailed descriptions o f all the

snap-back, free-vibration, and white-noise tests.

Table 5-1 tracks the shift in modal periods o f the test frame as it sustains increasing

levels o f damage from successive dynamic tests. Initially, the “undamaged” first-mode

period was approximately 0.30 seconds (some minimal cracking could be observed prior

to any testing due to construction and lead weight loading process). This period

lengthened to about 0.35 seconds after the Half-Yield Test in which flexural cracking was

observed. This period then shifted to about 0.82 seconds following the high level

Dynamic Test 1 and ended at around 0.93 seconds following Dynamic Test 2 and just

prior to it being tested to collapse. The second and third modes o f the structure followed a

similar pattern as the first mode throughout the testing program.

6 6


Table 5-1: Summary o f fram e modal properties

Tests Extract. Value 1st 2nd 3rdMethods mode mode mode

Initial Freq. Domain Period (sec) 0.303 0 . 1 0 1 0.069Elastic Methods Frequency 3.30 9.85 14.47Snap-Backs Time Domain Period (sec) 0.306 0 . 1 0 1 0.069

Methods Frequency 3.27 9.79 14.39Damping Ratio

(%)1.93 -1.85 2.13

Half-Yield Freq. Domain Period (sec) 0.341 0 . 1 2 0 0.081Test Free- Methods Frequency 2.93 8.32 12.33Vibration Time Domain Period (sec) 0.347 0 . 1 2 0 0.082

Methods Frequency 2 . 8 8 8.32 1 2 . 2 1

Damping Ratio (%)

N.A.* N.A.* N.A.*

White- Freq. Domain Period (sec) 0.350 0.115 0.080Noise Test Methods Frequency 2.85 8.67 12.53Dynamic Test 1 Free- Vibration

Freq. Domain Methods

Period (sec) 0.81 0.38 0.13

Frequency 1.23 2.64 7.85

Damaged Freq. Domain Period (sec) 0.82 0.26 0.15Snap-Backs Methods Frequency 1 . 2 1 3.91 6.67

Time Domain Period (sec) 0.74 0.24 0.093Methods Frequency 1.34 4.13 10.69

Damping Ratio (%)

13.4 N.A.** N.A.**

Dynamic Test 2 Free- Vibration

Freq. Domain Methods

Period (sec) 0.93 0.33 0.17

Frequency 1.08 3.00 5.79*: during the free-vibration period, the floating of the shaking table produced significant noise in free- vibration responses which forced a narrower filtering band around modal frequencies and prevented accurate damping ratio evaluation using this method.**: due to frame damage, second and third mode damping ratios could not be extracted accurately.

Figure 5-1 plots the first three modal frequencies o f the test frame versus the

maximum absolute values o f the roof and first-floor drift ratios obtained from each o f the

dynamic tests on the frame (including the initial ‘undamaged’ state snap-backs). This plot

illustrates the shift in modal frequencies with damage levels o f the frame.

67


— 1st Mode — 2nd Mode 3rd Mode .^.Eos.t.DynarHic Test 1

I " . - — — i — — — —Post Dynamite; Test 1 \

2 .5

d 1 .5

,.P.ost.:Halfr.YMd:iesL\ IVlnLtial.State______

Modal Frequencies (hz)

QL_oo

............... ....^.Eoat.D.ynanjic Test 1

\ PosFtfyhami^'iJesT

\ K \

\ : \ \

— 1 st Mode — 2nd Mode — 3rd Mode _

-----------------------------

i

\\

\ x \ \\ x \ \\ \

\\

\ \

V.P.ost. .Half-Yield .le s t . ... \ ............\

...............X

\.JDLtial.5tata...........................5 10

Modal Frequencies (hz)15

Figure 5-1: Modal frequencies vs. maximum absolute values o f roof andfirst-floordrift ratios for all tests

5.2 Initial Gravity-Load State

Measurements and analyses were conducted to identify the pre-existing

stresses/forces and strains/deformations due to gravity loading. For this purpose, readings

from load cells supporting the frame were taken at several intervals during the

6 8


construction process to monitor the change in loads on the structure as it was being

loaded. Load values were recorded: 1) just after the load cells were prestressed to the

shaking table and before any loads were placed on them, 2 ) just after the bare frame was

placed on the load cells, 3) just after the bare frame was prestressed onto the load cells, 4)

after all the lead weights and test apparatus were placed on the frame, and 5) after the

frame was removed from atop the load cells and while they were still prestressed to the

shaking table. Unfortunately, load cell readings exhibited large drifts between each

reading (particularly for axial loads) and could not be used to assess the initial gravity-

load-induced forces in the frame. As well, it was impractical to monitor the frame

gravity-load deformations (which are very small) during the erection and loading process.

This meant that the initial gravity-load-induced frame forces and their corresponding

deformations could only be estimated using an analytical model.

The analytical model used for this task is the OpenSEES model described in Chapter

3, which was adjusted to match actual frame material properties, loads, and elastic

(“undamaged”) periods and modes o f the structure. The calibrated model elastic periods

were 0.305 sec, 0.103 sec, and 0.066 sec, which compare well with measured initial

periods o f the test frame (see Table 5-1).

The analytical model gravity-load response values are summarized in Appendix

C2.3. Because all instruments were zeroed prior to the dynamic testing sequence, the

analytically obtained initial values in Appendix C.2.3 were added to measured values to

account approximately for the initial gravity-load state o f the test frame.

69


5.3 Half-Yield Dynamic Test Results

5.3.1 Global Behavior

After the initial snap-back tests, a Half-Yield level dynamic test was applied to the

specimen with the Llolleo (Chile) ground motion with amplitude scaling factor o f 0.3625.

During this test, all systems performed well- and only minor flexural cracks were

observed in the beams and columns. Cracks were marked and photographs were taken

(see Appendix E for photographs).

An overview o f the frame response is provided by the following:

> Figure 5-2 plots the input base acceleration (at footing level) and floor-level

horizontal acceleration responses. Positive acceleration is from West to East or

from column axis D to column axis A. The 3rd floor-level peak acceleration was

approximately twice the input peak acceleration.

> Figure 5-3 plots the story shear responses (see Appendix C for story shear

calculation details). Positive shear here corresponds to a positive drift (from West

to East).

> Figure 5-4 plots inter-story horizontal drift ratio responses for all floor levels (i.e.,

differential movement between floors divided by the story clear height). The clear

height is used here for comparison purposes with other experimental column

component tests. As a note, positive displacement is from West to East or from

column axis D to column axis A.

> Figure 5-5 plots the minimum and maximum inter-story horizontal drift ratio

profiles.

70


3rd Floor0.4

•B - 0 . 2

- 0.4 504540302520T im e (s e c ) 2nd Floor

0.4

lirr-0.2

-0.4 5040 453025T im e (s e c ) 1st Floor

0.2

0

-0.2

-0.4

' 0.2

0

1 -0.2

-0.4

_L i15 25 30

T im e (s e c ) Footing

25 30T im e (s e c )

Figure 5-2: Footing andfloor-level acceleration records - Half-yield test

3rd Story

-10

-15, 35 40 4520 25Tim e (se c )2nd Story

-10

-15,Tim e (sec ) 1 st Story

-10

-15, 40 45 5020 25Tim e (sec )

Figure 5-3: Story shear records - Half-yield test

71


3rd Story

0.5

DS'o

isC -0.55 10 20 25 30 35 40 45 5015

Time (sec) 2nd Story

s? 0 .5

Q£■ocoI£C -0.5

5 10 15 20 25 30 35 40 45 50Time (sec)1st Story

JT 0.5

£ -0.5

Time (sec)

Figure 5-4: Inter-story horizontal drift ratio records - Half-Yield Test

140

E 120CO

g 100 00 4—O3c (Do

80

60

CD>CD

OO

40

2 0

0-1 -0.5 0 0.5

Min./Max. Inter-Story Drifts (%)

Figure 5-5: Minimum and maximum inter-story horizontal drift ratio profdesHalf-Yield Test

72


Figure 5-6 plots the inter-story horizontal drift ratios versus story shears for all three

floors. The maximum interstory drifts o f both the first and second stories were

approximately the same whereas the second-story maximum shear was significantly

lower than that o f the first floor. This behavior is to be expected given that the first-story

columns are essentially fixed at their base whereas the second-story columns have

flexible end conditions at both ends that render them less stiff with respect to interstory

drift. Also in this figure, a softening o f stiffness with increasing drift is evident. This can

be attributed to the observed concrete flexural cracking and is discussed in more detail in

Sections 5.3.2 and 5.3.3. The 2nd and 3rd stories do not show as much softening as the 1st

story.

toQ .

(0CD. cCO>.

COCD

.CCO

oocoCO•oc

CM -10 -10

-15 -15-0.4 -0.2 0.2 0.4 0.6 -0.4 -0.2 0.2 0.42nd Story Drift (%) 3rd Story Drift (%)

coa .

coCD

. cCOCDCOCOm

-10

-150.2 0.3 0.4 0.5

1st Story Drift (%)

Figure 5-6: Inter-story horizontal drift ratios vs. shears - Half-Yield Test

73


Figure 5-7 plots the first-story column inter-story horizontal drift ratios versus

column shear forces. The center two columns are stiffer than the outer two. This is

consistent with the higher fixity conditions at the top o f the middle two columns. Column

B1 has higher shear values than Column C l, which is due to the higher longitudinal steel

ratio present in Column B l. Likewise, Column A1 has higher shear values than Column

D1 and these two columns have higher shear contributions when their axial load

increases and lower shear contributions when their axial load diminishes. Column

softening with increasing drift is apparent.

Column D1 Column C1 Column B1 Column A1

-0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5 -0.5 0Drift (%) Drift (%) Drift (%) Drift (%)

Figure 5-7: First-story column inter-story horizontal drift ratios vs. shears -H alf-Yield Test

Figure 5-8 plots the first-story column inter-story horizontal drift ratios versus axial

loads. Negative axial load signifies compression. Axial load in the middle columns B l

74


and Cl tended to reduce when the frame swayed in their direction, and vice versa. This

same behavior was observed in the analysis o f this frame and is due to the particular

beam-to-column stiffness ratios used.


Drift (%) Drift (%) Drift (%) Drift (%)

Figure 5-8: First-story column inter-story horizontal drift ratios vs. axial loads -Half-Yield Test

5.3.2 Flexure-Shear-Critical Column Behavior

Figure 5-9 plots the horizontal drift ratios o f Columns A1 and B l versus their top and

bottom moments. This figure illustrates the large difference in top fixity condition

between the two columns. Column B l, which frames into two beams at its top, has top

moments that are only slightly lower than the bottom ones where the column can be

considered fixed rotationally by the very large footing. Column A l, which frames into

one beam at its top, has top moments much smaller than bottom moments due to this

75


lower fixity condition. To further quantify this effect, the top versus bottom moments for

these two columns are plotted in Figure 5-10 and a linear regression line is passed

through the data with its slope written on the plots. This figure shows that the top

moment in Column B l is about 90% o f the bottom one whereas the top moment in

Column A1 is only about 76% o f the bottom one. The linearity o f the trends as observed

in Figure 5-10 also suggests that the frame is excited mostly in its first mode during this

dynamic test.

Column B1 Column A1

Bot. Moment Top Moment

Drift ( /o

0Drift (%)

Figure 5-9: Columns A1 & B l top and bottom moments vs. drift ratios — Half-Yield Test

Softening o f Column B l is observed at a moment o f about 60 kip-in. (Figure 5-9)

This is consistent with the cracking moment obtained from sectional analysis for an axial

load o f approximately 25 kips. Column A1 only shows a slight softening behavior when

76


its moments exceeded the estimated cracking moments during this test. This could be due

to the column having previously been partially cracked during construction. Minor

flexural cracks have been observed in most frame elements prior to the

Half-Yield Test.

Column B1 Column A1

Q_

CLO

10 0 r

80-

60-

40-

2 0 -

0 -

-20

-40-

-60-

-80-

■10?oo

r ii i i i i i

1Yv«. i i

Slbpe=-0.9

i

1 0 0

80

60

40

~ 2 0

§ oEo^ -20 Q.Ol_ -40

-60

-80

-50 0 50Bot. Moment (kip-in.)

1 0 0-1 (

■ i ii i

Slope—0.76

I 1


1 0 0

Figure 5-10: Columns A1 & B l bottom vs. top moments - Half-Yield Test

Figure 5-11 plots the total rotations o f Columns A1 and B l measured over a 6 ”

height from the top o f the footing (for bottom moments) or the soffit o f the beam (for top

moments) versus top and bottom moments. These rotations are total rotations including

effects o f longitudinal bar slip in the footings and joints (Appendix C.2.7). This figure

also shows a softening o f both Columns A1 and B l as indicated earlier. There is a slight

shift in the rotation for Column B l at its top during the test for which no other

explanation was found other than that instrument may have slipped during the test. A77


comparison between top and bottom column rotations for Columns A l, A2, B l, and B2 is

presented in Figure 5-12. A fairly linear trend between top and bottom rotations for the

first-story columns can be observed. The ratio between top and bottom column rotations

is different than that between top and bottom moments for these columns as seen earlier

in Figure 5-10.

Column B1 Top Column A1 TopIUUi

50cQ.litCCDEo

Q.O -50

-10C

Rotation(h=6in) - (rad) Column A1 Bot.

•3x 10

100i

cD.1*§ o-Eo2CL,2 -5 0 “

-100*Rotation(h=6in) - (rad)

Column B1 Bot.■3

x 10100

cQ.lcCDEo2

-10C

Rotation(h=6in) - (rad) -3x 10

100r

cQ.

ca)Eo2om -50 -

-10C

Rotation(h=6in) - (rad) ■3x 10

Figure 5-11: Columns A1 & B l total rotations v.v. moments - Half-Yield Test

78


„x 10 Column B2

6

4

CD 2

coro 0 o& - 2H

-4

-6

x 10

-2 0 2 Bot. Rotation (rad)

Column B1


x 10

_1

1

ii

a.iii

Sbpe=-0i64 i1

i^ i

-----------

!1

_ 4 ----------11

-3

6

4

to 2coro 0oa:& - 2 H

-4

x 10 Column A2

-4

,x 1 0


Column A1

x 10


6-3

x 10

1 1 1 1

-1 -I 1 1 1 1 1 11 1

De=-0.561 ii i

-----------

i i i i

i i i i

6-3

x 10

Figure 5-12: Columns A & B bottom vs. top total rotations - Half-Yield Test

5.3.3 Ductile Column Behavior

Figure 5-13 plots Columns Cl and D1 inter-story horizontal drift ratios versus top

and bottom moments. This figure clearly demonstrates the large difference in top fixity

condition between the two columns, similar to that observed for Columns A1 and B l.

Figure 5-14 plots top versus bottom moments for these two columns, including a linear

regression line passed through the data with its slope written on the plots.

It is noted that the ratios o f top to bottom moments for the ductile columns (Cl and

D l) are much closer to unity than those o f the shear-critical columns (A1 and B l). This is

consistent with the lower longitudinal steel ratio in the ductile columns, which makes

79


them more flexible relative to the beams they frame into and thus makes their behavior

tend more to fixed-fixed end conditions.

Column D1 Column C11 0 0

cI

Q_

(/>-*—•C0Eo -20

-40

-60

-80

100-0.5 0.5

Drift (%)

100— Bot. Moment — Top Moment

cI

Q.

COcCDEo -20

-40

-60

-80

-100-0.5 0.5

(%)Drift

Figure 5-13: Columns C l & D1 inter-story horizontal drift ratios vs. bottom and top moments- Half-Yield Test

Also in Figure 5-13 a softening o f Column C l is observed to occur at a moment o f

about 60 kip-in.. This moment is higher than the cracking moment o f 45 kip-in obtained

from sectional analysis for an axial load o f approximately 25 kips. Column D1 shows a

softening behavior when at a moment o f about 18 kip-in. for an axial load o f 5 kips and

45 kip-in. for an axial load o f 14 kips. These moments are close to calculated cracking

moments.

80


Column D1 Column C11 0 0

80

60

40

~ 2 0

cCDEoCLoI-

0

-20

-40

-60

-80

1 "

---------- 11 1

11

l_ _L

_L

----------

O 1

1II 1

<DQ_O i

82

i ii i


100

100

40Ci

Q_

Slope=-•H—'cCDEo

-20Q.Ol" -40

- 6 0 -

-80--

- % o -50 0 50Bot. Moment (kip-in.)

100

Figure 5-14: Columns Cl & D1 bottom vs. top moments - Half-Yield Test

5.3.4 Bar slip

The frame was instrumented for longitudinal bar slip from adjacent anchorages

(footings or beam-column joints) at several interfaces (see Appendix A.5.5.3 for

instrumentation details). Figure 5-15 plots the bar slip versus section moment at the top

and bottom o f Column Cl and at the bottom o f Column B l. These plots show a clear

bilinear behavior in which the slope o f the response has the same steepness in tension and

compression prior to cracking o f the concrete and a much lower slope in tension past

concrete cracking.

81


Column C1 Top100

' I 50

C<DEo2Q.OH

-50

-100

Slip (in. ■3x 10

Column C1 Bot.100

cI

Q.'LCCDEo2

om

-100

Slip (in.)

Column B1 Bot.1 0 0

Q.

-50co

-100

x 10Slip (in.)

x 10-3

Figure 5-15: Bar slip vs. end moments - Half-Yield Test

An interesting phenomenon to note in Figure 5-15 is that the bar slip response

exhibits some energy dissipation particularly after softening o f the response in tension.

All the instruments in this figure upon reaching a maximum extension and initiating load

reversal exhibit a delay in slip values until a substantial drop in the forcing moment

occurs. One explanation o f this could be that the surface friction at flexural tension-crack

interface has to be exceeded before the crack can begin to close again. Possibility o f some

instrument stiction cannot be dismissed.

82


5.4 Dynamic Test 1 Results


Following the half-yield level dynamic test a high intensity dynamic test was applied

to the specimen. The same Llolleo Chile ground motion was used with an amplitude

scaling factor o f 4.06 from the original recorded ground motion. This test was intended to

collapse the structure but the frame proved more resilient than anticipated.

During Dynamic Test 1, some lead weights decoupled from the frame. Figure 5-16

overlays base shear histories derived from load cell readings and floor inertia calculations

(derived from floor masses and acceleration readings). This figure shows only minor

discrepancies between the two base shear curves prior to shear failure initiation o f

Column B l (t=22.45sec). First lead weight decoupling was observed in test videos to

occur at about the same time as Column B l initiated shear failure. After shear failure

initiation, observed discrepancies in base shear curves increased but remained relatively

small indicating that decoupling o f the weights did not significantly affect the dynamic

behavior o f the frame during testing.

83


20

coQ.

k_(00.c

CO0(/)0

CO-10

-20

22 23 24 25 2618 19 20 21Time (sec)

— Source: Accelerometers — Source: Load Cells

20

wQ.

CO0wTO

CO-10

-20

28 4226 30 32 34 36 38 40 44Time (sec)

Figure 5-16: Base shear comparison between load cell readings andfloor inertia calculation (from accelerometers) - Dynamic Test 1

84


Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Figure 5-17 through Figure 5-20 plot accelerations, story shears, inter-story

horizontal drift ratios, and minimum and maximum inter-story horizontal drift ratio

profiles for this test.

3rd Floor

40T im e (s e c ) 2nd Floor

1 I 1 1 ! 1 1

nil I' JjllljLlllliUJU...it......a. T w , -

i i i i i i i

T im e ( s e c )

Figure 5-17: Footing andfloor-level acceleration records - Dynamic Test 1

85


-20-30

Tim e (sec )1st Story

40Tim e (sec )

Figure 5-18: Story shear records - Dynamic Test 1

3rd Story

—W

40Tim e (sec ) 2nd StoryT

40Tim e (se c ) 1 s t Story

2010 30 40 50 60 70 80Tim e (sec )

Figure 5-19: Inter-story horizontal drift ratio records — Dynamic Test 1

86


Figure 5-20: Minimum and maximum inter-story horizontal drift ratio profiles -Dynamic Test 1

Figure 5-21 is a photograph o f Column B l at the end o f the test. The column

sustained damage visible in shattered concrete and buckled longitudinal reinforcement,

Damage elsewhere in the frame was markedly less severe (Appendix E).

Figure 5-22 plots the column inter-story horizontal versus vertical drift ratios for all

the columns. Vertical drift ratio is defined as the column lengthening divided by column

clear height o f 39 inches. The vertical instrument at Column C2 did not function

properly, thus no data are reported for Column C2. Noteworthy aspects include:

elongation o f Column C l, consistent with opening o f flexural cracks; and significant

shortening o f Column B 1 apparently associated with initiation o f column shear and axial

failure. In this figure and others to follow, a square marker shows the point o f initiation o f

shear degradation in Column B 1.

Figure 5-23 plots the inter-story horizontal drift ratio versus story shears for all three

stories. Nonlinear response is especially evident for the first story. Figure 5-24 plots the

87


first-story column inter-story horizontal drift ratios versus column shear forces. Nonlinear

column response is evident in Figure 5-24; in strain gauges attached to longitudinal

reinforcement that indicated yielding o f that reinforcement (Appendix C.4); and in the

visible damage to Column B l (Figure 5-21). Damage to Column B l apparently resulted

in shedding some axial load to neighboring Columns A1 and C l (Figure 5-25, in which

negative axial load corresponds to compression). This axial load shedding o f Column B l

also generated an uplift axial force in Column D l. The initiation o f shear failure in

Column B l was determined to start at t = 22.45 seconds into the test and is marked in all

relevant plots by a square marker.

Figure 5-21: Column B l damaged state - Dynamic Test 1

88


Ver

t. Dr

ift (

%)

Ver

t. Dr

ift (%

) V

ert.

Drift

(%)


0 0 0

1= -0.5

-5 0 5Horiz. Drift (%) Column D2

0.5

0

-0.5

-1

0.5

0

-0.5

-iL

-5 0 5Horiz. Drift (%) Column C2

-5 0Horiz. Drift (%) Column B2


0.5

0

-0 .5


-5 0Horiz. Drift (%) Column B1

-5 0 5Horiz. Drift (%) Horiz. Drift (%) Horiz. Drift (%)

-5 0Horiz. Drift (%) Column A2

t -0 .5

-5 0 5Horiz. Drift (%) Column A1

S -° -5 >

V. -0 .5

-5 0 5Horiz. Drift (%)

Figure 5-22: Column inter-story horizontal vs. vertical drift ratios - Dynamic Test 1

89


Shea

r (k

ips)

-3 0 , -302nd Story Drift (%)

-5 03rd Story Drift (%)

.9- 10

58 -10co

-5 -4 -3 -21st Story Drift (%)

Figure 5-23: Inter-story horizontal drift ratios vs. shears - Dynamic Test 1


X :-2 .8 5 , Y :-6 .9 3 -

:-3 .1 5 , Y :-9 .8 9

-5 0 5Drift (%)

-5 0 5Drift (%)

-5 0 5Drift (%)

-5 0 5Drift (%)

Figure 5-24: First-story column inter-story horizontal drift ratios vs. shears - Dynamic Test 1

90


T------ 1 ---------- 1----- —------1--------- 'Column B1 Shear Failure Initiation ------Column A1

1 5 ------Column B1

i t ' MI ' ' ^ .......Column C1

J H ! ! 1 ■ i :Mi i Li i

Column D1L il l i Isitt 11! i , 1 L _ ---------

Column D1 Column D1

Column B1

Column A1Column A1

Column

Column B1

Column C1

30~ 40 50Time (sec)

10 20

Figure 5-25: First-story column axial load histories - Dynamic Test 1

Column B1 Shear Failure Initiation

© - 0.1

Footing B0|— Joint B1 Joint B2

22.5 Time (sec)

Figure 5-26: Vertical acceleration histories o f Footing B0 and Joints B l and B2 around the time o f Column B l shear failure- Dynamic Test 1

91


As can be seen in Figure 5-25, the axial load degradation o f Column B l occurred

over a span o f approximately 12 seconds. One degradation initiated, its duration roughly

coincided with the duration o f strong base motion. The axial load shed by Column B l at

the end o f the test is approximately 10.7 kips, which is taken up by an additional 4.3 kips

in Column A l, 8 . 8 kips in Column C l, and an uplift force o f 2.4 kips in Column D l. Due

to the gradualness o f the axial degradation o f Column B l, its initiation is difficult to

pinpoint and appears to start just after shear degradation is initiated in this column.

Vertical accelerations at Joints B l and B2 (Figure 5-26, positive vertical acceleration

upwards) show only slight increases in vertical accelerations just after initiation o f shear

and axial failure in Column B l, and it is unclear whether these are due to the failure or

due to another characteristic o f the frame response to the ever-varying input motion.

From Figure 5-23 we note that the maximum drift ratios o f both the first and second

stories were approximately the same but the second story maximum shear was

significantly lower that that o f the first story. This is partly due to the difference in end

fixity conditions between the first and second-story columns. The first and second stories

also show more nonlinearity than the third story. Strain gauge readings in Columns A l,

A2, B l, B2, and Beam AB1 show that all the longitudinal steel in these members has

yielded (Appendix C.4).

During this test, Column A l developed a shear crack at its base which could be seen

to open and close in the test videos. Column A l did not, however, show any shear or

axial capacity degradation at this stage. Shear and flexural cracks could also be observed

in the beams, with greater cracking severity in beams AB and BC at all levels. The more

extensive cracking in beams AB and BC may be attributable to increased forces and

92


deformations associated with their action to redistribute approximately 10.7 kips o f load

from Column B to Columns A and C. Also during this test, joints showed shear cracking

and in some cases spalling, with most severe damage at Joints A l and B l. Photographs o f

all locations are in Appendix E.


Figure 5-28 through Figure 5-38 plot various response quantities measured for

Columns A l, B l, A2, and B2. In relevant figures the point o f initiation o f shear force

degradation in Column B l is identified by a square marker and pertinent response values

at that point are written on the figures. Table 5-3 summarizes these response values. In

Figure 5-27 and Figure 5-28 the first appearance o f a shear crack is marked with a

diamond marker.

Figure 5-27 plots the dilation (that is, widening o f the column cross section in the

plane o f the frame) measured 6 in. above the top o f the footing for Columns A l and B l.

The values for this plot were taken directly from the displacement potentiometer that was

attached to the column horizontally at that level. Positive values signify extension (or

crack opening). Figure 5-28 plots the column inter-story horizontal drift ratio versus story

shear for Columns A l and B 1.

Shear failure o f Column B l is initiated at a drift o f approximately -3.15% and a

shear force o f -9.9 kips, as identified by a square maker in Figure 5-28. Shear failure is

defined here as the initiation o f shear force degradation associated with the development

o f a large shear crack in the column. As can be seen in Figure 5-27 a small shear crack

formed at the base o f Column B l (diamond marker, Figure 5-27 and Figure 5-28) during

a drift cycle prior to the cycle in which shear force degradation and larger crack opening93


occurred in the opposite direction (square marker, Figure 5-27 and Figure 5-28). The

initial shear cracking o f the column was not chosen as the point o f shear failure initiation

as the column showed no shear force loss at that point.

Figure 5-29 shows six video-frame captures o f the lower portions o f Column B l at

selected times. Table 5-2 provides the times for these captured frames and a description

o f the events they are showing.

Figure 5-30 plots the inter-story horizontal drift ratios versus axial loads for Columns

A l and B l. Negative axial loads signify compression. At the designated time o f shear

failure o f Column B l (22.45 seconds into the test), Column A l was experiencing -2.85%

drift and -6.9 kips shear. The difference in horizontal drifts between the two columns is

due to lengthening o f the beam between them. The axial loads in Columns A l and B l at

that time are, respectively, 1.18 kips (tension) and -24.8 kips (compression). Also, the

critical section bottom rotations o f Columns A l and B l at that point are 0.0258 rad and

0.0265 rad, respectively. Table 5-3 summarizes the relevant column response values at

the initiation o f the shear failure o f Column B l for both Columns A l and B l.

Figure 5-31 plots the inter-story vertical drift ratio history o f Column B l. Figure

5-32 plots the inter-story horizontal versus vertical drift ratios for Column B l. Figure

5-33 plots the axial load versus inter-story vertical drift ratio for Column B l.

Figure 5-34 plots the inter-story horizontal drift ratio versus bottom and top moments

for Columns A l and B l. Figure 5-35 plots the column critical section rotations versus top

and bottom moments for Columns A l and B l. The rotations mentioned here are total

rotations measured over a length o f 6 ” at either end o f the columns and include the effects

o f bar slip. Figure 5-36 plots the inter-story horizontal drift ratios versus top and bottom

94


critical section rotations for Columns A l and B l. Instruments at top o f Columns A l and

B l were impacted during the test just after shear failure o f Column B l. Their values were

zeroed from that point onward and an X is marked on the figure just after the zeroing

(i.e., the figure shows a few time steps after zeroing to illustrate the impact).

Figure 5-37 plots the column critical section rotations versus shears for Columns A l

and B l. Figure 5-38 plots the bottom versus top column critical section rotations for

Columns A l, B l, A2, and B2. Instruments at top o f Columns A l, B l and B2 were

impacted during the test, Column B2 at around t = 15.0 seconds and Columns A l and B l

just after shear failure o f Column B 1. Their values were zeroed from that point onward

and an X is marked on the figure just after the zeroing.

95


Figure 5-27:

C

I 0.12II

CO w ‘ 1 c8 0.08 (0

° 0 .0 6 ------------<I 0 .0 4 ------------

Q 0 . 0 2 ---------1

E

CD

- ° < -------- 3525Time (sec)

0.5

® 0.4

2 0 3025 35Time (sec)

Columns A1 and B1 dilation history at h-6in. from bottom — Dynamic Test 1

96


Column B1 Column A1

(AQ_!*:

Q.

COCD

_c:

X:-2.85, Y:-6.93

X:-3.15, Y:-9.89+- -10-1 0 ,6

Drift (%) Drift (%)

Figure 5-28: Columns A1 & B l inter-story horizontal drift ratios versus shears - Dynamic Test 1

Table 5-2: Column B l shear failure photograph descriptions - Dynamic Test 1

Frame Approx. Time (sec)

Description

( 1 ) 22.38 One frame prior to shear failure initiation(2 ) 22.45 Shear failure initiation(3) 22.98 First large shear crack in other drift direction(4) 25.11 Significant spalling on East side o f column, bar buckling and

start o f visible vertical collapse(5) 28.18 Column condition almost at the end o f “strong” shaking(6 ) 51.78 Column condition at end o f test

97


(5) t = 28.18sec. (6 ) t = 51,78sec.

Figure 5-29: Column B l bottom shear failure photographs - Dynamic Test 1

98


Axi

al L

oad

(kip

s)

Axi

al L

oad

(kip

s)

Column B1 Column A1

X:-2.85, Y:1.18 -

X:-3.15. Y:-24.75

-2 0 2 Drift (%)

Column B1

-2 0 2 4Drift (%)

Column A1

X:-2.85, Y:1.18

Q.

•20

25 •25

X:-3.15, Y:-24.75

6Drift (%) Drift (%)

Figure 5-30: Columns A1 & B l inter-story horizontal drift ratios versus axial loads (full test and 21.95 < t < 23.10 sec.) - Dynamic Test 1

99


Ver

tical

Drif

t (%

) V

ertic

al D

rift

(%)

Column B10.5

X:22.445, Y.--0.060

10 10 20 30 40 50 60 70 80Time (sec)

Column B10 .5| I ; I I I I I I I I I I ! I I r-

20 22 24 26 28 30 32 34 36Time (sec)

Figure 5-31: Column B l inter-story vertical drift ratio history - Dynamic Test 1

100


Ver

tical

Drif

t (%

)

Column B1T T T r i T n M : M ! N i ! M M M M 1 M 1 1 ! M I I M ! ! ! M ! 1 M 1 1 5 ! : 5 : i 1 i i

: : : : : : : : : 1 : : i : : : : : : 1 : : : : : : : : : 1 : : : : : : : : : 1 : : : : : : :I + f 1

: : : : : : : : :

* * , *_*. *

.......................; ....................................(.............................. * : ..........................

: : : ' * 4 * 4 * . ♦

...*..4— »•••»•••»—

•••*•••

............................................................... - - — » - - - .....................................

l t 1 M ! i 1 , I

-6 -4 -2 0 2 4 6Horizontal Drift (%)

Figure 5-32: Column B l inter-story horizontal vs. vertical drift ratios - Dynamic Test 1

101


Column B1

X:-24.75, Y:-0.060 Degrading Slope

Instantaneous Axial Stiffness:

-20 -15Axial Load (kips)

Column B10.5

X:-24.75, Y:-0.060

Qroot0> ■0.5

Axial Load (kips)

Figure 5-33: Column B l axial load vs. inter-story vertical drift ratio (full test and 21.95 < t < 23.10 sec.) — Dynamic Test 1

102


Column B1 -X:-3.15, Y:201.25-

Column A1

o -50

X:-3.15, Y:-211.67I ......... ..

Drift (%)

200

150

1 0 0

■? 50Q.

CO 0c <do -50

-100

-150

-200

- 6

. . ...r_.4...|______ £__ I____ 4 ..... . . . . U - —4—I—i—. - i~ fA

.......~y

Y - o o r Y - 1QO o q T ’ " " '/ i^ A .- Z .O O , Y . o o , 2 o _ r... ... ^ S h e — t / i - 1- /■

... .. ...I V lA i w l [ T : / | J T /

- r~i T l i j r ^ w T r 7 > r fa r ;/..

.... i ViSVjt H \ I jfflffflS 1 rJ f- w ittp H - j B H t B

...r l H W n H l n m ^

.....V r a w u m m r i

:: I.........r f : i....... i

E IE

/ll/n i

^ r r T i ^ ^ f f { *i r T T ™ H B i 1

i I :!

I Z m - - u | f l R W L \ - i V - - ... .. ....

\ Jppi k — V f \ - u - ..... -j \ t ffij n l n \j \

\ “ r l r f H ® n r n

..._ i - p . : . - . p p ....... ...- . . . y , a p r V. A OC y r A 1 i \\ . ~ ^ .O 0 , I . lO O . /O ^ i A ^

: ------

v-T

T o p M o m e n t

- 2 0Drift (%)

Figure 5-34: Columns A1 &B1 inter-story horizontal drift ratios vs. top and bottom moments - Dynamic Test 1

Column B1 Top Column A1 Top

200 200

.£ 100 .£ 100

-100 -100

200_ X:0.0132, Y:-135.75 J-0.06 -0.04 -0.02 0

_200 X:0.0207, Y:-211.67-0.06 -0.04 -0.02 0 0.02 0.04 0.060.02 0.04 0.06

Total Rotation over h=6in. - (rad) Column B1 Bottom

Total Rotation over h=6in. - (rad) Column A1 Bottom

X:-0.0265, Y:201.25200 200 X:-0.0258, Y:133.28

'S . 100 100

3 -100 3 -100

-2001- - - j --0.06 -0.04 -0.02

-2001------ I---- 4 --0.06 -0.04 -0.020 0.040.02 0.06 0 0.02 0.04 0.06

Total Rotation over h=6in. - (rad) Total Rotation over h=6in. - (rad)

Figure 5-35: Columns A1 & B l critical section rotations vs. top & bottom moments - Dynamic Test 1

103


Column B1 Top Column A1 Top0.06

0.04

<g 0.02

■5 -0.02

-= -0.04

-0.06,

Drift (%)Colum n B1 Bottom

0.06

0.04

<S> 0.02

= - 0.02

™ -0.04

-0.06,

Drift (%)

Figure 5-36: Columns A1 & B l relative section rotations - Dynami

0.06

0.04

<S> 0.02

■S - 0 .0 2

m -0.04

-0.06,

Drift (%)Column A1 Bottom

0.06

0.04

0.02

■S - 0 .0 2

m -0.04

-0.06,

Drift (%)

horizontal drifts v.v. top and bottom critical 2 Test 1

Colum n B1 Top

wo_

X:0.0207, Y:-9.87-0.04 -0.02 0 0.02 0.04 0.06

Total Rotation over h=6in. - (rad)Column B1 Bottom

10

-5

‘19.06

rim

------

/ r X:-0.0 265, Y:-9.87-0.04 -0.02 0 0.02 0.04

Total Rotation over h=6in. - (rad)

10Column A1 Top

10

-5

0.06 "-(9.06

------- 1 II r •* r

-

X:0.0132, Y:-6.91"-(9.06 -0.04 -0.02 0 0.02 0.04

Total Rotation over h=6in. - (rad) Column A1 Bottom

0.06

/ J O

| w f f l ' J

X:-0.0258, Y:-6.91-0.04 -0.02 0 0.02 0.04

Total Rotation over h=6in. - (rad)0.06

Figure 5-37: Columns A1 & B l critical section rotations vs. shears - Dynamic Test 1

104


C olum n B2 C olum n A2

0.06

0.04

2 0.02

ro us.a . - 0 . 0 2 o

-0.04

-0.06

0.060.06

0.040.04

5 0.02<5 0.02

d . - 0 . 0 2o . -0 .0 2

-0.04-0.04

0.02 0.04 0.06 - ° ^ 0 6 -0.04 -0.02'?(?06 -0.04 -0.02 0.02 0.04 0.06Bottom Rotation (rad)

C olum n B1Bottom Rotation (rad)

C olum n A1I I 1

1 1X:-0.0265 Y:0.0207-------

i i II I l1 1 1

1 1 1 1 1 ^1 1 11 ! 1 1 1 11 1 1

-0.04 -0.02 0 0.02 0.04 0.06Bottom Rotation (rad)

0.06

0.04

2 . 0.02 Coco 0oo'o . -0 .0 2ol-

-0.04

-0.06

-------

I I

X:-0.0258 Y: 3.0132 ____

-0.04 -0.02 0 0.02 0.04 0.06Bottom R otation (rad)

Figure 5-38: Columns A1 & B l bottom v.s\ top critical section rotations - Dynamic Test 1

Table 5-3: Columns A1 & B l states at initiation o f Column B l shear failureColumn B l Column A1

Horizontal Drift (%) -3.15 -2.85Shear Force (kips) -9.89 -6.93Axial Force (kips) -24.7 1 . 2

Bottom Moment (kip-in.) 2 0 1 133Bottom Rotation (rad) -0.0265 -0.0258Top Moment (kip-in.) - 2 1 2 -136Top Rotation (rad) 0.0207 0.0132

Column B l underwent a relatively large drift excursion in the positive direction

(max. drift=4.10%) just prior to failing in shear during the subsequent negative drift

excursion. Figure 5-35 shows that the maximum rotation reached in the preceding

positive drift is about 0.0473 rad while the axial load in B l at that point was about -17.7

kips (Figure 5-30). The recorded moment at the bottom o f Column B l during that105


maximum positive drift excursion was about -179 kip-in. and is lower than the bottom

moment at shear failure initiation which was about 212 kip-in. (Figure 5-34). Likewise,

the maximum shear during that positive drift excursion was slightly lower than at shear

failure and registered at about 9.5 kips (Figure 5-28). Both the shear and moment reading

are consistent with the observed axial load readings, which were lower in the positive

drift direction than in the negative drift direction. Apparently, the column was able to

sustain larger drifts and rotations under the lower axial loads o f the positive-drift

excursion than it was able to sustain under the higher axial loads o f the negative-drift

excursion. Accumulated damage may also have contributed to the subsequent failure at

lower drift in the negative-drift excursion.

Following the initiation o f shear failure, Column B l is seen in Figure 5-28 to reach a

residual shear strength o f about 2 kips This residual shear capacity subsequently degraded

gradually as the shaking progressed to reach a low o f about 1 kip, though the behavior is

erratic.

Figure 5-35 and Figure 5-38 show that the maximum plastic rotations incurred by the

top section o f the column generally were smaller than those at the bottom. The behavior

is attributed to the lower end fixity condition o f Column B l at the top when compared

with the bottom. Previous tests (see Chapter 2) have shown that shear failure is positively

correlated to the level o f inelastic deformation. The larger rotations at the base o f the

column, thus, may explain why the failure o f Column B 1 was at the bottom o f the column

rather than the top. (Note that the frame was cast in a horizontal position, so the usual

variations in concrete quality along column height were not present.)

106


Figure 5-36 shows a nearly linear relation between interstory drift ratio and rotation

along the top and bottom 6 in. o f the column length. This nearly linear relation extends

into the post-yield range, and is seen in both Columns A1 and B l, which have different

top fixity conditions (one-beam framing as opposed to two-beam framing). To quantify

these linear relations, standard linear regressions were run on the data from t= 1 0 sec. (to

eliminate very low amplitude bias) up to the initiation o f shear failure in Column B l,

with the following results:

Column B 1: Top Rotation (rad) = -0.44 x Bottom Rotation (rad) (R2 = 0.73)

Bottom Rotation (rad) = 0.0085 x Horizontal Drift (%) (R2 = 0.93)

Column A 1: Top Rotation (rad) = -0.58 Bottom Rotation (rad) (R2 = 0.91)

Bottom Rotation (rad) = 0.0076 Horizontal Drift (%) (R2 = 0.98)

Figure 5-25 and Figure 5-31 show that the axial degradation o f Column B l occurs

gradually over a period o f about 1 2 seconds, which corresponds to the period o f strongest

shaking after initiation o f shear failure. As such, it is difficult to identify exactly the point

o f initiation o f axial failure in the column, which seems to start almost immediately after

shear failure is initiated. During the degradation, axial load and axial deformation o f

Column B l have very large oscillations with a degrading mean (Figure 5-25, Figure 5-30,

and Figure 5-31). This behavior is evident immediately after shear failure initiation; axial

load drops to a low o f 16.7 kips at a drift o f -4.7% and picks-up again to its original

levels upon load reversal. This change in axial load is consistent with the axial

deformation behavior o f Column B 1; it shortens immediately after shear failure initiation

by about -0.54% and lengthens again to its undamaged values upon load reversal (Figure

5-32). This behavior can be seen in the test video showing the base o f Column B l (Figure

107


5-29). Apparently, in the cycles following shear failure initiation, Column B l pivots

around the remaining compression block at bottom o f the shear crack (marked in Figure

5-29). This pivoting generated an up and down movement that correlates well with

horizontal drift as seen in Figure 5-32. This occurs until the shear crack and compression

block are sufficiently damaged to no longer support the pivoting motion. At that point we

observe a gradual vertical drop in the column during both positive and negative drift

excursions. This transition occurs at a time o f approximately 28 seconds into the test.

Figure 5-33 indicates that the vertical drift oscillates significantly (for example, just

after the shear failure the column drops notably but then rises back to almost its original

vertical position upon load reversal. At any one time, however, there tends to be an

instantaneous axial stiffness as illustrated in the upper part of Figure 5-33, which tends to

remain nearly constant during the test. Superimposed on this, however, there is a trend

for decreasing column length with cycling with nearly linear trend line between axial

load and axial deformation. The observed behavior can be attributed partly to the

relatively constant stiffness o f the surrounding framing elements, which are relieving

Column B 1 from its axial load. The rate at which axial shortening accumulates likely is

linked to the rate at which “large” horizontal drift cycles occur, causing low-cycle fatigue

damage. Both the instantaneous and the degrading slopes are illustrated in Figure 5-33.

Figure 5-30 and Figure 5-31 show that the “instantaneous” oscillations in axial load

are un-related to the drift cycles o f the frame and instead have an oscillation period o f

about 0.7 to 1.0 sec. These periods are much longer than those o f the shaking table

vertical acceleration inputs (Figure 5-26). This behavior seems to indicate that the loss o f

vertical load carrying capacity o f a frame element is accompanied by dynamic vertical

108


oscillations that are related to the stiffness o f the framing elements relieving the

collapsing element from its axial load. The vertical dynamic amplifications resulting from

these oscillations are minor though compared with the gradual axial load loss in Column

B l ((Figure 5-26).

Figure 5-28, Figure 5-30, Figure 5-34, and Figure 5-35 show that Column A1

experiences horizontal drifts, axial loads, moments, and rotations similar to those o f

Column B 1 during the positive drift excursion just preceding the shear failure o f Column

B l. The major difference between behavior o f these two columns arose during the

negative drift excursion what resulted in axial tension in Column A1 and that caused

shear failure in Column B l. Because o f the tensile axial load, the moments and shears in

Column A1 were much lower than those in Column B l Thus, axial tension likely

protected this column from shear failure during the critical cycle that failed Column B l.

Subsequent to the shear failure o f Column B l and until the end o f this test, Column A1

did not sustain as high a combination o f plastic rotations and axial loads as those that

caused shear failure in Column B l.

Longitudinal reinforcement strain rates were estimated from strain gauge readings

During the deformation cycle just prior to the initiation o f shear failure o f Column B l,

calculated strain rates for Columns A1 and B l ranged from 0.05 to 0.2 (1/sec). Strain

rates in this range can result in measurable increase in material stress capacities (Malvar

1998). This subject is further analyzed in Chapter 6 .

In conclusion, critical section rotations seem to be a deciding factor in the shear and

axial failure o f these columns. Furthermore, axial load appears to play a major role in the

shear and axial failure, both by determining the demands (higher axial load resulted in

109


increased moment strength and, hence, shear demand) and possibly influencing the

capacity. These aspects are further considered in subsequent chapters.


Figure 5-39 plots the inter-story horizontal drift ratios versus story shears for

Columns Cl and D l. Figure 5-40 plots the inter-story horizontal drift ratios versus axial

loads for Columns Cl and D l. Figure 5-41 plots the inter-story horizontal drift ratios

versus bottom and top moments for Columns C l and D l. In all figures the point o f

initiation o f shear degradation in Column B l is identified by a square marker and

pertinent response values at that point are written on the figures.

Both Columns Cl and D l experienced yielding o f their longitudinal reinforcement at

their top and bottom sections. Due to the axial failure o f Column B l, Column C l picked

up additional compressive axial load while Column D l was uplifted. Extensive flexural

cracking was observed at their ends after the test.

110


Column D1 Column C1

• * | X:-3.37 Y:-6 25 r r H r • X:-3.37 Y:-6 79 ► r• ‘ ~ t i r r r r rn

0Drift (%)

-2 0 2 Drift (%)

Figure 5-39: Columns C l & D l inter-story horizontal drift ratios vs. shears - Dynamic Test 1

Column D1 Column C1

•X:-3.37 Y:-21.7

X:-3.37 Y:-17.1

Drift (%)0 2

Drift (%)

Figure 5-40: Columns Cl & D l inter-story horizontal drift ratios vs. axial loads - Dynamic Test 1

1 1 1


Column D1 Column C1

Bottom Moment Top Moment X:-3.37 Y: 118.1

X:-3.37 Y:115.05

n

X:-3.37 Y:-150.6kM-X:-3.37 Y:-174.4

Drift %

Figure 5-41: Columns Cl and D l horizontal drift vs. top & bottom moments - Dynamic Test 1

5.4.4 Bar slip

Figure 5-42 plots the bar slip versus bottom and top moments o f Column Cl and

bottom o f Column B 1 (this figure marks the point o f initiation o f shear failure in Column

B l with a square marker). These plots show a roughly bilinear behavior in which the

slope o f the response is much steeper in compression than in tension.

Figure 5-43 plots the bar slip versus column critical section rotation (this figure

marks the point o f initiation o f shear failure in Column B l with a square marker). This

relation is nearly linear well past the yielding o f the longitudinal steel.

1 1 2


C olum n C1 Top

X:0.0046 Y:-174.45-200 -

0 0 .05Slip (in.)

C o lum n C1 Bottom

0.15

C o lum n B1 B ottom

200

X:0.0986 Y:118.13C£ 100

cCDEo

§ -100oID

0 .05 0.1 0.150

200X:-9.56e-005 Y :201.25

_c

£ 100

cIDEoS

0 0.05 0.1 0.15Slip (in.)

Figure 5-42: Bar slip vs. end moments — Dynamic Test 1

Column B2 Top

Slip (in.)

0.01

0.005-oroconj -0.005

- 0.01

-0.015.

Slip (in.)

Column B1 Bottomx 10

-3

0.06

0.04

0.02co

- 0.02X:-9.56e-005 Y:-0.0265

-0.04-0.06 -0.04 - 0.02 0.02 0.04 0.06 0.08

Slip (in.)

Figure 5-43: Bar slip vs. end rotations - Dynamic Test 1

113


5.5 Dynamic Test 2


After the re-fastening o f all lead weights on the frame, a second high-intensity

dynamic test was run with nominally the same base motion as in Dynamic Test 1. This

test was intended to collapse the structure.



profiles for this test.

3rd Floor

H f#

1.61

0

-1■1.6

30 40T im e ( s e c )

50 60 70 8010 20

Figure 5-44: Footing andfloor-level acceleration records — Dynamic Test 2

114


3rd Story

r tUtfyHffrim rX -flUTf i ~1j j u~ ' 1 1 iTi| -*•[/* -

40 50Tim e (sec )2nd Story

_ 20

-20-30

4 0Tim e (sec )

50 70 80

1st Story


3rd StoryT T

-20-30

Tim e (se c )

0

-5 _ l_10 2 0 3 0 40

T im e (s e c ) 2nd Story

50 60 70 80

S' 5

4 0T im e ( s e c ) 1st Story

10 20 30 4 0 50 60 7 0 8 0T im e ( s e c )

Figure 5-46: Inter-story horizontal drift ratio records - Dynamic Test 2

115


140

R 1 2 0coECDCl)m

CCDO

1 0 0

80

60

a>>Cl)OO

40

20

-6 -4 -2 0 2 4Min./Max. R elative Drifts (%)

Figure 5-47: Minimum and maximum horizontal relative floor drift profdes Dynamic Test 2

Figure 5-48 shows photographs o f Column A1 at the end o f the test. The column

shows severe damage but not total collapse. Additional photographs are in Appendix E.

Figure 5-49 plots the column inter-story horizontal drift ratio versus vertical drift

ratio for all columns. The vertical instrument at Column C2 was found to be defective,

thus the joint C2 displacement plot is not available.

Figure 5-50 plots the inter-story horizontal drift ratio versus story shear for all three

stories. In this and subsequent figures o f this section, the initiation o f shear degradation in

Column A1 is identified by a square marker and pertinent response values at that point

are written on the figure.

Figure 5-51 plots the first-story column inter-story horizontal drift ratio versus

column shear force, Figure 5-52 plots the axial load histories o f all four first-story

columns, and Figure 5-53 plots the vertical accelerations recorded at Footing B0, and

Joints B l and B2.

116


Vert.

Drif

t (%

) V

ert.

Drift

(%

) V

ert.

Drift

(%

)

Figure 5-48: Column A1 damaged state - Dynamic Test 2


WE -0 Q -c £ - 1



0.5

g 0itT -0.5 O

> -1 .5

-5 0 5Horiz. Drift (%) Column B2


0.5

0

-0.5

-1

-1 .5

-2

0.5

0

•c ° -1

i a> -1-5

1 1 1 1 -1 1

0 .5 r 0.5

1 1 1sO U ' 0 s 0s

1 1 1Q 1 Q -11 1 !

1 1 !

1 1£ -1 .5 -

.0 -

i i ii i i

i i i i i------------- 1_

> -1 .5

-9

i i i

i i i _L I i



-5 0 5Horiz. Drift (%) Column B1


0.5

0

-0 .5

-1

-1.5

-2

0.5

^ 0 0s-

} 1 r 0.5

5 0 0s-

i ■1 1 f ii i ii j ii i i

0 .5

5 0 0s-~ r ------ --------------- - i c -0 .5

■c- r --------- ----------------1- rif

t' © Ol

!— — Ia -0 .5 ■c

_ ,---------_ ----------

i i D -1 ■e

i J a -1 ■e

Q -1■c

_L _ _ _ _ J ----------- 1_.i i '

i i i i i i

> -1-5

-2t — i — r

> -1.5

-2

> -1 .5

-2 _i_ 1 I

Horiz. Drift (%)-5 0 5

Horiz. Drift (%)-5 0

Horiz. Drift (%)-5 0 5

Horiz. Drift (%)

Figure 5-49: Column inter-story horizontal vs. vertical drift ratios — Dynamic Test 2

117


£ 10

-2 -1 0 1 2 3 4 52nd Story Drift (%)

-5 -4 -3 -2 -1 0 1 23rd Story Drift (%)

-15

-20,1st Story Drift (%)

Figure 5-50: Inter-story horizontal drift ratios ra. shears - Dynamic Test 2

Column D1 Column C1 Column B1

-5 0 5Drift (%)

0 5Drift (%)

-5

Column A1

0 5Drift (%)

X:3.26 Y:7.25J -

-5 0 5Drift (%)

Figure 5-51: First-story column inter-story horizontal drift ratios vs. shears Dynamic Test 2

118


Co umn A1 Shear Failure Initiation

Column Q1

Column

<S -15Column A1

Column C1

Column A1 Column B1 Column C1 Column D1

30 40 50Time (sec)

Figure 5-52: First-story column axial load histories - Dynamic Test 2

0.5 Footing BO Joint B1 Joint B20.4

0.3

0.2O)

0oo< oCDOC -0 .1 0 >

- 0.2

-0.3

-0.4 Colum n A1 S h ea r Failure Initiation

20.5 21.5 Time (sec)

22 22.5 23

Figure 5-53: Vertical accelerations o f Footing B0 and Joints B l and B2 during strong shaking - Dynamic Test 2

119


Although Column A1 sustained significant shear damage (Figure 5-48), it did not

shorten significantly (Figure 5-50), and continued to support axial load including

additional load that was further shed from Column B l (Figure 5-52). Column B l

continued to degrade during this test, sinking another 0.3 inches or 0.7% vertical inter

story drift ratio to a total o f approximately 0.6 inches or 1.4% vertical drift shorter than

its original undamaged state. Its shear resistance during this test hovered around a

residual values o f less than 1 kip while its axial load was reduced to about 5 kips

(compression). The difference in axial load was taken up by Columns A1 and C l while

Column D l was uplifted slightly in the process (Figure 5-52).

The axial load degradation o f Column B l continued in this test, most notably during

periods o f more intense base shaking. As in Dynamic Test 1, vertical dynamic

amplification, if present, was not prominent (Figure 5-53)

The maximum interstory drifts o f both the first and second stories were

approximately the same (about 4%) while that o f the third story was somewhat smaller

(about 3%) (Figure 5-50). The second-story shear was slightly higher than that o f the first

story at the time o f maximum lateral drift, reflecting the reduced resistance o f the first

story. The relations between lateral interstory drift ratio and story shear in the second and

third stories showed stiffening with increasing drift, while the first floor exhibited a

degrading stiffness.

Apart from damage to Column A1 and B l, column and beam frame members did not

show any substantial change in their crack patterns during this test. Joints showed

additional shear cracking and some spalling, particularly the first floor joints and the edge

joints. For pictures o f the frame components after this test see Appendix E.

120



Figure 5-54 through Figure 5-64 plot the various response quantities measured for

Columns A l, B l, A2 and B2. In relevant figures up to five behavioral milestones are

marked with the following markers:

1. Square: Shear crack opening and initiation o f shear failure

2. Diamond: First cycle o f shear strength degradation

3. Circle: Enlargement o f shear crack and further shear strength degradation (1st peak)

4. Five point star: Enlargement o f shear crack and further shear strength degradation

(2 nd peak)

5. Six point star: Enlargement o f shear crack and further shear strength degradation

(3rd peak)

These five milestones are presented in Figure 5-55 and Table 5-4. Pertinent response

values corresponding to the initial square marker are written on the figures. Table 5-5

summarizes these response values.

121


Column B1 Column A1

114 JJ . -X 3 26 Y:7.25

y , /* ' • /Vi

, ' / L

-2 0 2Drift (%) Drift (%)

Figure 5-54: Columns A1 & B l inter-story horizontal drift ratios vs. shears - Dynamic Test 2

Table 5-4: Column A l shear failure photograph descriptions — Dynamic Test 2

Frame Approx. Time (sec)

Description

( 1 ) 21.48 Shear crack opening and initiation o f shear failure(2 ) 22.29 First cycle o f shear strength degradation(3) 28.28 Enlargement o f shear crack and further shear strength

degradation ( 1 st peak)(4) 28.54 Enlargement o f shear crack and further shear strength

degradation (2 nd peak)(5) 29.98 Enlargement o f shear crack and further shear strength

degradation (3rd peak)(6 ) End o f test

1Condition at end o f test |

122


(5) t = 29.98sec. (6 ) End o f Test

Figure 5-55: Column A l bottom shear failure photographs - Dynamic Test 2

123


Botto

m Co

lum

n A1

Di

latio

n at

h=6i

n. (

in.)

e Bo

ttom

Colu

mn

A1

Dila

tion

at h=

6in.

(in

.)

40 50 60Time (sec)

90 100

re 5-56: Column A l dilation history at h=6in. from bottom - Dynamic Test 2

-1 0 Drift (%)

124


Figure 5-57: Columns A l inter-story horizontal drift ratio vs. dilation at h=6in.from bottom — Dynamic Test 2

Column B1 Column A1

X:3.26 Y:-21.47

Drift (%) Drift (%)

Figure 5-58: Columns A l & B l inter-story horizontal drift ratios vs. axial loads - Dynamic Test 2

125


Column A1

t -0.05

-0.15

30 40 50Time (sec)

Column B1

Column A1 Shear Failure Initiation

30 40 50Time (sec)

Figure 5-59: Columns A l & B l inter-story vertical drift ratio history — Dynamic Test 2

126


C olum n B1

L_

Q15o'■ eCD>

Dynamic Test 2 Dynamic Test 1

-1 .5-

-30 -25 -20 -15 -10Axial Load (kips)

Figure 5-60: Column B l axial load vs. inter-story vertical drift ratio — Dynamic Tests 1 & 2

Column B1 Column A1

Top Moment Bottom Moment

X:3.26 Y:157.1

w .

• * - s'ftffrvsv. v w;i -

::

X :3 .2 6 Y :-1 5 2 .9

Drift (%)- 6 - 4 - 2 0 2

Drift (%)

Figure 5-61: Columns A l & B l inter-story horizontal drift ratios vs. top and bottom moments — Dynamic Test 2

127


Botto

m M

omen

t (k

ip-in

.) Bo

ttom

Mom

ent

(kip

-in.)

Column A1 Bottom

150

1 0 0

-50

-100

-150X:0.0259 Y:-152.9

-0.04 - 0.02 0 0.02-0.08 -0.06 0.04Total Rotation over h=6in. - (rad)

Column A1 Bottom

150

1 0 0

50

-50

-100

-150X:0.0259 Y:-152.9

-0.08 -0.06 -0.04 - 0.02 0 0.02 0.04Total Rotation over h=6in. - (rad)

Figure 5-62: Column A l bottom critical section total rotation vs. bottom moment (full test and 21sec. < t < 31 sec.) - Dynamic Test 2

128


Column A1 Bottom0.04

3 -0.04

Drift (%)

Figure 5-63: Column A l inter-story horizontal drift ratio vs. bottom total critical section rotation - Dynamic Test 2

Column A1 Bottom

X:0.0259 Y:7.25

o .

-0.06 -0.04Total Rotation over h

- 0.02 0 Total Rotation over h=6in. (rad)

0.02 0.04

Figure 5-64: Column A l bottom total critical section rotation vs. shear - Dynamic Test 2

129


The shear failure o f the bottom o f Column A l initiated at a horizontal drift ratio o f

approximately +3.26% and a shear force o f 7.25 kips (Figure 5-54). One cycle prior to

this, a relatively large inclined crack initiated at the bottom o f Column A l (see Figure

5-56 and Figure 5-57), leading to softening o f the column response (Figure 5-54). This

point was not designated as the initiation o f shear failure as the column was able to

withstand a substantially higher shear force in the following cycle, after which shear

strength degradation was observed. Shear strength degradation was initiated at

approximately 21.48 seconds into the test. At that instant Column A l was under -21.5

kips o f axial load (Figure 5-58), its bottom moment was -153 kip-in., and its critical

bottom section rotation was 0.0259 rad.

Table 5-5 summarizes the relevant response values for Column A l at designated

time o f shear failure initiation, as well as the values for Column B l at its shear failure

initiation during the Dynamic Test 1. The drifts, axial loads, and rotation are similar for

the two columns at shear failure. However, the shear forces and moments are dissimilar.

Table 5-5: Column A l state at initiation o f shear failure (Dynamic Test 2) andColumn B l state at initiation o f shear failure (Dynamic Test 1)

Column A l Column BlDynamic Test 2 Dynamic Test 1

Horizontal Drift (%) 3.26 -3.15Shear Force (kips) 7.25 -9.89Axial Force (kips) -21.5 -24.7Bottom Moment (kip-in.) -153 2 0 1

Bottom Rotation (rad) 0.0259 -0.0265Top Moment (kip-in.) 157 - 2 1 2

Top Rotation (rad) N.A.* 0.0207*: value not available as instruments were impacted during previous test

Figure 5-28 and Figure 5-54,show different failure relations for Columns A l and B l.

Whereas Column B l appears to have failed during a single cycle, Column A l sustained130


multiple cycles at similar drift while the shear resistance degraded from cycle to cycle.

Figure 5-63 shows a nearly linear relation between bottom section rotation and horizontal

drift ratio for Column A l up to the substantial deterioration o f the shear crack at its

bottom (the five point star marker). Beyond that, the response became increasingly non-

symmetric (Figure 5-62 and Figure 5-64). The loss o f capacity in the concrete flexural

compression block at the bottom o f Column A l (Figure 5-55) apparently resulted in

softened response in the negative drift direction while it maintained its stiffness in the

positive drift direction where the flexural compression block was preserved.

Column B l continued to degrade axially during the strong shaking part o f the test

(Figure 5-59) as it shed most o f its axial load (Figure 5-60). The degrading relation

between axial load and vertical drift continued the downward trend observed in Dynamic

Test 1.


Figure 5-65 through 5.68 plot responses o f Columns Cl and D l. In all figures the

point o f initiation o f shear degradation in Column A l is identified by a square marker and

pertinent response values at that point are written on the figure.

131


Column D1

X:2.83 Y :2.76

-2 0 2 Drift (%)

Column C16 X:3.2 Y :4.95:

4

2

03Q.

r o (0 CD

-C

•2

-4

■6,

Drift (%)

Figure 5-65: Columns C l & D1 inter-story horizontal drift ratios vs. shears — Dynamic Test 2

Column D1 Column C1

X:2.83 Y:-2.32

<0 -15 K -15CL

X:3.2 Y:-34.8

-2 0 2 Drift (%)

-2 0 2 Drift (%)

Figure 5-66: Columns Cl & D1 inter-story horizontal drift ratios vs. axial loads - Dynamic Test 2

132


Column D1 Column C1

Bottom Moment Top Moment ! 7 X3 . 2 Y:121.6

X:2.83 Y:50.3

X:2.83 Y:-59.7

X:3.2 Y:-114.7

Drift (%)-6 - 4 - 2 0 2

Drift (%)

Figure 5-67: Columns C l & D1 inter-story horizontal drift ratios vs. top & bottom moments - Dynamic Test 2

Apart from some minor cover spalling at both the top and bottom o f Columns C l and

D l, these columns did not sustain any major damage during this test. The joints above

them (i.e., Joints C l and D l) suffered substantial cracking, and some minor spalling

occurred in Joint D l. This joint damage could explain the descending moment-drift

relation apparent past a drift o f about 3% in the top moments o f both columns (Figure

5-67) The bottom moments do not show this degrading behavior in their moment-drift

relation. This behavior was also observed in the non-ductile Columns A l and B l. During

this test, Column C l picked up more axial load from Column B l while Column D l was

uplifted (Figure 5-52).

133


5.5.4 Bar slip

Figure 5-68 plots the bar slip versus moment at the top and bottom o f Column Cl

(this figure marks the point o f initiation o f shear failure in Column A l with a square

marker). During this test, some cover spalling occurred under the bar slip instrument at

the top Column C l making the bar slip readings at the top o f Column Cl unreliable. They

are still presented here for completeness.

Column C1 Top

-0.05 0 0.05 0.1 0.15Slip (in.)

Column C1 Bottom

X:-0.00987 Y:-114.7

-0.05 0 0.05 0.1 0.15Slip (in.)

Figure 5-68: Column C l bar slip vs. end moments - Dynamic Test 2

The relation between bottom bar slip and moment (Figure 5-68) shows a gradually

softening tension behavior, with some apparent stiffening in compression. The cause o f

these observed behaviors was not resolved in the course o f this study.

134


5.6 Dynamic Test 3


Following Dynamic Test 2, the Llolleo ground motion record was input to the frame

with scaling factor increased from 4.06 to 5.8 times the original recorded motion. This

motion collapsed Columns A l and B l resulting in vertical collapse o f the East side o f the

frame by nearly 5 inches before the catching device halted it.



profiles for this test. In these and subsequent plots the frame response is only reported up

to the point at which the collapsing frame hits the catching device at time = 15.15

seconds into the test.

3rd Floor

10 11 T i m e l s e c ) 2nd Floor

1--------- 1---------1---------1-------- |--------q-------- 4 --------4-------- f --------F---------|

10 11 T im e ( s e c ) 1st Floor

-I 1---------------1- I- - I ------------H -------------4 --------------+ - F------- F-------- 1

T im e ( s e c ) F o o tin g

i -1 .65 6 7 8 9 10 11 12 13 14 15 16

T im e ( s e c )

Figure 5-69: Footing andfloor-level acceleration records — Dynamic Test 3

135


3rd Story

(/>Q.

COCD

_£=

-10,Tim e (sec )2nd Story

</>Q.

-10,Tim e (se c )1 s t Story

CD0•C

-10,Tim e (se c )


3rd Story

- -4,T im e (s e c )2nd Story

- -4,T im e ( s e c )1st Story

- -4,T im e ( s e c )

Figure 5-71: Inter-story horizontal drift ratio records - Dynamic Test 3

136


-6 -4 -2 0 2 4 6Min./Max. R ela tive Drifts (%)

Figure 5-72: Minimum and maximum horizontal relative floor drift profiles - Dynamic Test 3

Figure 5-73 and Figure 5-74 show photographs o f the damaged states o f columns A l

and B l as well as the entire frame at the end o f test. Column A l collapsed axially at t =

14.59sec and dragged the entire East side o f the frame with it. The West side o f the

frame, supported by ductile columns, held its axial load throughout the collapse but

showed large lateral drifts. These observed lateral drifts had the potential o f causing a

side-sway collapse mechanism on the West side o f the frame, potentially generating a full

collapse o f the frame. This cannot be verified here as the frame vertical drop was halted

on the East side by the catching device at a drop o f about 5 inches.

No significant damage to other frame members was observed prior to the collapse

(confirmed by examination o f test videos). At the end o f the test, however, joints showed

significant distress in the form o f X pattern cracks and cover spalling (Figure 5-73 and

Figure 5-74). Column D l had a longitudinal bar fracture at its base while both Columns

D l and Cl had buckled longitudinal bars.

137


Figure 5-75 through Figure 5-80 plot various recorded data, similar to data reported

for Dynamic Tests 1 and 2. In relevant figures the designated point o f initiation o f axial

degradation in Column A l is identified by a diamond marker and pertinent response

values at that point are written on the figures. In Figure 5-75 the vertical instrument at

Column C2 was defective so no data are reported.

Figure 5-73: Columns Bl(left) and A l (right) damaged states - Dynamic Test 3

138


Figure 5-74: Frame collapse state - Dynamic Test 3

C olum n D3 C olum n C3 Column B3 Column A3

- 2 0 2 Horiz. Drift (%) Column D2

-2 0 2 Horiz. Drift (%) Column C2

0.5

Q>

- 0.5

Horiz. Drift (%)Column B2

0.5

•cQtf<D>

- 0.5

Horiz. Drift (%)

0.5

- 0.5

Column D1

4 -2 0 2 4Horiz. Drift (%) Column C1

0.5

D■c<D>

- 0.5

Horiz. Drift (%)Column B1

0.5

a■cCD>

- 0.5

Horiz. Drift (%)Column A2

0.5

a

- 0.5

Horiz. Drift (%)Column A1

0.5

4=:•cQtf(l)>

- 0.5

Horiz. Drift (%)

0.5

Qtf a> > > -10> -10

0 22 4 -4 -2 4•4 •2 04Horiz. Drift (%)

Figure 5-75: Column inter-story horizontal vs. vertical drift ratios - Dynamic T

139


COQ.Lx:co0>

. ccoEro

CO■ocCM

-10

2nd Story Drift (%)

COQ.litCOd)

. cCO

oCO•gCO

-10

3rd Story Drift (%)

COQ_

COa>CO4)COCOCQ

-10

1st Story Drift (%)

Figure 5-76: Floor inter-story horizontal drift ratios vs. shears - Dynamic Test 3


4

2

0

•2

-4

■6■4 -2 0 2 4Drift (%)

-4 -2 0 2 4 -4 -2 0 2 4Drift (%)

6

4

2

0

■2

■4

•R

Drift (%)

6

4X: 1.61 Y:2.91

2

0

■2

■4

. f i

Drift (%)

Figure 5-77: First-story columns inter-story horizontal drift ratios vs. shears - Dynamic Test 3

140


Column A1 Axial Failure Initiation

-10

8 -15

-20

-25

-30

!---------- T-*-n-35

-40 — Column A1 — Column B1

Column C1 Column D1

-45

-50,

Time (sec)

Figure 5-78: First-story columns axial load histories - Dynamic Test 3


0

-10

V)C L

S -20■aTO0_ ito -301

-40

-50

0

- -10

-20

-30

-40

-50

0

-10

-20

-30

-40

-50

X :1 .61 Y :-1 6 .3

-4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4Drift (%) Drift (%) Drift (%)

-4 -2 0 2 4Drift (%)

Figure 5-79: First-story columns inter-story horizontal drift ratios vs. axial loads - Dynamic Test 3

141


— Footing BO Joint A1 Joint A2

Column A1 Axial Failure Initiation0.8

0.6

0.4

0.2

- 0.2

-0.4

- 0.6

- 0.8

Time (sec)

Figure 5-80: Vertical accelerations o f Footing B0 and Joints A l and A2 around axial failure- Dynamic Test 3

Maximum recorded story shears were about 10 kips for each o f the three stories

(Figure 5-76), which is much lower than the maximum values reached in previous tests.

Figure 5-76 shows that, at initiation o f axial failure (square marker), the third-story drift

was in the opposite direction than the first-story drift.

The axial failure o f Column A l initiated at a horizontal drift o f +1.6% with an axial

load o f -16.3 kips (Figure 5-75 and Figure 5-79). The column shear before axial collapse

hovered at less than 3 kips, a value reduced from the initial shear strength due to the shear

degradation it incurred in the previous test. As Column A l collapsed axially, the axial

load it carried dropped to a low o f about 1 0 kips initially and hovered between 1 0 and 15

142


kips subsequently until the frame collapse was halted by the catching device (Figure

5-78). During the collapse, the axial load o f Column B l increased by about 5 kips as it

was forced to shorten rapidly. Column Cl also picked up a significant amount o f axial

load (about 12 kips) as Columns A l and B l collapsed vertically. Column D l experienced

a slight uplift. Both Column A l and B l sustained relatively gradual axial collapses as

they were able to hold a significant amount o f axial load during their fall. This resulted in

a more controlled collapse with relatively small vertical accelerations (Figure 5-80).


Figure 5-81 though Figure 5-86 plot the various response quantities measured for

Columns A l and B l. In relevant figures the initiation o f axial load failure o f Column A l

is marked with a diamond marker. Pertinent response values corresponding to that point

are written on the figures. Table 5-6 summarizes these response values.

Column B1 Column A16

4 X :1.61 Y:2.91

2

wQ.

•2

-4

•6 •2 2■4 0 4Drift (%)

Figure 5-81: Columns A 1 & B l inter-story horizontal drift ratios vs. shears -Dynamic Test 3

143


Column B1 Column A1

(/)•§--10■oCDO

~ -1 5

-20

-2 5-4

Figure 5-82:loads -

- 2 0Drift (%)

-2 0 Drift (%)

Columns A l & B l inter-story horizontal drift ratios vs. axial Dynamic Test 3

• • w - r < rV

i_QCDOtCD>

-10— Column A1 — Column B1 C o lu m n A1 A xial F a ilu re In itia tio n

Time (sec)

Figure 5-83: Columns A l & B l inter-story vertical drift ratio historiesDynamic Test 3

144


Column A1

•X:1.61 Y:-0.104

QrootCD>

Horizontal Drift (%)

Figure 5-84: Column A l inter-story horizontal vs. vertical drift ratiosDynamic Test 3

Column A1

X:-16.3 Y:-0.104

■20Axial Load (kips)

Figure 5-85:Dynamic Test

Column A l axial load vs. inter-story vertical drift ratio ■ 3

145


Column B1 Column A1

150

100

50Q.

w 0cCD

-50

-100

-150

.......................

s s i i i 1 1 i i

1,1 1 i

i w k £ • / ■ * \ i u *

I W - V f t - f ' t - t '. f t f l t f . f t t - ' f

!!■ f f f i

•i”f t ”f I ' f f f

: : : i s : i : 1 |

f 1 f -t f t t t - c U f t f t f 1 -f t f ’ ^ ' f f f f f f f f f

\ ■ ,••f .t--f " f ' - f f f f f “l“f •t"f"t“f*»‘,f

-

-I> 0 2 i

150

100

Q.

« 0

-100

Top Moment 1 — Bottom Moment

X:1.61 Y:84.19

1.61 Y:-38.08

-150-

Drift (%)0

Drift (%)

Figure 5-86:bottom

Columns A1 & B1 inter-story horizontal drift ratios vs. top and moments - Dynamic Test 3

Table 5-6: Columns A1 state at initiation o f its axial failure - Dynamic Test 3Column A l

Horizontal Drift (%) l . 6 lShear Force (kips) 2.91Axial Force (kips) -16.3Bottom Moment (kip-in.) -38.1Bottom Rotation (rad) N.A.*Top Moment (kip-in.) 84.2Top Rotation (rad) N.A.*

*: R otations v a lu es are n ot ava ilab le as the instrum ents w ere d isp la ced during the p rev io u s test

As mentioned previously, Column A1 collapsed axially due the failure o f its lower

section at time = 15.15 seconds. As can be seen in Figure 5-83, Figure 5-84 and Figure

5-85, the vertical drop o f Column A1 did not show any signs o f pivoting around the shear

crack and forcing the column upwards as the drift direction reversed (as was seen for

146


Column B l). The axial load in the column at that point was -16.3 kips, and included load

that had been redistributed to it from failure o f Column B 1. The column shear and drift at

failure (2.9 kips and 1.6%) were relatively low, suggesting effects o f fatigue. Critical

section rotations for this column could not be measured for this test.


Figure 5-87 through Figure 5-89 plot response quantities for Columns Cl and D l. In

all figures the designated initiation o f axial degradation in Column A1 is identified by a

diamond marker and pertinent response values at that point are written on the figure.

Column D1

X:1.04 Y:2.58

COQ.

\_COCl)

-CC/3

Drift (%)

Column C1

X:1.44 Y:4.5:

c/3

Drift (%)

Figure 5-87: Columns C l & D l inter-story horizontal drift ratios vs. shears - Dynamic Test 3

147


Column C1Column D1

X:1.04 Y:-7.48

X:1.44 Y:-37.8

.44*f'4'*t**f*4**f“i*.... 44-+4 P-+~i4-4.4<4**i**t**f • 4 -4 - f4 . - f .u 4 - f . f . . — *4'*f*'i~4"f"4~ ~4**4*4~4*'f'4"f ~t'*4*

q.4--f-4-4"h-f

-4 -2 0Drift (%)

-4 -2 0Drift (%)

Figure 5-88: Columns Cl & D l inter-story horizontal drift ratios vs. axial loads - Dynamic Test 3

Column D1 Column C1150

10 0 -

1 50r

Q .

<n 0ca)£o

X:1.44 Y:128Top Moment Bottom Moment

- :- :- :X.1.04 Y.71

X:1.04 Y:-31.1X:1.44 Y:-67.01

4.4..4.4..J..4

Drift (%)

-100

-150^0

Drift (%)

Figure 5-89: Columns C l & D l inter-story horizontal drift ratios vs. top & bottom moments - Dynamic Test 3

148


Shears in Columns C l and D l dropped and even reversed during the collapse o f

Column A1 while their horizontal drift remained around 3% (Figure 5-87). This is

observed as well in their moment diagrams (Figure 5-89) where their top moments are

relieved and even reversed for Column D l at a constant horizontal drift o f about 3%. This

is consistent with the introduced rotation at their upper ends due to the collapse o f the

East side o f the frame. During this test, Column Cl picked up more axial load while

Column D l was uplifted further (Figure 5-88).

5.6.4 Bar slip

Due to the high levels o f concrete cover spalling across the frame the bar slip

measurements were not reliable during this test.

149


6 Evaluation of Analytical Models

6.1 Improved Analytical Model of Test Frame

Chapter 3 presented an analytical model used to design the test program. That model

is refined to include more representative analytical models and more accurate material

properties derived from the frame test. The new formulation utilizes the LimitState shear

and axial failure materials and elements described in Chapter 2, and adds an improved

bar slip model, a more efficient column and beam discretization scheme, strain-rate

effects on longitudinal steel properties, and as-built material properties and damping

throughout the frame model. Damping is modeled with constant stiffness and mass

proportional Rayleigh damping based on the 1st and 2nd “initial” elastic modes o f

vibration o f the structure. The damping ratio was taken as 2% o f critical based on

experimental observations.

The following sections describe the improved analytical model o f the test frame. A

comparison between the analytical and experimental results is presented for both the

Half-Yield Test and Dynamic Test 1 to demonstrate effectiveness o f the model.

6.1.1 Column and Beam Discretizations

In the predictive analysis o f the frame (Section 3.3) the columns were discretized

into twelve equal length displacement-formulation sub-elements. The more accurate

force-formulation elements [Spacone et al. (1996)] were not used as they were

numerically unstable at high deformations. In this section, this issue is revisited for

purposes o f accuracy and efficiency.

150


With the introduction o f more robust solution-algorithm switching and time-step

division schemes, numerical instabilities associated with the force-formulation elements

were better managed in the refined analytical model. This allowed the use o f these force-

formulation elements and eliminated the need to subdivide the columns into as many sub

elements as was required for accuracy with the displacement-formulation. This

effectively reduced the number o f column sub-elements from twelve to three as

illustrated in Figure 6-1. Three sub-elements were maintained in this new formulation in

order to fix column plastic hinge length to column height (h). This hinge length was

chosen so that most, if not all, plastic rotations occur within column end elements. This

choice was also made for the simplicity it affords in plastic hinge length evaluation. In

this discretization scheme, the hinge elements at column ends were constructed using two

fiber sections (one at each end) while the middle element had five fiber sections. The

column discretization scheme shown in Figure 6-1 is applicable to all columns in the

frame with differences between the ductile and shear critical columns being the absence

o f the LimitState zero-length springs in the ductile columns.

Beams were discretized into six force-formulation sub-elements containing two fiber

sections each. These sub-elements spanned between lead-weight and out-of-plane bracing

loading points. This approach produced sub-elements at the ends o f the beams 12 in.

long. The effects o f beam end-element lengths on model response were minimal as the

beams did not exhibit significant softening.

151


Zero-LengthFiber-Sectior

LimitState StAxial Springs

Elastic Shear Springs

Zero-Length

— *rZero-Length

Rigid Rotational Spring / / / / /

Figure 6-1: Shear critical column analytical representation

6.1.2 LimitState Materials

LimitState material models and elements developed by Elwood (2002) and described

in Section 2.1 were used to model shear and axial failures at the base o f all shear critical

columns o f the frame. The zero-length spring elements associated with them are inserted

at the bottom o f the columns as illustrated in Figure 6-1. A rigid rotational spring was

added in parallel with the shear and axial springs to lock rotational motion between the

connecting zero-length nodes. The material properties used for the definition o f the shear

and axial LimitState elements are presented in Appendix D.

6.1.3 Shear Deformations

Shear deformations were introduced into the analytical model using zero-length

elastic spring elements at both ends o f columns and beams (Figure 6-1). The stiffnesses152


o f these springs were calibrated to the gross section shear stiffness o f the elements, given

by:

shear

With:

c Ee (6-2)2 ( 1 + v)

Ec = concrete modulus o f elasticity

u = concrete Poisson ratio (taken as 0.25)

Ag = gross section area

L = element clear length

6.1.4 Bar Slip Model

Several approaches for modeling bar slip at the column or beam interface are

described in Section 2.3. In modeling dynamic behavior o f the test frame a zero-length

fiber-section representation o f the interface plane is used (Figure 6-1) with some

modifications from available methods [Berry (2006); Zhao and Sritharan (2007)]. This

method assumes that the bar-slip-induced rigid body rotations are centered at the flexural

neutral axis and implicitly models that effect through strain compatibility in the zero-

length fiber-section (plane-section assumption, see Figure 6-2). In this way, the fiber-

section method automatically adapts its center o f rotation to variations in member axial

loads and lengths o f bar slip. This sets this approach apart from most other simplified

methods that use constant flexural stiffness properties that are user-calibrated at constant

axial loads. It was important for this study as the columns exhibited large axial load

variations due to framing effects.

153


Frame Elem ent Uni-Axial Steel

Fram e Element Fiber-Section ^

Bar Slip Element Fiber-Section

Material (fy,£y,b)

Fram e E lem ent Uni-Axial ConcreteMaterial (f„,£’r.,fi,»,£..«)

(fc,£c)-^^/~(fi,£s)

(fc,£cbs)— ; 1

Fram e Elem ent Fiber-Sectlon Strain Profile

Bar Slip Fiber-Section Strain Profile

Bar Slip Uni-Axial Steel Material(f.,s„b)Bar Slip Uni-Axial Concrete Material(f*c,£ ebs—£ £«»Sy/£y)

Frame Element Steel Fibers

fy B a r S lip S t e e l F ib e r s

Steel Fiber S tress-S train Relations

fcF r a m e E l e m e n t C o n c r e t e F ib e r s B a r S lip C o n c r e t e F ib e r s

f c

fult

Bei

o c b se'c SuitC oncrete Fiber S tress-S train Relations

Figure 6-2: Bar slip fiber-section equilibrium, strain profiles and materials

In this formulation, the bar slip fiber-section has the same geometry as the fiber-

sections o f the element it is attached to but different uni-axial material properties for its

steel and concrete fibers. Figure 6-2 illustrates the bar slip zero-length fiber-section

154


equilibrium with the adjacent frame element fiber-section. Shear force (V), axial load (P),

and moment (M) applied to the bar slip fiber-section are equal to those applied to the

adjacent frame element end-fiber-section. The assumption that bar-slip-induced rigid

body rotations are centered at the flexural neutral axis o f the adjacent frame element

requires the bar slip fiber-section strain profile illustrated in Figure 6-2. In this profile, the

bar slip compression block depth (c) must be equal to that o f the adjacent frame element

fiber-section for any combination o f P, V, and M. As well, longitudinal stress

compatibility between concrete (fc) and steel (fs) fibers o f both adjacent fiber-sections is

required for any combination o f P, V, and M.

For a given loading, the bar slip rotation Obs (Figure 6-2) is given by Ss/c ’ (Ss=bar

slip o f longitudinal bars at distance c ’ from neutral axis). The frame element fiber-section

curvature Kfc is given by ss/c ’ (es =longitudinal bar strain). Thus ObS= Kfe(Ss/Es) for any

loading condition. This implies that concrete strains in any fiber o f the bar slip fiber-

section (8 cbs) must be related to concrete strains in frame element fibers by the ratio

r=(Ss/£s) to maintain compatibility o f material stresses and neutral axis location between

bar slip and frame element fiber-sections.

Flence, selecting identical steel and concrete material models (OpenSEES steel02

and concrete0 2 in this case) in bar slip and frame element fiber-sections and scaling bar

slip material strains from frame element material strains by the ratio ry=(Sy/sy) (Sy=bar

slip at yield, ey=bar strain at yield - Figure 6-2) achieves compatibility o f material

stresses and neutral axis location over the full hysteretic behavior o f material models.

This choice o f material models and parameters contrasts available zero-length fiber-

section bar slip methods developed by Berry (2006) and Zhao and Sritharan (2007) in

155


which concrete material properties are chosen empirically or arbitrarily. These latter

methods do not achieve compatibility o f material stresses and neutral axis location

between adjacent bar slip and frame element fiber sections.

In this formulation, the only term required to calibrate bar slip fiber-section steel and

concrete material parameters is the longitudinal bar slip at yield Sy. The yield slip is

evaluated using the constant bond model developed by Lehman and Moehle (2000) and

later applied by Sezen (2002) (Equations 2-7 and 2-8). The elastic bond stress used to

calculate the bar slip at yield was taken as 12-yJ f ' c (psi) for the column-footing interface,

based on tests conducted by Sezen (2002). Lowes et al. (2003) suggest a much higher

elastic bond stress value o f 2 1 A/ / ' c (psi) at joint interfaces; however, due to the short

development lengths in the test frame joints and the high levels o f damage and

deformations observed in the joints, the lower bond stress value o f 1 2 / f ' c (psi) is used

at the joint to column and beam interfaces. The hardening slope o f the bar slip material is

taken as identical to the longitudinal steel hardening at 1 % o f the elastic stiffness,

resulting in a post-yield bond stress value o f 3.24y jf'c (psi) as imposed by Equation 2-

8 ). Appendix D summarizes the bar slip material properties used in the zero-length bar

slip fiber sections.

This bar slip implementation method requires bar stress versus slip relations to be o f

the same form as relations for longitudinal bar steel (i.e., bi-linear with hardening). At

small to moderate bar slip levels, a bi-linear stress-slip relation is adequate in modeling

bar slip [Lowes et al. (2003); Berry (2006)]. However, at large bar slip levels where bond

deterioration occurs, the hardening steel material models are no longer appropriate as

they do not model the softening due to bond deterioration. A limitation o f this bar slip156


implementation method, which is also present in methods utilizing calibrated rotational

springs, is that it is not effective in modeling local frame element deformations in cases

o f section softening (negative moment-curvature stiffness). In these cases, rotational

deformations become localized in either the frame element or the bar slip element, which

automatically triggers the unloading o f the other section. This results in erroneous

estimates o f bar-slip-induced rotations and element plastic rotations. In the case o f fiber-

section representations o f bar slip, section softening also results in discrepancies in

neutral axis location and steel stresses across the bar slip interface.

Despite the above-mentioned limitations, the proposed fiber-section approach to

modeling bar slip produced fairly accurate results (Section 6.2) and is expected to

perform well in other cases where bond deterioration and frame section softening are not

present.

6.1.5 Material Properties and Strain-Rate Effects

In the refined analytical model, the as-built material properties were used for the uni

axial materials. Confined concrete was modeled using the method developed by Mander

et al. (1988) and bar slip material properties were chosen as described in the previous

section.

Sectional analyses for first-story ductile and flexure-shear-critical columns were

conducted with as-built steel and concrete material properties (Appendix D.2). These

analyses produced yield moments significantly lower than those observed for these

columns during Dynamic Test 1. As noted in Section 5.4.2 maximum longitudinal

reinforcement strain rates estimated from strain gauge readings just prior to shear failure

o f Column B1 were in the range o f 0.05 to 0.2 (1/sec). Strain rates in this range can result

157


in increases in material yield stress capacities in the range o f 21 to 26% (Malvar (1998).

Therefore, the yield stresses for all longitudinal steel in the frame were increased to 1.25

times the measured static yield stress. Sectional analyses o f first-story columns were

repeated with the increased yield stresses, resulting in improved yield moment estimates

Appendix D.2. Appendix D .l lists the material models and parameters used in the test

frame.

6.2 Comparison between Analytical Model and Experimental

Results

This section presents a detailed comparison between the refined analytical model and

experimental results for both the Half-Yield Test and Dynamic Test 1.

6.2.1 Half-Yield Level Test

6.2.1.1 Global Behavior

Table 6-1 summarizes the first three apparent modal periods o f the test frame before

and after the Half-Yield dynamic test and contrasts them with the analytical ones as

obtained from model eigenvalues. This table shows excellent agreement between the two

sets.

Table 6-1: Analytical vs. experimental frame dynamic properties - Half-Yield TestExperimental Analytical

Initial "Un Post Half-Yield Initial "Un Post Half-Yieldcracked" Test "Cracked" cracked" Test "Cracked"

1st Period (sec) 0.31 0.35 0.32 0.342nd Period (sec) 0 . 1 0 1 0.115 0.107 0.1143rd Period (sec) 0.069 0.08 0.068 0.073

158


Figures similar to those o f Section 5.3.1 are presented in this section to compare the

analytical model results with the experimental results. Figure 6-4 through Figure 6-7 plot

floor-level and footing-level horizontal acceleration records, story shear records, inter

story horizontal drift ratio records, inter-story horizontal drift ratios versus floor shears,

and first-story column inter-story horizontal drift ratios versus axial loads.

Figure 6-3 through Figure 6-5, comparing floor-level accelerations, drifts, and story

shears show reasonably good agreement between analytical and experimental results.

Amplification o f base motion accelerations at the floor levels is represented well with

only slight over-shooting by the analytical model. The analytical story shear and drift

amplitudes and phasing follow the experimental results up to t~=27 seconds. At

approximately t = 27 sec the analytical and experimental results diverge. No explanation

o f this divergence was identified.

3rd Story

E x p e rim en t

— A n a ly s is'T' 10

co -10

1510

CD. ccr>


1------

10 15 2 0 25Time (sec) 1st Story

30 35 40

— 10 COQ.

CO - 1 0

-15 402 0T im e ( s e c )

Figure 6-3: Story shear histories - Half-Yield Test

159


Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

Hor

iz.

Acc

el.

(G)

3rd Floor

0 .4

0.2

-0.2-0 .4

T im e 2 n d f

0 .4

0.2

T im e J 's e c ) 1 s t R o o r

'im e { se c ) F o o t in gExperiment

— Analysis0.2

- 0.2

22 2 316 17 18 19 20 21 2 4 2 515T im e ( s e c )

3 rd F lo o r

2 9 3 0 31T im e ( s e c )2 n d F lo o r

1 s t R o o r

'im e ( s e c ) F o o t in g- Experiment

-Analysis0.2

-0.22 625 2 7 2 8 2 9 3 0 31 3 2 3 3 3 4 3 5

T im e ( s e c )

Figure 6-4: Floor-level acceleration histories — Half-Yield Test

160


3rd Story

0.5 — EXpe rime nt — Analysis

2 -0.540


0.5

2 -0.5

Time (sec) 1st Story

0.5

5 -0.510 15 2 0 25 30 35 40

Time (sec)

Figure 6-5: Inter-story horizontal drift ratio histories - Half-Yield Test

(J)Q . Q.

CD0

.C

oC0 "DCN - 1 0 CO -1 0 |

-15 -15-0.4 -0 .22nd

0.22nd Story Drift (%)

0.4 0 .6 -0.4 -0.23rd Story Drift (%)

0 .2(%)

0.4 0 .6

— Experiment — Analysis

CD<DJZV)CDtfiCDm

- 1 0

-15-0.4 -0 .2 0 .2 0.4 0 .6

1st Story Drift (%)

Figure 6 -6 : Inter-story horizontal drift ratios vs. shears - Half-Yield Test

161


Column D1 Column C1


-5

- 1 0

-15

- 2 0

-25

Column B1O f--------- 1--------- r

Column A1

-0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5Drift (%) Drift (%) Drift (%) Drift (%)

Figure 6-7: First-story column inter-story horizontal drift ratios vs. axial loads -Half-Yield Test

Excellent agreement between analysis and experiment was obtained for the first-

story lateral stiffness (Figure 6 -6 ). The analytical model for that story adequately

represented both the initial “un-cracked” stiffness as well as softening for higher-

amplitude loading. The analytical model o f the second and third stories was stiffer

response than that observed. Rigid-element treatment o f the joints and the choice o f

elastic bond stress for joint bar slip likely contributed to the overestimation.

Finally, Figure 6-7 shows a very good agreement between analysis and experiment

for the first-story column axial loads.

162


6.2.1.2 Flexure-Shear-Critical Column Behavior

Figure 6 - 8 through Figure 6-10 compare analytical and experimental results for the

first-story flexure-shear-critical columns at axes A and B. Good agreement between

analysis and experiment can be seen at both the column local level (column moment

versus critical section rotations - Figure 6-10) and global level (drift versus shears or

moments - Figure 6 - 8 and Figure 6-9). Both initial and “post-cracking” softened

stiffnesses are reasonably well modeled. This suggests that the elastic bond stress o f

1 2 J f ' c (psi), concrete ultimate tension stress o f 7.5-yJf'c (psi), and tension-softening

slope o f Et=Eo/5 were appropriate parameters for the analytical model.

Column B1 Column A1

Experiment — Analysis/'

/

Cl Q_

r oCO -1CO -1

0 .2 0 .4 0 .6 0.2 0.4 0.6Drift (%) Drift (%)

Figure 6 -8 : Columns A1 & B l inter-story horizontal drift ratios vs. shears - Half-Yield Test

163


Column B1 Top Moments Column A1 Top Moments1 0 0100


40

Q.Q.

- 2 0- 2 0

-40-40 A-60-60

-80-80

-100-100 0.2 0.4 0.6-0.4 -0.20.5-0.5(%)DriftDrift (%)

Column B1 Bottom Moments Column A1 Bottom Moments100

Experiment; — Analysis I

cI

Q_

<n>*-»cCDEo

2

- 2 0

-40

-60

-80

-100 0.2 0.4 0.6(%)Drift

1 0 0

wcCDEo

2

- 2 0

-40

-60

-80

-100 -0.5 0.5Drift (%)

Figure 6-9: Columns A l & B1 inter-story horizontal drift ratios v.s\ top & bottommoments - Half-Yield Test

164


100

- T 50Q.

§ oEo2& -50

1-


-10CL-6

1 0 0

.9- 50

®E 0 o

| -50o co

-1 0 0 .

t »-2 0 2

Column B1 Bottom x 10-3

^ : : :

V

-2 0 2 Rotation(h=6in.) - (rad)

x 10

100

-50

-1 0 0 ,■3Column A1 Bottom

x 101 0 0— Experiment — Analysis

-50

-1 0 0 ,Rotation(h=6in.) - (rad) 3

x 10

Figure 6-10: Columns A l & B1 total end rotations us-, moments - Half-Yield Test

During this test, Columns A l and B1 experienced very different axial load histories.

Column A l starts the Half-Yield Test with about half the axial load o f Column B1 (11.3

kips versus 20.7 kips) and experiences axial load variation between 5 and 15 kips

compression, while the axial load o f Column B1 remains fairly constant (Figure 6-7). The

good correlation between measured and calculated load-deformation behaviors suggests

that the fiber-section column elements and the zero-length fiber-section representation o f

bar slip are adapting to variations in axial load with sufficient accuracy.

6.2.1.3 Ductile Column Behavior

Figure 6-11 and Figure 6-12 compare analytical and experimental results for the

first-story ductile columns at axes C and D. Load-deformation responses compare

favorably throughout the test.

165


Shea

r (k

ips)

Column D1 Column C15

4

3

2

1

0

1

2

■3 --

■4

5 0.2 0.4 0.6-0.4 -0.2 0

wCL

CO CD

W -1

- 2

-3

-4

-5

Drift (%)

\ \ 1| — Experiment

_j— Analysis

1i / V

---------! i i i i • i

ijm fi ;

/tJjm i

i i

W i i i i

i i i i

-----1 i i-0.4 -0.2 0 0.2 0.4 0.6

Drift (%)

Figure 6-11: Columns C l & D l inter-story horizontal drift ratios v.s\ shears -H alf- Yield Test

166


Column D1 Top Moments Column C1 Top Moments100100

Experim entA nalysis

cI

Q_ Q.

c/> -♦—* c 0) E o -20 - 2 0>gjg

-40 -40

-60 -60

-80 -80

-100 -100-0.5 0.5 -0.5 0.5Drift (%) Drift (%)

Column D1 Bottom Moments Column C1 Bottom Moments1 0 0

Q.

- 2 0

-40

-60

-80

-100 -0.5 0.5Drift (%)

1 0 0— Experim ent — A nalysis

03cCDEo -20

-40

-60

-80

-100 -0.5 0.5Drift (%)

Figure 6-12: Columns C l & D l inter-story horizontal drift ratios v.s\ top and bottom moments- Half-Yield Test

167


6.2.2 Dynamic Test 1

6.2.2.1 Global Behavior

Figure 6-13 through Figure 6-20 compare analytical and laboratory model results for

representative response quantities.

3rd StoryExperiment

— Analysis

w -20

25Time (sec) 2nd Story

u>Q.

!_ uCOCD

w -20

Time (sec) 1st Story

w - 2 0

25Time (sec)

Figure 6-13: Story shear histories - Dynamic Test 1

168


Experiment— Analysis

_ 1.6CD

d)O<!N

01T im e ( s e c ) 2 n d F lo o r

00)INO

X- 1.6

0

oX

- 1.6

T im e ( s e c ) F o o t in g

_ 1.60o>I 0

i -11 -i.§

T im e ( s e c )

3 rd F lo o r1.6

0o>oo<

.NO

X

24 25T im e ( s e c )2 n d F lo o r

0d>o<.NO

X

0d>oo<NO

X

T im e ( s e c ) F o o t in gExperiment

— Analysisod)o

oX

T im e ( s e c )

Figure 6-14: Floor-level acceleration histories — Dynamic Test 1

169


3rd Story

□£> 0 o35aj -5 c


10 15 2 0 25Time (sec) 2nd Story

30 35 40

□£■0351©C

30 35 4010 15 2 0 25Time (sec) 1st Story

„po'

Q0

CO1 0c

10 15 2 0 25 30 35 40Time (sec)

Figure 6-15: Inter-story horizontal drift ratio histories - Dynamic Test 1

<n -20 m -20

2 0 2 2nd Story Drift (%)

-2 0 2 3rd Story Drift (%)

E x p e rim e n t A n a ly s is

-2 0 2 1st Story Drift (%)

Figure 6-16: Inter-story horizontal drift ratios vs. shears - Dynamic Test 1

170


-1

-1.5L

— Column A1 - Experiment Column B1 - Experiment

— Column A1 - Analysis --Column B1 - Analysis

— Column B1 S hear Failure Initiation - Experiment — Column B1 Shear Failure Initiation - Analysis i______ i______ i______ i______ i_____25 30 35 40 45Time (sec)

1 0 15 2 0 50

Figure 6-17: Columns A1 & B l inter-story vertical drift ratio history - Dynamic Test 1

C o lu m n A1 - E xperim en t C o lu m n A1 - A n a ly sis— C o lu m n B1 S h e a r F a ilu re In itiation - E x p e r im e n t ' — C o lu m n B1 S h e a r F a ilu re In itiation - A n a ly sis

1 0 15 2 0 25 30Time (sec)

35 40 45 50

Figure 6-18: Column A1 axial load histories — Dynamic Test 1

171


Column B1 -Experiment —Column B1 - Analysis

I— Column B1 Shear Failure Initiation - Experiment ! — Column B1 Shear Failure Initiation - Analysis

* -20

20 25 30Time (sec)

Figure 6-19: Column B1 axial load histories - Dynamic Test 1

p i I s p if f n V

C olum n C1 - Experim ent C olum n D1 - Experim ent C olum n C1 - A nalysis C olum n D1 -A nalysis C olum n B1 S h e a r Failure Initiation - Experim ent C olum n B1 S h e a r Failure Initiation - A nalysis* - 2 0

20 25 30Time (sec)

Figure 6-20: Columns C l & D1 axial load histories - Dynamic Test 1

172


During Dynamic Test 1, Column B1 sustained severe shear damage and strength

degradation along with gradual but incomplete axial “failure.” Column A1 did not

experience either shear or axial degradations. The analytical model, however, showed

shear failures o f both Columns A1 and B l, with axial failure initiation in both columns as

well. The analytical shear failures o f Columns A1 and B l occurred at about the same

time t=22sec, about a half cycle prior to the actual shear failure initiation o f Column B 1

in the experiment. The shear and axial failures o f Columns A1 and B l will be discussed

in more detail in the subsequent section.

Prior to the initiation o f the shear failures, the analytical model floor-level

accelerations are roughly in phase with the experimental ones, but substantially over

shoot the response peaks. Analytical story shears and drifts, on the other hand show

closer agreement with the experimental results. Figure 6-16 compares experimental and

analytical first-story shears. The results compare reasonably well for the first story prior

to shear failure. For the second and third stories, magnitudes o f story shears compare well

but the analytical model exhibits a stiffer response than was measured. This additional

stiffness was also observed during the Half-Yield dynamic test.

The axial failures o f Columns A1 and B l occur in the analytical model shortly after

shear failures at the points where the columns reach their residual shear capacity. These

failures occur much more rapidly in the model than in the test-frame (Figure 6-17). The

axial load shed by Column B l in the model is transferred to Columns A1 and Cl while

generating some uplift in Column D l; a behavior that is similar to the one observed in the

laboratory test.

173


6.2.2.2 Flexure-Shear-Critical Column Behavior

Figure 6-21 through Figure 6-26 compare analytical and experimental results for the

first-story flexure-shear-critical columns at axes A and B. These figures show good

agreement between analysis and experiment up to the initiation o f shear failures in

Columns A1 and B l in the analysis. The analytical critical section rotations presented in

Figure 6-25 match fairly well the experimental rotations, suggesting that the column

discretization scheme and the bar slip fiber-section representation implemented in the

analytical model modeled behavior fairly well. This translated to a similarly good

modeling at the column global level as well (Figure 6-21 and Figure 6-26).

Column B1 Column A1

Experiment— Analysis

Q.

- 1 0

Drift (%)

Q.

-10

Drift (%)

Figure 6-21: Columns A1 & B l inter-story horizontal drift ratios versus shears - Dynamic Test 1

174


Column B1 Column A1

E x p e n m e n t A n a ly s is

0Drift (%)

0Drift (%)

Figure 6-22: Columns A1 & B l inter-story horizontal drift ratios versus axial loads - Dynamic Test 1

Column B1 Column A10.5 0.5

E x p e rim en t — A n a ly sis

QCDOECD> -0.5 -0.5

Horizontal Drift (%) Horizontal Drift (%)

Figure 6-23: Columns A1 & B l inter-story horizontal vs. vertical drift ratios - Dynamic Test 1

175


Botto

m M

omen

t (k

ip-in

.) To

p M

omen

t (k

ip-in

.)

Experiment Analysis

-25 -20 -15Axial Load (kips)

Figure 6-24: Column B l axial load vs. inter-story vertical drift ratio — Dynamic Test 1


200

-100

- 2 0 0 J -

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

2 0 0

1 0 0

-100

-200[______-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Column B1 Bottom Column A1 Botttom200 Experiment

— Analysis10 0

-100

-2 0 0 1- , --0.06 -0.04 -0.02 0 0.02 0.04 0.06

200

1 0 0

-100

-200 [- — :— -

-0.06 -0.04 -0.02 0 0.02 0.04 0.06Rotation(h=6in.) - (rad) Rotation(h=6in.) - (rad)

Figure 6-25: Columns A1 & B l critical section rotations vs. top & bottom moments - Dynamic Test 1

176


Mom

ents

(k

ip-in

.) M

omen

ts

(kip

-in.)

Column B1 Top Moments Column A1 Top Moments

200

150

1 0 0

/"?

■5 0 5Drift (%)

Column B1 Bottom Moments

Drift (%)

200

150 - U -

1 0 0

5 0 5

200 ExperimentAnalysis

150

100

_ciQ_

tn -*—.c0Eo

05 5Drift (%)

Column A1 Bottom Moments

200 ExperimentAnalysis

150

1 0 0

ci

Q.

Wc0Eo

100

150

■200

5 0 5Drift (%)

Figure 6-26: Columns A1 & B l inter-story horizontal drift ratios vs. top and bottom moments - Dynamic Test 1

111


As can be seen in Figure 6-21 Columns A1 and B l sustained shear failures in the

analytical model at nearly identical times and at drift ratios o f 2.22% and 2.47%

respectively. These drifts are lower than the experimental drift ratio at shear failure o f

Column B l o f 3.24%. Clearly, improvements in the shear failure triggering model are

required to better simulate shear failure in the test frame.

The shear LimitState spring attached to Column B l appears to model the shear

degrading slope o f that column fairly well even though the failure in the analysis

occurred half a cycle prior the experimental failure (Figure 6-21). After reaching its

residual capacity, the shear behavior o f Column B 1 is observed to be fairly random; this

is not surprising considering the complex geometry o f the failed section and the

continually varying axial load. This makes modeling that behavior very difficult; the

LimitState model approach o f keeping the analytical column shear capacity close to the

residual capacity appears to be a reasonable simplification o f this behavior.

In the analysis, the axial failures o f Columns A1 and B l initiated at the point where

these columns reached their residual shear strength (Figure 6-21). Column B l sheds a

significant amount o f axial load past that point (Figure 6-19) while Column A1 shortens

appreciably while taking on additional axial load from Column B l (Figure 6-23 and

Figure 6-18). Figure 6-23 illustrates the behavior o f the LimitState axial failure springs.

In its current formulation, the LimitState axial failure model forces the axial spring

element to follow the shear-friction model vertical deformation curve (see Section 2.1) so

long as the lateral drift o f the column exceeds the axial failure envelope. Once the column

drift reverses direction the axial spring is redefined elastically with a reduced stiffness

equivalent to 1 / 1 0 0 th o f the original stiffness to account for the damage in the column

178


which effectively halts the axial collapse o f the column. This behavior does not represent

behavior observed in the dynamic tests (Sections 5.4.2 and 5.5.2), with the main

differences between analysis and experiment being: 1 ) the test frame columns were

observed to initiate loss o f axial capacity due to the degradation o f the column shear

capacity to its residual and not due to the columns reaching an axial failure drift

envelope, and 2 ) the axial degradation was far more gradual, appeared to be related to the

cyclic damage o f the failed section, and occurred throughout the cyclic response and not

just beyond the axial drift envelope.

6.2.2.3 Ductile Column Behavior

Figure 6-27 and Figure 6-28 compare analytical and experimental results for the

first-story ductile columns at axes C and D. Load-deformation responses compare

favorably up to the yield point. Ultimate moments and shears are under-estimated in the

analysis.

179


Column D1 Top Moments Column C1 Top Moments

o_

C0»coEo

1 5 0

1 0 0

5 0

-5 0

-100

- 1 5 0

Column D1 Bottom Moments

ExperimentAnalysis

05 5Drift (%)

Column C1 Bottom Moments

1 5 0

1 0 0

5 0Q.

1*:w+jc<pEo -50

-100

-150

1 5 0

1 0 0

5 0

Q.

«C<DEo

- 5 0

-100

- 1 5 0

ExperimentAnalysis

-5 0 5 -5 0n r i f t 10/ \ n r i f t 10,

Figure 6-27: Columns C l and D1 inter-story horizontal drift ratios vs. top and bottom moments - Dynamic Test 1

180


Column D1 Column C1

Experimentj — Analysis j

CDCD

JZC/3

Drift (%)

COQ.!*:

CO

Drift (%)

Figure 6-28: Columns C l & D1 inter-story horizontal drift ratios vs. shears - Dynamic Test 1

6.3 Equivalent Elastic Column Flexural Stiffnesses

To obtain specific frame element stiffnesses it is necessary to consider experimental

results o f each element individually. The force-deformation relations o f the first-story

columns were recorded but due to the variable end-fixity conditions o f these columns at

their tops, a direct stiffness measure is not available from the recorded data.

An analytical exercise was undertaken to identify the effective stiffness o f the first-

story columns as modeled by the OpenSees analytical model. For this purpose, cantilever

columns extending from the base (top o f footing) to the column midheight were

developed in OpenSees using the same modeling properties used in the OpenSees

analytical model o f the test frame. These cantilever column models included the bar slip

zero-length fiber-section implementation described in Section 6.1.4. Under

181


monotonically increasing lateral loads, with constant axial loads equal to the initial

values, these analytical models resulted in initial “un-cracked” stiffnesses (tangent

stiffness at zero-load) o f 69.2 kip/in. for Column A1 and 70.6 kip/in. for Column B l, and

secant stiffnesses (measured between zero-load and the yield point) o f 32.5 kip/in. for

Column A1 and 34.5 kip/in. for Column B l. These values are equivalent to columns with

elastic flexural stiffness o f 0.58EIgross for the tangent stiffness and 0.28EIgrOss for the

secant stiffness (with E=2750 ksi).

182


7 Flexure-Shear-Critical Column Shear

Failure Models

As noted in Chapters 5 and 6 , shear failure appears to be related to inelastic

deformation demands. Furthermore, these demands appear to be different at opposite

ends o f the column because o f different boundary conditions and loadings, suggesting

that a shear failure model should directly consider the inelastic demands at the column

ends rather than a smeared deformation demand for the entire column. A new shear

failure model that relates shear strength degradation to column end rotation in flexure-

shear-critical columns is proposed. A database o f 56 column tests is used in a parametric

regression analysis to determine factors that most significantly affect the rotation capacity

o f this type o f column. Factors affecting the rate o f shear strength degradation are also

investigated and incorporated in a simplified model.

As mentioned in Section 2.1.1, some models for estimating column shear strength

given imposed deformations can be inaccurate for the inverse problem o f estimating

column deformations given shear force demands. Models that are directly derived to

estimate deformations are preferable. Some models previously derived for this purpose

[Pujol et al. (1999); Kato and Ohnishi (2002); Elwood and Moehle (2005b)] relate

horizontal drift ratio at shear failure to various configuration and demand parameters.

These models were derived empirically from column tests with essentially fixed-fixed

end conditions. Because o f variable fixity conditions and other loading parameters, actual

column response in a building frame may not resemble fixed-fixed conditions (see for

183


example, Section 5.4.2) An alternative approach is developed here in which deformation

at shear failure is related to end rotations o f the column, thereby making the model more

suitable for frames in which end rotations are not the same at opposite ends o f a column.

Beyond initiation o f shear failure, shear strength degradation is defined in terms o f

column shear deformations rather than end rotations because rotations o f shear-damaged

sections are not well defined.

7.1 Column Database

A database o f 56 tests conducted on flexure-shear-critical columns with light

transverse reinforcement (p”<0.007) is used to develop the proposed shear failure

models. All tests were conducted under reversed cyclic deformations, and four were

conducted dynamically. All tests were subjected to horizontal deformations in a single

plane. Table 7-1 summarizes geometric, material, and experimental setup properties o f

these columns. The first fifty column properties and test results were compiled by Sezen

(2002). The database includes columns with the following range o f properties:

• shear span to depth ratio: 2.0<a/d<4.0 (mean=3.0)

. transverse reinforcement spacing to depth ratio: 0.2<s/d< \ . 2 (mean=0.62)

concrete compressive strength: 1900</c<6500 psi (mean=3700 psi)

• longitudinal-reinforcement yield stress: 47</;,/<80 ksi (mean=60 ksi)

• longitudinal reinforcement ratio: 0.01<p/<0.04 (mean=0.023)

• transverse-reinforcement yield stress: 46<fyt<\00 ksi (mean=65 ksi)

transverse reinforcement ratio: 0 .0010</> ”<0.0065 (mean=0.0028)

. maximum nominal shear stress: 2.8< v / ^ ] f 'c ,psi<8 . 6 (mean=5.5)

axial load ratio: 0.0<P!Agf c <0.6 (mean=0.2)

184


where a is the shear span, d is the column depth from extreme compression fiber to

centerline o f outermost tension reinforcement, s is the spacing o f transverse

reinforcement, p/=Asi/bh; A si is the area o f the longitudinal reinforcement; b is the column

section width, h is the column section depth; p”=Ast/bs, A st is the area o f transverse

reinforcement in the direction o f lateral load at spacing s, v is the maximum nominal

shear stress in psi, f c is the concrete cylinder compressive strength, P is the axial load,

and Ag is the gross cross-sectional area o f the column.

Table 7-1: Column database properties

ColumnDesignation

b h d a s Pi P" fyi fyt f; TestType

in. in. in. in. in. ksi ksi ksiSezen (2002)

SE2CLD12 18 18 15.5 58 12 0.025 0.0017 64 68 3.06 DC/CSE2CHD12 18 18 15.5 58 12 0.025 0.0017 64 68 3.06 DC/CSE2CVD12**

18 18 15.5 58 12 0.025 0.0017 64 68 3.03 DC/C

SE2CLD12M 18 18 15.5 58 12 0.025 0.0017 64 68 3.16 DC/C

Lynn (2001)LY_3CLH18 18 18 15 58 18 0.030 0.0012 48 58 3.71 DC/CLY3SLH18 18 18 15 58 18 0.030 0.0012 48 58 3.71 DC/CLY2CLH18 18 18 15 58 18 0.019 0.0012 48 58 4.8 DC/CLY2SLH18 18 18 15 58 18 0.019 0.0012 48 58 4.8 DC/CLY2CMH18 18 18 15 58 18 0.019 0.0012 48 58 3.73 DC/CLY3CM H18 18 18 15 58 18 0.030 0.0012 48 58 4.01 DC/CLY3CM D12 18 18 15 58 12 0.030 0.0017 48 58 4.01 DC/CLY3SM D12 18 18 15 58 12 0.030 0.0017 48 58 3.73 DC/C

Ohue et al. (1985)OH2D16RS 7.87 7.87 6.89 15.7 1.97 0.020 0.0056 54 46 4.65 DC/COH4D13RS 7.87 7.87 6.89 15.7 1.97 0.025 0.0056 54 46 4.34 DC/C

Esaki (1996)ES_H_2_1_5 7.87 7.87 6.89 15.7 1.97 0.025 0.0052 52 53 3.34 DC/CES_HT_2_1_5 7.87 7.87 6.89 15.7 2.95 0.025 0.0052 52 53 2.93 DC/CES_H_2_1_3 7.87 7.87 6.89 15.7 1.57 0.025 0.0065 52 53 3.34 DC/CES_HT_2_1_3 7.87 7.87 6.89 15.7 2.36 0.025 0.0065 52 53 2.93 DC/C

Li et al. (1991)LI_U_7 15.8 15.8 14.8 39.4 4.7 0.024 0.0047 64.7 55.4 4.21 SC/CLI U 8 15.8 15.8 14.8 39.4 4.7 0.024 0.0052 64.7 55.4 4.86 SC/CLI U 9 15.8 15.8 14.8 39.4 4.7 0.024 0.0057 64.7 55.4 4.95 SC/C

Saatcioglu and Ozcebe (1989)

185


S A JJl 13.8 13.8 12 39.4 5.9 0.033 0.0030 62.4 68.2 6.32 SC/CS A U 2 13.8 13.8 12 39.4 5.9 0.033 0.0030 65.7 68.2 4.38 SC/CSA U 3 13.8 13.8 12 39.4 2.95 0.033 0.0060 62.4 68.2 5.05 SC/C

Yalcin and Saatcioglu (2000)Y A B R S 1 21.7 21.7 19 58.5 11.8 0.020 0.0010 64.5 61.6 6.5 SC/C

Ikeda (1968)*IK_43 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 63 81 2.84 SC/CI K 4 4 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 63 81 2.84 SC/CI K 4 5 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 63 81 2.84 SC/CI K 4 6 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 63 81 2.84 SC/CI K 6 2 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 50 69 2.84 SC/CI K 6 3 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 50 69 2.84 SC/CI K 6 4 7.87 7.87 6.81 19.7 3.9 0.020 0.0028 50 69 2.84 SC/C

Umemura and Endo (19760)*UM_205 7.87 7.87 7.09 23.6 3.9 0.020 0.0028 67 47 2.55 SC/CUM_207 7.87 7.87 7.09 15.8 3.9 0.020 0.0028 67 47 2.55 SC/CUM_214 7.87 7.87 7.09 23.6 7.9 0.020 0.0014 67 47 2.55 SC/CU M 220 7.87 7.87 7.09 15.8 4.7 0.012 0.0011 55 94 4.77 SC/CUM231 7.87 7.87 7.09 15.8 3.9 0.010 0.0013 47 76 2.14 SC/CUM_232 7.87 7.87 7.09 15.8 3.9 0.010 0.0013 47 76 1.9 SC/CUM_233 7.87 7.87 7.09 15.8 3.9 0.012 0.0013 54 76 2.02 SC/CUM_234 7.87 7.87 7.09 15.8 3.9 0.012 0.0013 54 76 1.9 SC/C

Kokusho (1964)*KO_372 7.87 7.87 6.69 19.7 3.9 0.008 0.0031 76 51 2.88 SC/CKO_373 7.87 7.87 6.69 19.7 3.9 0.020 0.0031 76 51 2.96 SC/C

Kokusho and Fukuhara (1965)*K 0 452 7.87 7.87 6.69 19.7 3.9 0.030 0.0031 52 88 3.18 SC/CKO_454 7.87 7.87 6.69 19.7 3.9 0.040 0.0031 52 88 3.18 SC/C

Wight and Sozen (1973)WI_40_033aW 6 12 10.5 34.5 5 0.025 0.0033 72 50 5.03 SC/C

WI_40_033E 6 12 10.5 34.5 5 0.025 0.0033 72 50 4.87 SC/CWI_25_033E 6 12 10.5 34.5 5 0.025 0.0033 72 50 4.88 SC/CWI 0 033E 6 12 10.5 34.5 5 0.025 0.0033 72 50 4.64 SC/CWI 40 048W 6 12 10.5 34.5 3.5 0.025 0.0047 72 50 3.78 SC/CWI 0 048W 6 12 10.5 34.5 3.5 0.025 0.0047 72 50 3.75 SC/C

Elwood (2002)E L s p l 9 9 7.75 29 6 0.025 0.0018 69.5 100 3.56 DC/DEL_sp2 9 9 7.75 29 6 0.025 0.0018 69.5 100 3.47 DC/D

Current WorkGH ColA l 6 6 5.15 19.5 4 0.025 0.0015 80 95 3.57 DC/DGHColB 1 6 6 5 .15 19.5 4 0 .0 2 5 0 .0 0 1 5 80 95 3.57 DC/D

Yoshimura et al. (2003)Y O N 06 11.8 11.8 10 23.6 3.94 0.018 0.0019 59.3 56.8 4.45 DC/CYO_No7 11.8 11.8 10 23.6 5.9 0.018 0.0013 59.3 56.8 4.45 DC/C

* Data reported by Masaya (1973)Notation: DC=double-curvature test; SC=single-curvature test; C=cyclic test; D=dynamic test.

186


For most columns only a shear force versus lateral displacement plot was available.

Relevant experimental response values were extracted from these plots and are

summarized in Table 7-2. Figure 7-1 illustrates these response values.

max

max

(5shear

Figure 7-1: Column shear versus drift ratio envelope - illustration o f notation

Table 7-2: Column database extracted response values

ColumnDesignation

Vy 8y Y P/ A f

Vv max 6 m \ Kdeg

kips % kips % kip/% (drift)SE 2CLD12 55.7 0.90 0.25 0.15 70.8 1.90 -28.9SE 2CHD12 64.1 0.49 0.53 0.61 80.7 0.88 -76.7SE 2CVD12 61.8 0.66 0.39 0.51 67.6 0.95 -31.3SE 2CLD12M 53.0 0.96 0.22 0.15 66.2 2.07 -17.7LY 3CLH18 54.9 0.67 0.30 0.09 61 1.03 -47.0LY 3SLH18 51.5 0.53 0.36 0.09 60 0.78 -21.4LY 2CLH18 45.0 0.62 0.24 0.07 54 2.59 -57.3LY 2SLH18 48.0 0.54 0.29 0.07 52 1.08 -12.5LY 2CMH18 65.0 0.53 0.46 0.28 71 1.03 N.A.LY 3CMH18 70.0 0.71 0.35 0.26 76 0.91 -47.6LY 3CMD12 70.0 0.64 0.39 0.26 80 1.03 -41.0LY 3SMD12 72.0 0.74 0.36 0.28 85 1.55 -142.5OH 2D16RS 19.2 0.96 0.13 0.14 22.9 2.74 -7.8OH 4D13RS 20.5 0.83 0.17 0.15 24.9 1.72 -8.0ES H 2 1 5 16.5 0.51 0.25 0.17 23.2 2.04 -8.3

187


ES HT 2 1 5 17.8 0.61 0.25 0.18 22.9 1.87 -7.6ES H 2 1 3 19.7 0.45 0.34 0.29 27.1 1.06 -5.9ES HT 2 1 3 20.6 0.61 0.28 0.29 25.1 1.51 -5.4LI U 7 68.3 0.89 0.21 0.10 73.7 3.55 -34.9LI U 8 79.1 0.84 0.24 0.20 88.3 1.26 -18.0LI U 9 80.4 0.76 0.26 0.30 96.6 2.26 -26.2SA U1 50.5 1.70 0.11 0.00 61.8 4.52 -5.8SA U2 50.7 1.50 0.15 0.16 60.7 3.03 -14.9SA U3 51.5 1.60 0.14 0.14 60.3 2.72 -6.2YA BR SI 120.4 0.55 0.30 0.15 130 1.01 -100.0IK 43 13.7 0.66 0.28 0.10 16.6 2.13 N.A.IK 44 14.3 0.66 0.29 0.10 17.2 1.62 N.A.IK 45 16.0 0.96 0.22 0.20 18.5 1.62 N.A.IK 46 17.0 0.96 0.23 0.20 18.1 1.22 N.A.IK 62 11.9 0.61 0.26 0.10 13 1.76 N.A.IK 63 12.8 0.61 0.28 0.20 15.4 2.35 N.A.IK 64 14.6 0.71 0.27 0.20 15.4 1.89 N.A.UM 205 14.0 0.81 0.35 0.22 16 2.08 N.A.UM 207 21.6 1.01 0.19 0.22 23.8 1.27 N.A.UM 214 17.6 1.02 0.35 0.56 18.6 1.48 N.A.UM 220 14.6 0.38 0.25 0.12 17.6 2.03 N.A.UM 231 9.8 0.25 0.38 0.26 11.4 1.01 N.A.UM 232 10.8 0.32 0.36 0.30 13.1 1.01 N.A.UM 233 13.0 0.38 0.35 0.28 15.5 1.71 N.A.UM 234 13.1 0.38 0.36 0.30 15.1 2.03 N.A.KO 372 13.4 0.51 0.35 0.20 16.7 1.98 -35.5KO 373 16.1 0.71 0.30 0.19 19.8 1.87 -53.6KO 452 20.3 0.61 0.42 0.45 24.8 1.27 0.0KO 454 19.7 0.46 0.54 0.45 24.8 1.02 -44.7WI 40 033aW 20.3 0.87 0.27 0.12 21.5 2.64 0.0WI 40 033E 20.6 1.39 0.17 0.11 19.9 3.88 0.0WI 25 033E 18.0 1.36 0.15 0.07 18.4 3.59 -9.3WI 0 033E 15.2 0.87 0.21 0.00 18.2 2.61 -5.1WI 40 048W 21.2 1.65 0.17 0.15 21.3 5.54 N.A.WI 0 048W 16.5 1.54 0.14 0.00 19.3 6.35 N.A.EL spl 16.3 1.31 0.19 0.10 18.1 2.62 -4.0EL sp2 18.7 1.36 0.21 0.24 19.8 1.69 -3.2GH ColAl 8.1 N/A 0.28 0.17 7.25 3.26 N.A.GH ColBl 8.1 N/A 0.28 0.19 9.87 3.15 -3.9YO No6 38.8 0.54 0.22 0.20 49.3 2.00 N.A.YO No7 37.1 0.52 0.22 0.20 47.9 1.50 N.A.

Notation: Vy=column shear force at flexural yielding; 5y= drift ratio at yielding; y= Ieffective/Igross; Igross=column section moment of inertia; Ieffective=column section effective moment of inertia = Vya3/(3EAy); E=concrete modulus of elasticity as per ACI 318-05 [ACI (2005)]; Ay=a5y/100; P=axial load (at time of shear failure initiation); Vmax=maximum shear at shear failure initiation; 5max=column drift ratio at Vmax; Kdeg=column degrading slope due to shear strength degradation.

188


Table 7-2 presents shear (Vy) and drift ratio (8 y) values at flexural yielding. For

specimens with no reported yield displacement, the yield displacement was estimated by

running a secant to intersect the lateral load-displacement relation at 70% o f the

maximum lateral load (Figure 7-2). This line was extended to the intersection with a

horizontal line drawn at maximum lateral load, and then projected onto the horizontal

axis to obtain the yield displacement (Ay= 8y*a/100). Shear force at yield (Vy) was taken

at the intersection o f the vertical projection o f Ay with the lateral load-displacement

relation, and the coordinate (Ay, Vy) defines the yield point. This method was shown to

give reasonable accuracy by Sezen (2002).

80

60

40

I 2 0

8 o"mIS -20

-40

-80

—80- 6 - 4 -2 0 2 4 8

lateral displacement fln.)

Figure 7-2: Illustration o f yield displacement and shear force estimation (adaptedfrom Sezen (2002))

From the experimentally obtained values Vy and Sy, equivalent column elastic

stiffnesses were calculated (Keff=3EIeff/a3= Vy/ Ay). Axial load (P), shear force (Vmax),

189


and drift ratio (5max) values extracted just prior to shear failure initiation are presented in

the table as well. Initiation o f column shear failure is defined in this study as the point o f

maximum shear at which columns begin to lose shear strength. Residual shear strength

(Vr) for all columns in the database is fixed at 15% o f Vmax. A more detailed assessment

o f residual shear strength was not warranted because o f observed erratic behavior in shear

strength beyond residual capacity, particularly in dynamic tests.

When possible, slopes o f column shear degradation (Kdeg, illustrated in Figure 7-1)

are estimated and presented in Table 7-2. In this approach a linear degrading behavior is

assumed where Kdeg values are obtained by drawing a line between the point o f shear

failure initiation (5max, Vmax) and the point on the load-displacement relation envelope

closest to Vr with coordinates (5f, Vf). Thus, Kdeg is given by:

Note that the rate o f degradation as represented by Kdcg likely is strongly influenced by

deformation history during the degrading portion o f the test. For example, the degrading

slope o f the test column shown in Figure 7-2 probably would have been less steep had the

the degrading stage (Sezen 2002).

7.2 Analytical Representation of Database Columns

7.2.1 Analytical Model Description

For most o f the column tests in the database, the available test data were limited to

the global relation between shear force and lateral displacement. To better understand

^max ~ V f f k i p s ' ' (7-1)

max % Jm a x

column been tested under monotonically increasing drift rather than several cycles during

190


local distributions o f deformations, the fiber-section column model presented in Chapter

6 was used to model all database columns. (Although this analytical model was fairly

accurate in modeling the test frame columns, it cannot be expected that this model is

accurate in all cases. Therefore, the analytic results obtained from the model must be

understood to be only an indicator o f likely behavior, but not a true measure o f it.) All

column specimens were modeled as cantilever elements having lengths equal to half

column specimen length for double-curvature test and equal to column specimen length

for single-curvature tests. Pushover analyses were performed on all column analytical

models with increasing lateral deformations applied at cantilever tips. Figure 7-3 presents

a sample pushover curve overlaid on the scaled (from double-curvature test results)

experimental shear-drift relation for column SE 2CLD12.

60

40

wT 20CL

- 2 0

-40

-60

-803 •2 1 0 1 2 3

Drift (in.)

Figure 7-3: Sample pushover curve overlaid on experimental shear-drift relation(for column SE 2CLD12)

191


Concrete material properties in the analytical column models were based on reported

f’c values and ACI 318-05 [ACI (2005)] recommendations for E (concrete modulus o f

elasticity). Steel material properties were based on reported fyi values, modulus o f

elasticity Es=29,000 ksi, and a hardening ratio o f 0.01. Column flexural deformations

were then calculated using these properties and the OpenSees column model. The bond

stress for the bond-slip model was then varied to match analytical column stiffnesses with

experimental ones.

The bond stress that, in the aggregate, resulted in the best fit between analytical and

experimental column stiffnesses was ue= l l -Jf'c (psi). This elastic bond-stress was used

to determine bar-slip fiber-section material properties in the same fashion as described in

Section6.1.4. The resulting error between column analytical and experimental elastic

Stiffnesses is defined as; e s — ( K y - a n a l y s i s - K y-experiment)/ Ky-experiment (Ky-analysis — Column

analytical elastic stiffness; Ky_experiment = column experimental elastic stiffness). The

choice o f ue= 1 1 f ' c (psi) produced a mean error in elastic stiffness across all database

columns o f 0.01 with a standard deviation o f 0.39.

7.2.2 Analytical Model Results

Pushover analyses conducted on column models yielded several column rotation

measures (Table 7-3). Flexural rotations presented in Table 7-3 are measured over a

plastic hinge length h=column section height.

In cases o f column flexural softening, erroneous bar slip and flexural rotations can

arise in the fiber-section formulation because plastic rotations concentrate in either the

column element or bar-slip element, which results in the unloading o f the other element.

To adjust for this effect, the ratio Obf) o f bar-slip rotations to column flexural rotations

192


measured over Lp is evaluated just prior to softening. This ratio is assumed constant from

initiation o f softening up to 5max. Thus, at 8 max total rotations (bar slip rotations + flexural

rotations over Lp) are extracted and split into bar slip and column flexural rotations

according to the ratio rbf. Total rotations are shown not to be significantly affected by

column softening in Section 6 .1.4.

Table 7-3: Column database analytical rotation values

ColumnDesignation 0 f V 0fPlmax 0fTotmax 0RSv 0BSPlmax 0BSTotmax 0TotPlmax 0Totmax

rad rad rad rad rad rad rad radSE 2CLD12 0.0040 0.0039 0.0078 0.0042 0.0058 0.0100 0.0097 0.0178SE 2CHD12 0.0021 0.0015 0.0036 0.0023 0.0020 0.0042 0.0035 0.0078SE 2CVD12 0.0027 0.0012 0.0039 0.0031 0.0015 0.0046 0.0026 0.0084SE 2CLD12M 0.0043 0.0044 0.0086 0.0045 0.0064 0.0109 0.0108 0.0196LY 3CLH18 0.0033 0.0016 0.0049 0.0027 0.0018 0.0045 0.0033 0.0094LY 3SLH18 0.0027 0.0011 0.0037 0.0021 0.0010 0.0031 0.0021 0.0069LY 2CLH18 0.0035 0.0107 0.0142 0.0022 0.0087 0.0109 0.0194 0.0251LY 2SLH18 0.0031 0.0028 0.0060 0.0019 0.0022 0.0041 0.0051 0.0101LY 2CMH18 0.0028 0.0026 0.0054 0.0020 0.0021 0.0041 0.0047 0.0095LY 3CMH18 0.0035 0.0009 0.0044 0.0028 0.0009 0.0037 0.0018 0.0081LY 3CMD12 0.0031 0.0018 0.0050 0.0025 0.0019 0.0044 0.0037 0.0093LY 3SMD12 0.0036 0.0041 0.0077 0.0030 0.0040 0.0069 0.0080 0.0146OH 2D16RS 0.0042 0.0071 0.0113 0.0052 0.0101 0.0153 0.0172 0.0266OH 4D13RS 0.0041 0.0038 0.0079 0.0040 0.0045 0.0085 0.0083 0.0164ES H 2 1 5 0.0024 0.0067 0.0092 0.0025 0.0079 0.0104 0.0147 0.0196ES HT 2 1 5 0.0030 0.0051 0.0081 0.0033 0.0064 0.0096 0.0115 0.0177ES H 2 1 3 0.0021 0.0026 0.0047 0.0022 0.0031 0.0052 0.0057 0.0100ES HT 2 1 3 0.0029 0.0037 0.0067 0.0032 0.0046 0.0078 0.0083 0.0145LI U 7 0.0044 0.0119 0.0164 0.0041 0.0144 0.0186 0.0264 0.0349LI U 8 0.0043 0.0019 0.0062 0.0037 0.0021 0.0058 0.0040 0.0121LI U 9 0.0039 0.0074 0.0112 0.0033 0.0074 0.0107 0.0147 0.0219SA U1 0.0080 0.0122 0.0202 0.0083 0.0156 0.0239 0.0278 0.0441SA U2 0.0064 0.0063 0.0127 0.0078 0.0087 0.0165 0.0150 0.0292SA U3 0.0072 0.0050 0.0122 0.0081 0.0060 0.0141 0.0109 0.0262YA BR SI 0.0032 0.0026 0.0057 0.0020 0.0018 0.0038 0.0044 0.0095IK 43 0.0026 0.0048 0.0074 0.0038 0.0094 0.0132 0.0142 0.0205IK 44 0.0026 0.0031 0.0057 0.0038 0.0060 0.0097 0.0091 0.0155IK 45 0.0037 0.0020 0.0057 0.0056 0.0041 0.0097 0.0061 0.0154IK 46 0.0037 0.0007 0.0044 0.0056 0.0014 0.0069 0.0020 0.0113IK 62 0.0027 0.0042 0.0069 0.0032 0.0069 0.0101 0.0112 0.0170IK 63 0.0026 0.0072 0.0098 0.0032 0.0096 0.0128 0.0168 0.0226IK 64 0.0030 0.0047 0.0078 0.0038 0.0064 0.0102 0.0112 0.0180

193


UM 205 0.0033 0.0043 0.0076 0.0041 0.0078 0.0120 0.0122 0.0196UM 207 0.0039 0.0007 0.0046 0.0060 0.0012 0.0072 0.0019 0.0118UM 214 0.0039 0.0018 0.0057 0.0055 0.0025 0.0081 0.0043 0.0137UM 220 0.0021 0.0084 0.0104 0.0016 0.0075 0.0091 0.0158 0.0195UM 231 0.0013 0.0035 0.0049 0.0011 0.0034 0.0045 0.0069 0.0094UM 232 0.0016 0.0033 0.0049 0.0014 0.0031 0.0045 0.0063 0.0094UM 233 0.0018 0.0058 0.0075 0.0019 0.0069 0.0088 0.0127 0.0163UM 234 0.0017 0.0074 0.0091 0.0019 0.0085 0.0104 0.0158 0.0195KO 372 0.0021 0.0061 0.0082 0.0028 0.0081 0.0109 0.0142 0.0191KO 373 0.0024 0.0037 0.0061 0.0044 0.0074 0.0118 0.0111 0.0179KO 452 0.0023 0.0023 0.0046 0.0034 0.0038 0.0071 0.0060 0.0117KO 454 0.0016 0.0018 0.0034 0.0026 0.0031 0.0057 0.0049 0.0091WI 40 033aW 0.0041 0.0072 0.0113 0.0039 0.0102 0.0141 0.0173 0.0254WI 40 033E 0.0063 0.0100 0.0163 0.0070 0.0146 0.0216 0.0246 0.0379WI 25 033E 0.0061 0.0090 0.0151 0.0069 0.0130 0.0199 0.0220 0.0350WI 0 033E 0.0041 0.0069 0.0109 0.0040 0.0102 0.0142 0.0170 0.0251WI 40 048W 0.0069 0.0151 0.0220 0.0089 0.0235 0.0324 0.0386 0.0544WI 0 048W 0.0064 0.0179 0.0243 0.0082 0.0298 0.0380 0.0477 0.0623EL spl 0.0059 0.0056 0.0115 0.0061 0.0071 0.0131 0.0126 0.0246EL sp2 0.0062 0.0012 0.0073 0.0064 0.0016 0.0080 0.0027 0.0154GH C olA l 0.0047 0.0079 0.0126 0.0056 0.0128 0.0184 0.0208 0.0310GH C olBl 0.0046 0.0075 0.0121 0.0056 0.0118 0.0174 0.0193 0.0295YO No6 0.0031 0.0078 0.0109 0.0023 0.0062 0.0085 0.0140 0.0194YO No7 0.0031 0.0049 0.0080 0.0023 0.0040 0.0063 0.0089 0.0143

Notation: 0 T„ im a x = c o \ w m n total rotations at shear failure initiation m easured over a p lastic h inge length Lp in clud ing bar-slip induced rotations; O f T o tm a x = c o \ u m n flexural rotations at shear failure in itiation m easured over a p lastic h in ge length Lp exclu din g bar-slip induced rotations; #BS7brma*= bar-slip com ponent o f d Tomax= 0Tolmm-9fTolmax; 6W /m ot=plastic rotation com ponent o f Orotmax', 0ff>/mox=plastic rotation com ponent o f dfrotmax', % =colum n flexural rotations over Lp at y ie ld exclu d in g bar-slip rotations; <9s ,sy=bar-slip induced rotations at y ield; 8BSpimax=bar-slip p lastic rotations at shear failure in itiation = 6BsTotmax-9BSy

To assess the sensitivity o f rotation values presented in Table 7-3 to assumed bond-

stress values, column pushover analyses were undertaken for ue= f ' c (psi), with the

bond-stress parameter X=6 , 11, and 18. From these analyses, the total rotation at 5max

(0Totmax), which includes flexural rotations over Lp and bar-slip rotations, was found to be

insensitive to bond-stress assumption. Figure 7-4 plots the relative differences in 0Totmax

for the various bond-stress parameters. These relative differences are defined for each

column as: (0TOtmax(7.=6 or 18)- 0Totmax(A.=l 1))/ 0Totmax(^=l 1)- Figure 7-4 shows variation

o f less than 2% in ©Totmax between the various bond-stress scenarios. This indicates that194


0 Totmax values are insensitive to the bar-slip model assumptions and can be used to define

shear failure initiation without bar-slip model constraints.

0.02

0.015

0.01

ra -0.005<DCC-0 .01,

o

o °

O Elastic Bond-Stress Parameter = 6 — Elastic Bond-Stress Parameter = 11 * Elastic Bond-Stress Parameter = 18

° !

0i

i itt * • 0

* 6

hOo ° * : 9

° >*°*o

*

WS o*®Cg*To* ***b° ; * : °°i i

* O 1i i i i i i

10 20 30 40Column Number

50 60

Figure 7-4: Variations in dfotmax with changes in bond-stress assumption

Figure 7 -5 plots the ratio (0 T Otmax/Smax) for all columns in the database. This figure

shows a strong relation between 0 i otmax and 5 max whereby 0Totmax~O.95 5 max. This indicates

that 0 Totmax and 8 max could be used interchangeably in the proposed shear failure model.

,o°.O O CoO C O

oToa:a

3EoKo

2 0 40Column Number

Figure 7-5: drotmax/ drift ratio (dmax) for all columns

195


The proportions o f column flexural rotations over Lp (0fTotmax) and bar-slip rotations

(0 BSTotmax) that comprise ©totmax were found to vary significantly with bond-stress

parameter. Figure 7-6 plots the ratios o f rft=0frotmax/0Totmax and rbst=0BSTotmax/0Totmax for all

columns and for various bond stresses. This figure shows the significant effect o f bond

stress parameter on these rotations, which indicates that ©rrotmax or ©esTotmax values in

Table 7-3 are specific to the bar-slip model and bond-slip parameters used here and

should not be used to define shear failure initiation in conjunction with other bar-slip

models. The mean values o f these ratios are also plotted in Figure 7-6 as solid horizontal

lines across all column numbers. For the bond stress value o f interest (i.e., A,=ll), the

means o f these ratios are mrft=0.46 and mrbSt=0.54, with most values within + /- 0.1 from

mean. This close clustering o f column ratios indicates that direct scaling from 0 iotmax to

either 0 frotmax or 0 BSTotmax by the ratios rfi and rbst may be done without much loss in

accuracy.

196


Figure 7-6:

0.8

0.7

0 .6(0 q:

0.5

0.4

0.3

y ^ v vV V v

,w v

« 5 T - V _ iV _ v v _ _

i ^ Iw-

w- '“V^W

7 * * i * 1 1 1- - * I------------------- 4 .----------------------1---------------4 . -----------------

i * l . i i ♦

* ♦—!— *** I

*i "

1 0 20 30 40Column Number

50 60

0 .8

0.7

0 .6ro

CL0.5

0.4

0.3

0 _ . 10- . - E l a s t ic B o n d - S t r e s s P a r a m e t e r = 11fTotmax Totmax

v v v _ v** n* v* I *

V 1 V 1 V 1

* ; v s v !v v v w

l

-***■,*»*** % **

10 20 30 40Column Number

50 60

0 .8

0.7

0 .6ro

CL

.o 1 ro o CL 0.4

0.3

0 _ . 10- . - E la s t ic B o n d - S t r e s s P a r a m e t e r = 1 8fTotmax Totmax

* t**

** * ' ' + +♦ ' *'* * ; ♦;*** ** f___________ L _ .. _«#♦, ? _ _V_ _ _ v ________ 1'V V v 1 i V ^ V ^7

y V V i i v ^ 1 V ■? w -

V V 7v v

0 .^10 20 30 40

Column Number50 60

Proportion o f column flexural rotations over Lp (9fTotmax) and bar-slip rotations (9BsTotmax) comprising 9Totmaxfor different bond-slip parameters

197


7.3 Shear Failure Initiation Model

A model to estimate column deformation at initiation o f shear failure in flexure-

shear-critical columns with light transverse reinforcement is proposed. This model is

intended to estimate mean response values o f flexure-shear-critical columns.

In this model it is postulated that the shear strength (Vr) o f flexure-shear-critical

columns prior to shear strength degradation is a sum o f shear strength o f column sections

under tensile strains (Vct), column sections under compression (Vcc), and transverse ties

(Vs). These terms are illustrated in Figure 7-7. Vr can be written out as:

V r = V c t + V c c + V s ( 7 - 2 )

p

Vcc.Vct

£ c

Figure 7-7: Illustration o f column shear strength components

Research into the effects o f tensile strains on concrete member shear strength

[Vecchio and Collins (1986); Belarbi and Hsu (1995)] has shown strength decreases with

increasing axial tension strains. Studies on effects o f high compressive axial stresses on

shear strength [Gupta and Collins (2001)] show a drop in shear strength o f members

198


under high compression loads. It is also well know that concrete compressive strength

and transverse reinforcement play an important role in shear strength o f reinforced

concrete members under either tension or compression. Thus, Vct can be written out as

function o f concrete compressive strength (f c), concrete tensile strains at critical shear-

failure section (et), and transverse reinforcement properties (s/d, p”, fyt). Likewise, Vcc

can be written out as a function o f concrete compressive strength ( f c), concrete

compressive stresses or strains at critical shear-failure section (ac, or sc), and transverse

reinforcement properties (s/d, p”, fyt). This leads to a relation o f the following form for

Vr:

Vr = f (s/d, p”, fyt, f c, st, ac, sc) < V (=imposed shear force) (7-3)

Several proxies for the shear-strength predictor variables listed in Equation (7-3) are

investigated to generate the proposed shear failure model. Namely, column flexural

rotations evaluated over a critical column length are investigated as proxies for (et).

is used a measure o f V (v=column shear stress= Vmax/bd at shear failure

initiation). Transverse reinforcement ratio (p”), spacing o f transverse ties (s) normalized

by d or s/d, and p”fyt are explored to represent the effects o f transverse ties. P/(Agf c), the

normalized average concrete compressive stress in base-column-section fibers covering a

distance h/4 from extreme compression fiber (ocW f c), and the corresponding normalized

strains (£c_h/4/sc; £c=concrete strain at f c) are used to represent oc and ec. The ratio a/d is

investigated as a variable that accounts for shear to moment ratio in columns.

The proposed model thus takes the following form at shear failure initiation:

8max = f (s/d, p”, p”fyt, a/d , P/(Agf c), , CcW f c, S c W S c ) ( 7 ' 4 )

199


with 0 max=column section rotation at initiation o f shear failure evaluated over a plastic

hinge length h. The proposed model is presented in four formulations that use four

different column rotation measures to define shear failure initiation: 0 max= ©Totmax, ©fTotmax

0TotPimax, or 0fpimax (defined in Table 7-3). These rotation measures were considered as

they would allow use o f the proposed model with most lumped-plasticity or fiber-section

column analytical implementations. The model formulation with 0TOtmax has the

advantage over the other three model formulations o f being insensitive to bar slip

modeling parameters. The remaining three formulations must be used in conjunction with

analytical bar-slip models that produce similar bar slip rotations as the ones estimated in

Section 7.2.

Figure 7-8 plots values o f the predictor variables listed in Equation (7-4) versus

0Totmax for all columns in the database. Similar trends were observed between the

predictor variables and 0frotmax, 0fPimax, and 0 TotPimax-

2 0 0


Totm

ax

^ra

d)

^Tot

max

(r

ad

) °T

otm

ax

(rad

) ^T

otm

ax

(rad

^

0.07(-

0 .06-

0 .05-

0 .04-

0 .03-

0.02

0.01 r

0

OTJ- g o 8o d>

r *o

x 1 00.07

0.06-

0 .05-

0.04

0 .03-

0.02 r - ° o ° $ —'oo O lO P

OO0.01

r"f

0.07

0 .06 -

_ 0 0 5 "

£ 0.04X

I 0 .03 -t-O

0.02

0.01

- o -e

$

8 o 1X i0®

0.4 0.6 0.8 s/d

1.2

0.07

0.06

0 .05 -

0.04X

1O 0.03t-o

0.02

o o0.01 - - o» —

2.5 3.5a/d

0.05-

0.04

0.03

0.02

0.01

0.

0

n i.

I

-----------! ----------- :----------- ! -

i i i l l

L 1„ ' 0 9 i

o _1 0 6 P ° 1

„ l O O 1 o < * g - © , - - o

t t • .

oo 0

0.1 0.2 0.3 0.4 0.5P/(Agfc)

0.6

0.07

0.06-

0 .05-

0.04

0 .0 3 ------u

0.02

0.01 6o

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2Normalized S tress.h/4

0.7

0.07

0.06

■uCD

0.04

io 0.03 ■<TO“I-O 0.02

0.01

0.07

0.06

0.04

I 0.03t-o

0.02

0 .0 1 - 0o

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1Normalized Strain.h/4

Figure 7-8: Predictor variables versus 0Totmax

2 0 1


Figure 7-8 shows little relation between p”, or p ” fyt and ©Totmax- ©Totmax, however,

increases with decreasing s/d, which suggests that the spacing o f column ties is more

influential on shear failure initiation than the amount and strength o f these ties. The

shear-span to column-depth ratio (a/d) shows no clear relation to ©Totmax- The values o f

v / 7 7 7 are seen in Figure 7-8 to increase as 0T Otmax decreases. This illustrates the

detrimental effect o f shear stresses on column deformation capacity prior to shear failure.

0Totmax values decrease significantly with increasing P/Agf c values. This detrimental

effect o f axial load on deformation capacity o f flexure-shear-critical columns is also

expressed in plots o f ac_h/4/ f c and Sc-h/Vsc with respect to ©Totmax- These plots indicate that

columns with compression blocks under high compressive stresses and strains have

reduced rotational capacity prior to shear failure.

Based on the aforementioned observations, a forward stepwise linear regression o f

the form [0 max = bo + b] Xi +© 2 X 2 + ........] (with, 0 max = least squares estimate o f 0 max;

bo, bi, ... = linear regression parameters; X i , X 2 , ... = predictor variables) is used with

variables that exhibited trends with respect to column rotations. These variables are: p”,

s/d, p”fyt, P/(Ag f’c), v/ y j f 'c , oc_h/4/ f c, and £cW sc- Forward stepwise regression starts

with no model terms (b, X j ) and adds the most statistically significant term (the one with

the highest F statistic or lowest p-value) at each step until no significant terms are left.

This regression technique is applied to all four column rotations under consideration (i.e.,

©Totmax, ©fTotmax, ©Totpimax, or ©fpimax). The most significant predictor variables for ©Totmax

and ©frotmax were found in this way to be s/d, P/(Ag f c), acW f c and EcW ^ c while those

for ©Totpimax, and ©fpimax were s/d, P/(Ag f c), and v/ -y/ f \ . Given the redundancy o f the

terms P/(Ag f c), Oc-h/4/ f c, and Sc-h/4/£c, as they all relate to column compression-block202


state, and considering that O cW fc, and ScWEc are difficult to extract analytically, the

stepwise regression for 0Totmax and 0m>tmax were re-evaluated without OcW f c, and ec_

h/4fsc. The end result for all rotations under consideration was that s/d, P/(Agf c), and

v/V f ' c are the most significant terms to include in the model. Thus, the least squares

estimate o f 0 max takes the final form:

O max — //() T" //| + bnA f c

+ b,v z

(7-5)

An iteratively re-weighted least squares algorithm was used to determine the

regression parameters bo, b\, b2, and //?. This robust regression method uses weights at

each iteration calculated by applying the bi-square function to the residuals from the

previous iteration. This technique minimizes the effects o f outliers and produces a better

fit through the bulk o f data points. Table 7-4 lists the linear regression parameters bo, bj,

b2, and bj obtained from the robust regression fits performed on all four rotations (0-rotmax,

0fTotmax? ©Totpimax, or 0fpimax)- This table also presents the coefficients o f multiple

determination (R2) for these fits.

Table 7-4: Column-rotation robust regression parameters

0 Totmax OfTotmax ©TotPlmax OfPlmaxb0 0.0437 0 . 0 2 1 0 0.0317 0.0149bi -0.0171 -0.0077 -0.0138 -0.0067b2 -0 . 0 2 1 1 -0.0088 -0.0165 -0.0065b3 -0 . 0 0 2 0 -0 . 0 0 1 1 -0.0016 -0.00082R 2 0.53 0.49 0.44 0.43

From Table 7-4 one can note that 0frotmaX regression parameters relate to those o f

©Totmax by an approximate factor o f 0.45. 0fpimax regression parameters are also found to

203


relate to those o f 0TotPimax by a ratio o f 0.45. Hence, Equation (7-5) was defined for

Oiotmax and 0 Totpimax while OfTotmax and 0 fpimax values were related to them by a factor o f

0.45. This simplification resulted in little loss o f accuracy. A simple relation between

total rotations and plastic rotations could not be implemented as it resulted in significant

accuracy losses in plastic rotation estimates. Thus, the least squares estimates o f column

rotations at shear failure initiation are given by:

(7-6)®Total = 0 -0 4 4 -0 .0 1 7 0.021

^ F le x u ra l 0*45 SjQi max

\ “

> 0.00405

' P ' A f ' c

- 0.0020c \

v> 0.009

® T ota l-P la stic ~ 0.032 0.014j

0.017f P '

A J 'c-0 .0 0 1 6

p s i u n its

> 0 . 0

@ Flexural Plastic ~ 0.456*^^max > 0.0

with, ^T-otafdeast squares estimate o f 0 7 ’o/max=column total rotation at shear failure

initiation measured over a plastic hinge length h including bar-slip induced rotations;

0Fiexurai=least squares estimate o f ^/r^max^column flexural rotation at shear failure

initiation measured over a plastic hinge length h excluding bar-slip induced rotations;

# 7b?a/-/>/a1/;c=plastic rotation portion o f dTotah 0Fiexurai-piastic plastic rotation component o f

Flexural', .s=transverse reinforcement spacing, <7=column depth from extreme compression

fiber to centerline o f outermost tension reinforcement; /^colum n axial load; d ?=column

gross section area; / c=concrete cylinder compressive strength; v=column section shear

stress =V/bd(F=column shear force);

In this relation the lower value o f ©Total is limited to 0.009, which is a bound observed

in Figure 7-8. This bound safeguards against estimating shear failure much prior to

flexural yielding. Plastic rotation estimates derived from Equation (7-6) are limited to the

204


positive range. It is good to note that total rotations in this relation are bounded by 0.009

and 0.044 (which correspond roughly to drift ratios o f 0.9% and 4.4%). Total plastic

rotations (plastic bar-slip + plastic flexural rotations over h) are bound by 0.0 and 0.032.

Figure 7-9 compares measured rotations with those estimated using Equation (7-6).

The shear failure initiation model presented in Equation (7-6) should only be used

with columns that have material and geometric parameters in the same ranges as those o f

columns in the database (ranges presented in Section 7.1).

0.03i0.07

0.06- 0.025-

0.05-0.02

& 0.04 o oxI 0.015-oto

0.02

0.005-0.01

0.01 0.02 0.030 T , Totmax

0.04 0.05 0.06 0.07Estim ated (rad)

0.005 0.01 0.015 0.02 0.025 0.03Estim ated (rad)fTotmax

0,05. 0.02

0.040.015-

■o2

X(13Ea.Ot-o

0.01fc 0.02

0.005-0.01

o o

0.02 0.03 Estim ated (rad)

0.04 0.05 0.005O,

0.01 Estim ated (rad)

0.015 0.02T otPlmax fpimax

Figure 7-9: Shear failure initiation model estimates o f rotations versus databasecolumn rotations

1A Shear Strength Degradation Model

A simplified model that represents the degrading shear-strength behavior o f flexure-

shear-critical columns past shear failure initiation is proposed. In this model, the

205


degrading shear-strength to shear-deformation relation is assumed to be linear. Using

Kdeg (presented in Table 7-2) and Vr=0.15Vmax, the drift ratio at residual shear strength

(5r) is calculated (see Figure 7-1 for illustration). Not all column tests in the database

were conducted up to residual shear strength; thus, 5r values are projected based on Kdeg.

0.85km a x / o

m a x

The degrading slopes (K^g) observed in force-deformation relations o f database

columns reflects both the degrading stiffness o f shear-damaged column sections as well

as the elastic unloading stiffness o f the column outside the failure zone. The elastic

unloading stiffness is dependent on whether a test is conducted in single or double

curvature, thus creating dependence o f Kdeg and 8 r on test setup. To avoid this

dependence, shear deformations ( A s h e a r ) o f shear-damaged column sections are used to

define the degrading behavior o f flexure-shear-critical columns. Shear deformations up to

residual shear strength are extrapolated from 5r values and evaluated using the following

relation:

A * .,- , = ( $ . - < * _ +0.85 S , ) ^ ( i n . ) (7-8>

with c= l for single-curvature tests and c=2 for double-curvature tests. All values in the

equation are from measured data.

Table 7-5 summarizes values o f 5r, A s h e a r - r and A Sh e a r - r / h for column tests where Kdeg

could be extracted.

206


Table 7-5: Column drifts and shear deformations at residual shear strength

ColumnDesignation 5r Ashear-r Ashear-r/h

% in.SE2CLD12 3.98 3.30 0.184SE2CHD12 1.77 1.52 0.085SE2CVD12 2.79 2.78 0.154SE_2CLD12M 5.24 4.63 0.257LY3CLH18 2.14 1.94 0.108LY3SLH18 3.15 3.28 0.182LY2CLH18 3.39 1.54 0.086LY2SLH18 4.61 4.64 0.258LY3CMH18 2.26 2.27 0.126LY 3CMD12 2.69 2.55 0.142LY_3SMD12 2.06 1.32 0.073OH2D16RS 5.23 1.04 0.132OH4D13RS 4.35 1.05 0.133ES_H_2_1_5 4.41 0.88 0.112ES_HT_2_1_5 4.44 0.97 0.123ES_H_2_1_3 4.99 1.35 0.172ES_HT_2_1_3 5.47 1.40 0.178LI_U_7 5.35 1.00 0.064LI_U_8 5.43 1.93 0.122LI_U_9 5.39 1.49 0.094S A U l 13.54 4.12 0.299SA_U2 6.49 1.86 0.135SA_U3 11.04 3.82 0.277Y A B R S 1 2.11 0.92 0.042K 0 372 2.38 0.16 0.021KO_373 2.18 0.18 0.023KO_454 1.49 0.17 0.022WI_25_033E 5.28 0.98 0.082WI 0 033E 5.64 1.30 0.108E L s p l 6.47 2.88 0.320EL_sp2 6.92 3.70 0.412G HColBl 5.30 1.21 0.202

Figure 7-10 explores relations between the response variable ( A s h e a r - r / h ) and the

following possible predictor variables: a/d, s/d, p”fyt, p”fytAg/P, P/(Agf c) and SF. SF is a

shear-friction model term developed by Elwood and Moehle (2005a) to estimate axial

drift capacities o f flexure-shear-critical columns. SF is given by:207


SF1 + (tan 6 y (7-9)

tan G + Py Astf ytd M nB

where, 0 is the shear-failure-plane angle from horizontal and is taken as 65°;

A st=transverse reinforcement area; dc=conerete core depth from centerline to centerline o f

ties.

0.5

^ 0.401 0.3

8 02 CD

2> 0.1co

co

0 ,

0.5

0.4

0.3

0.2

0.1

0

Q

----------------------- h _ _ _ o _ _ _o

o

o o

@

8

O

00

0

o________ a _ _

o

o

o o

° § .

° 8

0

co‘-H-ICD

E

ai□

0.5

0.4

0.3<

0.2co0

CO

0.5

0.4

0.3

8 0.2 CD

® 0.1 co

2.5 3a/d

3.5

o !

o- o — 11111

o o

c11

1

h ._ — .

o

0 o

0

» o ° . .0

0

O 1 i i i i

■ O O

OO

------------11111

0.4

0.1 0.2r " f

0.2 0.4

P/(Agf'c)

0.6 0.8 s/d

L O

o

0o 0

o o

& > ° oO ^ O o

o o o

0

_______° o

0.5

0.4

0.3E

8 0.2 co

0.1co

0.3 0.4 0.2 0.4r”f A / P

yt gT

o

r

______o %

o o ® eo

o

0

0.6

1.2

------------ 1 1 ' ' - X

1 :

! o

|0

? ° °

< ? ° o %

8 ° a < P 9 0 oO q 9 O

! o o o ; O :

o

0.6 0.8

coa o.i

Figure 7-10: Predictor variables versus Ashear-/h

208


As can be seen from Figure 7-10, the predictor variables do not show significant

linear trends with respect to A s h e a r - r / h . Some trends can be observed for p ” f y t A g / P , and

P / ( A g f c), with the clearest trend being the decrease in column shear deformation capacity

with increasing P / ( A g f c) ratio. A robust regression fit was performed to determine the

least squares estimate for a linear relation between P / ( A g f c) and AShear-r/h. The resulting

relation is given by:

A „ P (7-10)ihear-r = Q. 1 7 — 0.1 5 ------ -

k AJ *

No limit is given to this relation as it naturally tends to zero as P/(Agf c) tends to a

value o f 1.0. Figure 7-11 shows the estimated A Sh e a r - r / h relation versus observed values. A

key parameter not investigated in this simplified model that contributes to the large

scatter in observed shear strength degrading slopes involves the loading histories that

columns undergo though shear degradation. Introducing loading history into the

degrading model, however, requires the assessment o f flexure-shear-critical column

degrading hysteretic behavior, which should include damage and pinching parameters

(Sections 5.4.2 and 5.6.2). This is outside the scope o f this simplified degrading.

209


0.5

0.4

COCOE£0O 0.2L_co0

. cCO

0.2 0.80.4 0.6P/(Af'c)

Figure 7-11: Estimated versus observed P/(Agfc) versus Ashear-dh

210


8 Conclusions and Future Work

8.1 Summary

The broad objective o f this study was to investigate, both experimentally and

analytically, the seismic collapse behavior o f non-seismically detailed reinforced concrete

frames containing flexure-shear critical columns with light transverse reinforcement. The

emphasis was structural collapse caused by shear and axial failure o f the columns.

8.1.1 Experimental Phase

The experimental portion o f this study involved building and dynamically testing to

collapse a 2D, three-bay, three-story, third-scale reinforced concrete frame. The test

frame contained both non-seismically detailed flexure-shear critical columns and ductile

columns, the latter introduced to control the mode o f failure o f the test frame. The scope

o f this study did not encompass bi-directional column loading, joint failures, or lap-splice

failures, but focused on shear failure leading to loss o f axial load carrying capacity o f the

flexure-shear-critical columns due to uni-directional seismic loading. The test frame was

subjected to a series o f dynamic tests before it suffered a partial collapse mechanism due

loss o f axial load carrying capacity o f the lightly reinforced columns in the first story.

The main dynamic tests imparted on the test frame were a one half-yield level dynamic

test and three high intensity dynamic tests (Dynamic Tests 1 through 3).

Experimental results were presented for each o f the main dynamic tests. In Dynamic

Test 1, the flexure-shear critical Column B1 (first story, column axis B) suffered

211


significant shear and axial strength degradation. Shear failure in Column B 1 initiated at a

drift ratio o f 3.1%. Axial degradation in Column B1 was very gradual and appeared to

initiate immediately after shear failure initiation. Even though first-story drift ratios

reached 5.2%, the frame did not collapse. The failure o f Column B1 was concentrated

just above the footing level, where measured column flexural rotations were highest.

Vertical acceleration dynamic amplifications were not evident during the collapse o f

Column B l, probably because o f the gradual nature o f the axial failure. The rate at which

Column B l shortened was observed to relate to the number o f large horizontal drift

cycles that the column underwent, which suggests a damage related mode o f failure.

In Dynamic Test 2, Column B l further degraded axially and the neighboring flexure-

shear critical Column A1 sustained shear strength degradation but not axial failure. As

with Column B l, damage o f Column A1 concentrated just above footing level where

column rotations were highest, suggesting that column critical section rotations are

related to shear failure in this type o f column. After initiation o f shear failure, Column A1

was subjected to several deformation cycles with amplitudes near the amplitude that

initiated shear failure, resulting in a more gradual, though significant, shear degradation

than was observed for Column B l. This demonstrates the importance o f low-cycle

fatigue damage for modeling behavior o f shear-critical columns o f the type represented in

the test frame.

In Dynamic Test 3, Column A1 further degraded in shear and finally lost axial load

carrying capacity. This collapsed the East side o f the frame. The rate o f axial shortening

o f Column A1 was controlled by concrete crushing in the failing section. It was observed

212


that the column held about two-thirds o f the at-rest axial load throughout collapse. As a

result, vertical-acceleration dynamic amplifications were not dominant.

8.1.2 Analytical Phase

Two analytical models representing the test frame were developed. The first more

preliminary model was developed to design the test frame. The elastic dynamic properties

o f this model were found in retrospect to match fairly well those o f the test frame. This

model was also used to evaluate the collapse vulnerability o f this type o f frame structure

to a near-fault earthquake scenario. Both components o f seven near-fault ground motion

records from the 1994 Northridge earthquake were imparted on the frame model.

Selected ground motion sites were located in the same general area and had similar soft

soil site classifications. The responses o f the test frame model to these ground motions

varied widely, from almost no yielding o f longitudinal steel in columns to collapse o f the

frame. A new ground motion intensity measure is proposed based on the Housner

spectrum intensity measure. This modified Housner spectrum intensity measure

integrates the velocity spectrum between Ti (first mode period) and 1.5Ti. This measure

was found to correlate well with damage o f the frame.

A more sophisticated analytical model was developed to more accurately simulate

the experimental behavior o f the test frame. This model represents beams and columns as

force-formulation fiber-section elements. This formulation allows the elements to adapt

to varying axial loads and to reproduce experimental plastic hinge rotations with

reasonable accuracy. A new zero-length fiber-section implementation o f bar-slip

rotational effects is introduced in this model. This new implementation produces

213


consistent neutral axis depths and longitudinal steel stresses between the bar-slip zero-

length fiber-section and the adjacent frame element fiber-section. An elastic bond stress

between longitudinal bars and anchoring concrete o f 1 2 -J f c (psi) was found to produce

frame element stiffnesses that match fairly accurately those o f the test frame. LimitState

shear and axial failure elements [Elwood (2002)] were used to model the degrading shear

and axial behaviors o f test frame flexure-shear critical columns. When subjected to the

measured input base motions from the test, the analytical model produced shear failure in

both Columns A1 and B l earlier than was observed in the shaking table test. Several

possible sources o f the discrepancy between measured and calculated response were

identified. One possible contributing factor is that the LimitState model formulation is

based on total drift and thus does not account for variable end fixity conditions that arise

in frame columns. LimitState axial failure elements estimated axial failure initiation in

both Columns A1 and B l once residual shear capacities were reached at a drift o f about

5%. The degrading behavior o f these axial elements did not accurately reproduce the

observed axial degradation o f test frame columns as it does not consider axial failure and

degradation due to damage o f column critical section at lower drifts than those defined by

an empirical axial failure envelope.

A new shear failure model is introduced that determines column rotations at which

shear strength degradation (or shear failure) in flexure-shear-critical columns is initiated.

This model is intended for use in performance-based design applications in which

structural performance objectives are related to element critical-section rotations. The

proposed model is based on a parametric regression analysis that was performed on a

database o f 56 column tests. This analysis demonstrated that column rotational capacity

214


prior to shear failure initiation is negatively correlated with transverse reinforcement

spacing, compressive axial loads, and shear stresses. Axial load was found to relate to the

rate o f shear strength degradation past shear failure initiation.

8.2 Conclusions

8.2.1 Experimental Phase

1. Shear failure o f flexure-shear critical columns was found to relate to column plastic

hinge region rotations rather than column drifts.

2. Shear strength degradation in flexure-shear-critical columns was found to relate to

cyclic damage in shear damaged regions as well as to maximum deformation

demands.

3. Axial failure in flexure-shear critical columns was found to be gradual even for end

columns where crushing o f column concrete controlled the rate o f collapse.

4. Relatively low dynamic amplification o f vertical accelerations was observed due to

gradual column axial failures.

5. The test frame showed high resiliency to seismic excitation as it sustained first-story

drifts in excess o f 5% and three high intensity ground motions before reaching

collapse.

8.2.2 Analytical Phase

8.2.2.1 Collapse Vulnerability Study

1. The variability o f ground motions from site to site (so called intra-event variability)

plays an important role in analytical prediction o f structural collapse.

215


2. Directivity effects produce contrasting ground motion components that consequently

affect structural response significantly.

3. Common site classification parameters: site soil classification, soil shear wave

velocity (first 30m), and distance from fault rupture plane, were found to have little

correlation with the damage state induced in the structure.

4. Common ground motion intensity measures: PGV (peak ground velocity) and SaTi

(spectral acceleration at first mode period) were found to relate only mildly to frame

damage.

5. A proposed modified Housner spectrum intensity measure is found to correlate well

with damage for this type o f structure.

6 . Study results suggest that local site variability may be a key factor in observed

collapse statistics o f major earthquakes.

8.2.2.2 Analytical Work

1. A force-formulation fiber-section implementation o f beam-column elements used in

conjunction with the proposed zero-length fiber-section bar-slip element, reproduced

test frame results with relatively high accuracy (particularly plastic hinge region

rotations).

2. An elastic bond stress value o f \ (psi) between longitudinal bars and anchoring

concrete was found to produce frame element stiffnesses that match fairly accurately

those o f the test frame.

3. The 56-column database results were best matched with an elastic bond stress o f

11 \ (psi) corroborating the 12-Jf\ value used in test frame analysis.

216


4. Rotational capacity o f flexure-shear-critical columns prior to shear failure initiation is

found to be negatively correlated with transverse reinforcement spacing, compressive

axial loads, and shear stresses.

5. Axial load was found to impact to the rate o f shear strength degradation past shear

failure initiation.

8.3 Future Work

Additional test data are required to better quantify mechanisms that control shear and

axial failures in flexure-shear critical columns. Particular attention needs to be given to

local column response values such as bar-slip rotations, flexural rotations and shear

deformations in plastic hinge regions, and concrete stresses and strains within critical

regions. Further column and frame system dynamic tests need to be performed with a

wide range o f ground motions (including near-fault motions) to improve understanding

and quantification o f rate effects and cyclic damage effects on column shear and axial

failures. Also, test data need to be extended to encompass bi-directional loading. Full 3D

frame tests, which include slab systems, need to be performed to assess the impact o f

slabs on collapse frame systems. This is o f particular importance in situations where large

vertical deformations can activate catenary action in slabs.

The full hysteretic shear degrading behavior o f flexure-shear-critical columns needs

to be quantified with particular attention placed on hysteretic damage parameter

calibrations. Implementation o f the proposed shear failure initiation model along with

improved hysteretic rules into an appropriate analysis platform should be performed.

Improved axial failure models based on recent experimental evidence need to be

217


developed and combined with shear failure models since there is evidence o f interaction

between shear and axial failure behaviors. Once adequate accuracy is achieved with shear

and axial failure elements, existing buildings can be analyzed and region-wide collapse

vulnerability studies can be performed.

218


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230


Appendix A: Test Frame Details and

Experimental Setup

A .l Material Properties

A.1.1 Concrete Properties

A.I.1.1 Mix Design

Test frame concrete was pre-mixed and delivered to the site. It was poured into test

frame forms by gravity flow. The mix design used is summarized in Table A -l.

Table A-l: Concrete mix designCement ASTM C-150 Type IIWater reducer Pozzolith 322N ASTM C-494 Tape AMinimum 28-day strength 3000 psiMaximum 2 8 -day strength 3500 psiCementitious material 4.52 sacksMaximum aggregate size 3/8 in. (pea gravel allowed)Slump 5 in. +/- 1 in.Water/Cement ratio 0.718

A. 1.1.2 Physical Properties

At the time o f casting, standard cylinders 6 in. in diameter by 12 in. in height were

cast according to ASTM C31 requirements. The cylinders were kept in the same

environment as the test specimen, and were stripped on the same day the forms were

removed. The cylinders were capped with high-strength sulfur mortar and tested to

determine concrete compressive strength according to ASTM C39. Series o f three

cylinders were tested in compression at 3, 7, 14, 21, and 28 days from the day o f casting

to monitor strength gain. Due to low initial concrete compressive strength gain, curing

231


was maintained for 14 days on the specimen. After the final dynamic test, which

collapsed the test frame, three cylinders were tested in compression and three others were

tested in splitting tension according to ASTM C496. 162 days had elapsed between the

last cylinder tests and concrete casting.

Table A-2 and Figure A -l summarize key results from cylinder compression tests

while calculated tensile stresses obtained from splitting tests are summarized in Table

A-3. Concrete stress-strain relationships are presented in Figure A-2 for compressive tests

conducted 162 days after casting. Table A-4 summarizes key concrete compressive

material properties (mean o f three cylinder tests).

Table A-2: Concrete compressive strength history

Days after Casting

Concrete Compressive Stress (ksi) Cylinder 1 Cylinder 2 Cylinder 3

Avg.(ksi)

3 1.29 1.32 1.29 1.307 1.77 1.73 1.67 1.7214 1.93 2 . 0 1 2.03 1.992 1 2.49 2.39 2.47 2.4528 2.23 2.90 - 2.56162 3.53 3.61 3.57 3.57

3.5

3 5 2 .5

O 0 .5

0 50 100 150 200T im e (d ay s)

Figure A-l: Concrete compressive strength history

232


Table A-3: Concrete splitting test results

Load(kips)

Tensile Stress, ft (ksi) *

Cracking Tensile Stress, fcr (ksi) **

Cylinder 1 50.20 0.44 0.50Cylinder 3 45.20 0.40 0.45Cylinder 3 37.30 0.33 0.37

Avg 44.23 0.39 0.44

* Tensile stress (ft) = 2*Load/(7idl) (d= diameter= 6 in., 1= length= 12 in.)**Cracking tensile stress (fcr): ACI 318-05 [American Concrete Institute (ACI) Committee 318 (2005)] recommends f,= 6.7*(f c)0 5= 0.40 ksi (which is close to test results) and fcr= 7.5*(f c)0 5. Thus in this table fcr was taken as fCT= 7.5/6.7*ft.

— C y lin d e r 1

— C y lin d e r 2 — C y lin d e r 33 .5

2 .5

WCO0)i—

CO

Strain •3x 10

Figure A-2: Concrete measuredstress-strain curves

Table A-4: Concrete measured mean material properties

Parameter Value Units Explanationf’c 3.57 ksi compressive strength

£c 0.0029 Strain at compressive strengthfApcu -1.5 ksi crushing strength

£cu -0.00565 Strain at crushing strengthEc 2748 ksi Initial tangent Slope

N o te : the ACI 318-05 recommendation for Ec= 57000(fc)°5= 3406 ksi. The modulus obtained from material testing is much lower. This can be due to softer aggregates in use in northern California as well as the mix design limit on maximum aggregate size of 3/8 in. diameter.

233


A. 1.2 Reinforcing Steel Properties

For each bar size, three coupons were tested in tension according to ASTM A370. In

these tests reinforcing bars were tested as-is without machining. The areas used for

calculation o f bar stresses were taken as the nominal area for each bar size. Tested bar

sizes were #3 (3/8 in. diameter) and #2 (2/8 in. diameter) A615 Grade 60 deformed bars,

as well as 3/16 in. (W2.9) and 2/16 in. (W1.2) diameter straightened basic bright wires

(used as ties, hoops, and stirrups). Figure A-3 through Figure A - 6 plot tensile stress-strain

relations for bar coupons, while Table A-5 summarizes mean values o f key parameters

for each bar size.

100— Coupon 1 — Coupon 2

— Coupon 3

(/>

wCOCDL_

-4—*cn

0 .05 0 .15 0.2Strain

Figure A-3: #3 reinforcing steel bar stress-strain curves

234


100— Coupon 1 — Coupon 2

— Coupon 3

c/3

wc/30

c /3 40

0 .05 0 .15 0.2Strain

Figure A-4: #2 reinforcing steel bar stress-strain curves

1 0 0

80

C/3 60C/3J*C/3C/30

»C/3 40

20

0 ,

| — Coupon 1 — Coupon 2

— Coupon 3

0 0 .05 0.1 0 .15Strain

0.2

Figure A-5: 3/16 in. diameter steel wire stress-strain curves

235

0 .25


1 0 0

w

wW01—

Ct.)

20— Coupon 1— Coupon 2— Coupon 3

0.02 0 .0 2 50 .005 0.01 0 .015Strain

Figure A-6 : 2/16 in. diameter steel wire stress-strain curves

Table A-5: Reinforcing steel mean measured material propertiesParameter #3 Bars #2 Bars 3/16 in. W ire 2/16 in. W ire

Assumed Nominal Bar Area (in.2) 0 . 1 1 0.049 0.028 0 . 0 1 2

Yield Stress (ksi) 64.0 70.0* 80.71 95.0*Yield Strain 2.34e-3 2.64e-3* 3.65e-3 3.61e-3*Elastic Modulus (ksi) 27300 26500 27175 26300Ultimate Stress (ksi) 84.7 90.4 80.7 98.7Ultimate Strain 0.125 0.0962 N.A. 0.0125

* v a lu es obta ined b y in tersectin g tw o linear fits o n e before and o n e after y ie ld

In Table A-5 the elastic moduli o f the #2 and #3 bars are slightly lower than

expected (i.e., 29000 ksi). This could be due to the assumed nominal bar areas which can

differ from actual bar areas.

236


Reproduced with

permission

of the copyright owner.

Further reproduction prohibited

without permission.

toOJ-o

o r e="S

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W est\

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Detail

1/2" T>

5-10" 5-10" 5-10"Detail D i Detail F i Detail H

5'-4"

f f lf f iE -E i T F T - 3 T F T F3 1/2“ c/c19 stirrups

(typical all beams)

Deta "C“ Detail "E V Detail “G"

C (typical all beams)

Detail "C“ — \ Detai ' E DetailJ'G' Section E-E typical for 'all joints at axes A & B '

ffffm8 ties @ 1 1/4" c/c 03

13 ties e , J T I 1^ually spaced 3 ^ 3

m

j-1/2" Typical

6"Tap II1 1/2" Typical

Co)

Frame Dimensions and Reinforcing Details

A.2 Test Fram

e A

s-Built Draw

ings

90 degree hooks 4 bar diam eter radius 12 bar diameter extentions

3/ 16" dia. ties @ 1 %" c/c

14" 1/8 — |—

'± -r -- +

- 6 " -

. V 2"

90 degree hooks 4 bar diameter radius 12 bar diameter extentions

DETAIL "B"

4" 1/8

DETAIL "D"

90 degree hooks J. 4 bar diam eter radius

y2"

12 bar diam eter extentions A

y 6" dia. ties@ 1 y4" c/c:

- 6 " -

4 ” 1/8

-x2"f— 6 “ —4

DETAIL ”A"

K2”- 6 " -

9"

ffi %6" dia- ties @ 1 c/c ‘

4" 1/8

t?6 " -

DETAIL "C"


(-4" 1/8—-j— j.

y 9"

m 3y 6" dia. ties “ @ i y 4" c /c"

_ L

- 6 ' ' -

r t i y 2- H

4" 1/8

3/le" dia. ties 1 y4 c/c

rDETAIL "F"

- 6 ” -

DETAIL "H"

90 degree hooks -4 bar diameter radius 12 bar diameter extentions

y2-


DETAIL "E" DETAIL "G"

Figure A -8 : Frame reinforcing details — As-Built Details

238


Reproduced with

permission

of the copyright owner.

Further reproduction prohibited

without permission.

90Gn>'is

s ’

5

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ci6

I

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90 degree hooks alternate location %" extension

135 degree hooks alternate location %" extension

W1.2 wire ties @ 4" c/c 2/3" clear cover^

90 degree hooks alternate location 1" extension

8 # 3 bars135 degree hooks alternatelocation 1 V{' extension

W2.9 wire ties @ 1 V4" c/c

8 # 2 bars

2/3" clear cover ■ to longitudinal bars SECTION B-Bto longitudinal bars SECTION A-A

■8 # 3 bars 135 degree hooks alternate135 degree hooks 1 y2" extension

W2.9 wire ties1 /4" c/c

location 1" extension \

2/3" clear cover q f p t io n F-F to longitudinal bars 1IUIN t b

135 degree hooks alternate location 2" extension \

\r- 4 # 3 bars top~T W2.9 wire

=s=l

I stirrups @ 3 c/c 9

3/4" clear cover

2/3" clear cover1 to longitudinal bars SECTION C-C

-1-5"-------

F

4 # 5 bars top

- #3 stirrups @ 3" c/c

■ 4 # 5 bars bottomSECTION D-D

A.3 Frame and Test Setup Weights

Table A-6 : Frame component weights

Component Width(in.)

Height(in-)

Length(in.)

Density(kip/ft3)

UnitWeight(kips)

Quantity

Footing 17 1 2 32 0.155 0.59 4Column 6 6 39 0.155 0.13 1 2

Joint 6 9 6 0.155 0.03 1 2

Beam 6 9 64 0.155 0.31 9Footing plate 9.5 2 9.5 0.49 0.051 16

Out-of-plane bracing - - - - 0 . 2 5Lead bundle - - - - 3.0 18

HSS lead clamp (beams A B 1 &

AB2)

0.17 1 2

Table A - l : Frame group weightsWeight Group Weight

(kips)Total frame 64.93Total frame - footings & plates 61.75Total column axis A 12.06Total column axis A - footing 11.27Total column axis B 21.53Total column axis B - footing 20.74Total column axis C 20.40Total column axis C - footing 19.61Total column axis D 10.94Total column axis D - footing 10.15Footings + plates 3.18Footings + plates + Vi columns 3.44First floor + Vi columns 21.33Second floor + Vi columns 20.45Third floor + Vi columns 19.71


A.4 Out-of-Plane Bracing Mechanism

Test frame out-of-plane bracing mechanisms were designed to minimize motion in

the out-of-plane direction as the test frame goes through the expected in-plane (both

horizontal and vertical) ranges of motion. Five such mechanisms were distributed

throughout the frame at the mid-span o f beams AB1, AB2, AB3, CD1 and CD5. A

picture o f the mechanisms at beams AB2 and AB3 is shown in Figure A -10. Detailed

drawings o f a typical mechanism are shown in Figure A -ll . These mechanisms were

attached to the outer edges of the out-of-plane bracing steel frames by hollow tube

sections which had universally jointed clevis pins at both ends. The mechanisms were

attached to the test frame through stiff C-sections that were prestressed to the sides of

beams.

241


Figure A-10: Out-of-plane bracing picture

2 4 2


8'-5'

Universal Joints

2 " j

2 " dia., Me" thick hollow tubes, A36 steel

Plan ViewPlane of Motion

Ij ) ' Jp frg

dia. solid A36 steel pinC4X7.25

A36 Steel

2-7'

Elevation View

Figure A -l 1: Out-of-plane bracing details

A.5 Instrumentation

The instrumentation used in this experiment can be grouped into the following

categories:

2 4 3


1. Shaking table instruments that measure vertical and horizontal displacements, and

accelerations at the four comers of the table.

2. Force transducers (or load cells) that measure shear, axial, and bending forces at

the base of test frame footings.

3. Strain gauges that measure longitudinal steel strain in columns and beams.

4. Accelerometers that measure horizontal and vertical accelerations at various

points on the frame.

5. Displacement transducers that measure both local column, and global frame

deformations.

Table A-8 lists the various instruments by data acquisition channel number and

provides instrument designations and a brief description of each. In Table A-8 certain

channels (shaded) were used for multiple purposes when instruments failed or in between

dynamic tests for snap-back tests.

Table A-8: Instrumentation listChannel Instrument Description Designation

1 actuator stroke Shaking table horizontal displacement N-S direction* h lo stroke2 actuator stroke Shaking table horizontal displacement E-W direction* h2o stroke3 actuator stroke Shaking table horizontal displacement N-S direction* h3o stroke4 actuator stroke Shaking table horizontal displacement E-W direction* h4o stroke5 actuator stroke Shaking table vertical displacement (NW Actuator)* vlo stroke6 actuator stroke Shaking table vertical displacement (SW Actuator)* v2o stroke7 actuator stroke Shaking table vertical displacement (SE Actuator)* v3o stroke8 actuator stroke Shaking table vertical displacement (NE Actuator)* v4o stroke

9 accelerometerShaking table horizontal acceleration N-S direction (W Actuator)* h i-2 acc

10 accelerometerShaking table horizontal acceleration N-S direction (E Actuator)* h3-4 acc

11 accelerometerShaking table horizontal acceleration E-W direction (N Actuator)* h4-l acc

12 accelerometerShaking table horizontal acceleration E-W direction (S Actuator)* h2-3 acc

13 accelerometer Shaking table vertical acceleration (NW Actuator)* lv acc14 accelerometer Shaking table vertical acceleration (SW Actuator)* 2v acc15 accelerometer Shaking table vertical acceleration (SE Actuator)* 3v acc

244


16 accelerometer Shaking table vertical acceleration (NE Actuator)* 4v acc17 force transducer Load Cell East Axis A - Axial LCAEastAx19 force transducer Load Cell East Axis A - Shear LCAEastSh20 force transducer Load Cell East Axis A - Moment LCAEastMo21 force transducer Load Cell west Axis A - Axial LCAWestAx22 force transducer Load Cell west Axis A - Shear LCAWestSh23 force transducer Load Cell west Axis A - Moment LCAWestMo24 force transducer Load Cell East Axis B - Axial LCBEastAx25 force transducer Load Cell EastAxis B - Shear LCBEastSh26 force transducer Load Cell East Axis B - Moment LCBEastMo27 force transducer Load Cell west Axis B - Axial LCBWestAx28 force transducer Load Cell west Axis B - Shear LCBWestSh29 force transducer Load Cell westAxis B - Moment LCBWestMo30 force transducer Load Cell East Axis C - Axial LCCEastAx31 force transducer Load Cell East Axis C - Shear LCCEastSh32 force transducer Load Cell East Axis C - Moment LCCEastMo33 force transducer Load Cell west Axis C - Axial LCCWestAx34 force transducer Load Cell west Axis C - Shear LCCWestSh35 force transducer Load Cell west Axis C - Moment LCCWestMo36 force transducer Load Cell East Axis D - Axial LCDEastAx37 force transducer Load Cell East Axis D - Shear LCDEastSh38 force transducer Load Cell East Axis D - Moment LCDEastMo39 force transducer Load Cell west Axis D - Axial LCDWestAx40 force transducer Load Cell west Axis D - Shear LCDWestSh41 force transducer Load Cell west Axis D - Moment LCDWestMo42 strain gauge Column A1 Bottom-East-South StrAlBES43 strain gauge Column A1 Bottom-East-North StrAlBEN44 strain gauge Column A1 Bottom-West-South StrAlBWS45 strain gauge Column A1 Bottom-West-North StrAlBWN46 wire pot Off-table to Joint A1 - diagonal - +/-20 in. TOffAlH47 strain gauge Column A1 Top-East-North StrAlTEN48 strain gauge Column A1 Top-West-South StrAlTWS49 strain gauge Column A1 Top-West-North StrAlTWN50 strain gauge Column A2 Bottom-East-South StrA2BES51 strain gauge Column A2 Bottom-East-North StrA2BEN52 strain gauge Column A2 Bottom-West-South StrA2BWS53 strain gauge Column A2 Bottom-West-North StrA2BWN54 strain gauge Column A2 Top-East-South StrA2TES55 strain gauge Column A2 Top-East-North StrA2TEN56 strain gauge Column A2 Top-West-South StrA2TWS57 strain gauge Column B 1 Bottom-East-North StrBlBEN58 strain gauge Column B1 Bottom-West-South (to Test 1) StrBlBWS58 accelerometer Lead Packet AB1 Horizontal-Bottom-West (from Test 2) AccclLABl59 strain gauge Column B1 Bottom-West-North StrBlBWN60 strain gauge Column B1 Top-East-South StrBlTES61 strain gauge Column B1 Top-East-North StrBlTEN62 strain gauge Column B1 Top-West-South StrBlTWS63 strain gauge Column B1 Top-West-North StrBlTWN

245


64 strain gauge Column B2 Bottom-East-South StrB2BES65 strain gauge Column B2 Bottom-East-North StrB2BEN66 strain gauge Column B2 Bottom-West-South StrB2BWS67 strain gauge Column B2 Bottom-West-North StrB2BWN68 strain gauge Column B2 Top-East-South StrB2TES69 strain gauge Column B2 Top-East-North StrB2TEN70 strain gauge Column B2 Top-West-South StrB2TWS71 strain gauge Beam AB1 Bottom-East-South StrBeBES72 strain gauge Beam AB1 Top-East-South StrBeTES73 strain gauge Beam AB1 Bottom-West-South StrBeBWS74 strain gauge Beam AB1 Top-West-South StrBeTIF75 accelerometer Joint A 1 Horizontal AccelAlH76 accelerometer Joint A1 Vertical AccelAlV77 accelerometer Joint A2 Horizontal AccelA2H78 accelerometer Joint A2 Vertical AccelA2V79 accelerometer Footing B0 Horizontal AccelBOH80 accelerometer Footing B0 Vertical AccelBOV81 accelerometer Joint B 1 Horizontal AccelBlH82 accelerometer Joint B1 Vertical AccelBlV83 accelerometer Joint B2 Horizontal AccelB2H84 accelerometer Joint B2 Vertical AccelB2V85 accelerometer Joint D1 Horizontal AccelDlH86 accelerometer Joint D3 Horizontal AccelD2H87 accelerometer Joint D3 Horizontal AccelD3H88 wire pot Off-table to Footing A0 - Horizontal - +/-20 in. TOffAOH89 wire pot Off-table to Column A2 - Diagonal - +/-20 in. TOfFA2D90 wire pot OIT-lahle to Joint A1 - Horizontal - : -20 in. TO ffA lH

90 DCDTATemporary snap-back - olf-table to Joint A I - 1 Iorizontal - +.'-1/2 in. SnapA11L

91 wire pot Off-table to Joint A2 -1 lori/ontal - - /-2 0 in. 1 OffA211

91 FX’DTTemporary snap-back - off-table to Joint A2 - 1 lori/ontal - I/-1/2 in. SnapA2H

92 wire pot OIT-table to Joint A3 - Horizontal - t . -20 in. TOIFA3I1

92 DCDTTemporary snap-back - off-table to Joint A3 - Horizontal - -/-I/2 in. SnapAiH

93 wire potOff-table to Footing A0 - Horizontal out of plane - +/-20 in. TOffAOHX

94 wire pot Off-table to Column A3 - Diagonal - +/-20 in. TOffA3D95 wire pot On-table Column A1 - Vertical - +/-20 in. TOnAlV96 wire pot On-table Column A2 - Vertical - +/-20 in. TOnA2V97 NovotechnikAA On-table Column A3 - Vertical - +/-1 in. TOnA3V98 wire pot On-table Column B1 - Vertical - +/-20 in. TOnBlV9 9 wire pot On-table Column B2 - Vertical - +/-20 in. TOnB2V100 Novotechnik On-table Column B3 - Vertical - +1-2 in. TOnB3V101 wire pot On-table Column C l - Vertical - +/-20 in. TOnCIV102 DCDT On-table Column C2 - Vertical - +/-3 in. TOnC2V103 Novotechnik On-table Column C3 - Vertical - +/-1 in. TOnC3V104 wire pot On-table Column D1 - Vertical - +/-20 in. TOnDIV105 DCDT On-table Column D2 - Vertical - +/-3 in. TOnD2V

2 4 6


106 Novotechnik On-table Column D3 - Vertical - +/-1 in. TOnD3V107 DCDT On-table Beam AB1 - Horizontal - +/-3 in. TOnABlH108 DCDT On-table Beam AB2 - Horizontal - +/-3 in. TOnAB2H109 DCDT On-table Beam AB3 - Horizontal - +/-3 in. TOnAB3H110 DCDT On-table Beam BC1 - Horizontal - +/-3 in. TOnBCIH111 DCDT On-table Beam BC2 - Horizontal - +/-3 in. TOnBC2H112 DCDT On-table Beam BC3 - Horizontal - +/-3 in. TOnBC3H113 DCDT On-table Beam CD1 - Horizontal - +/-1 in. TOnCDlH114 DCDT On-table Beam CD2 - Horizontal - +/-1 in. TOnCD2H115 DCDT On-table Beam CD3 - Horizontal - +/-1 in. TOnCD3H116 wire pot On-table A0 to B 1 - Diagonal - +/-20 in. TOnAOBID117 wire pot On-table A1 to B2 - Diagonal - +/-20 in. TOnAlB2D118 DCDT On-table A2 to B3 - Diagonal - +/-3 in. TOnA2B3D119 wire pot On-table B0 to C l - Diagonal - +/-20 in. TOnBOCID120 wire pot On-table B1 to C2 - Diagonal - +/-20 in. TOnBlC2D121 DCDT On-table B2 to C3 - Diagonal - +/-3 in. TOnB2C3D122 wire pot On-table CO to D1 - Diagonal - +/-20 in. TOnCODID123 wire pot On-table Cl to D2 - Diagonal - +/-20 in. TOnClD2D124 DCDT On-table C2 to D3 - Diagonal - +/-3 in. TOnC2D3D125 wire pot Off-table to Footing DO - Horizontal - +/-20 in. TOffDOH125 force transducer l.oad cell used for snap-back tests only Pull Back I. C

126 wire potOff-table to Footing DO - Horizontal out of plane - +/-20 in. TOffDOHX

127 wire pot Off-table to Joint A3 - Horizontal out of plane - +/-20 in. TOffA3HX128 DCDT Local Column A l- Bottom-Vertical-West - +/-1 in. ColAlBVW129 DCDT Local Column Al - Bottom-Diagonal - +1-2 in. ColAlBD130 DCDT Local Column A l- Bottom-Vertical-East - +/-1 in. ColAlBVE131 DCDT Local Column A l- Top-Vertical-West - +/-1 in. ColAlTVW132 DCDT Local Column Al - Top-Diagonal - +1-2 in. ColAlTD133 DCDT Local Column A l- Top-Vertical-East - +/-1 in. ColAlTVE135 DCDT Local ColumnBl- Bottom-Vertical-West - +/-1 in. ColBlBVW135 accelerometer Lead Packet AB3 Horizontal-Bottom-West (from l ost 2 ) Accel LAB3136 DCDT Local Column B l- Bottom-Diagonal - r/-2 in. C olBIBD136 accelerometer Lead Packet C’DI Hori/.ontal-Bottom-East (from Test 2) Accel LCD 1138 DCDT Local Column Bl - Bottom-Vertical-East - 1 -1 in. ColBlBVF.138 accelerometer Lead Packet CD3 llorizonlal-Bottom-East (from Test 2) Accel LCD3139 DCDT Local Column B l- Top-Vertical-West - +/-1 in. ColBITVW140 DCDT Local Column Bl - Top-Diagonal - +/-1 in. ColBlTD141 DCDT Local Column Bl - Top-Vertical-East - +/-1 in. ColBlTVE142 DCDT Local Column A2- Bottom-Vertical-West - +/-1 in. ColA2BVW144 DCDT Local Column A2- Bottom-Diagonal - +/-1 in. ColA2BD145 DCDT Local Column A2- Bottom-Vertical-East - +/-1 in. ColA2BVE146 DCDT Local Column A2- Top-Vertical-West - +/-1 in. ColA2TVW147 DCDT Local Column A2- Top-Diagonal - +/-1 in. ColA2TD148 DCDT Local Column A2- Top-Vertical-East - +/-1 in. ColA2TVE149 DCDT Local Column B2- Bottom-Vertical-West - +/-1 in. ColB2BVW150 DCDT Local Column B2- Bottom-Diagonal - +/-1 in. ColB2BD151 DCDT Local Column B2- Bottom-Vertical-East - +/-1 in. ColB2BVE152 DCDT Local Column B2- Top-Vertical-West - +/-1 in. ColB2TVW

2 4 7


153 DCDT Local Column B2- Top-Diagonal - +/-1 in. ColB2TD154 DCDT Local Column B2- Top-Vertical-East - +/-1 in. ColB2TVE155 Novotechnik Local Column Al - Bottom-Horizontal - +1-2 in. ColAlBH156 Novotechnik Local Column A l- Middle-Vertical-West - +1-2 in. ColAlMVW157 Novotechnik Local Column A l - Middle-Diagonal - +1-2 in. ColAlMD158 Novotechnik Local Column Al - Middle-Vertical-East - +1-2 in. ColAlMVE159 Novotechnik Local Column Al - Top-Horizontal - +1-2 in. ColAlTH160 Novotechnik Local Column A2- Bottom-Horizontal - +1-2 in. ColA2BH161 Novotechnik Local Column A2- Middle-Vertical-West - +1-2 in. ColA2MVW162 Novotechnik Local Column A2- Middle-Diagonal - +1-2 in. ColA2MD163 Novotechnik Local Column A2- Middle-Vertical-East - +1-2 in. ColA2MVE164 Novotechnik Local Column A2- Top-Horizontal - +1-2 in. ColA2TH165 Novotechnik Local Column B l - Bottom-Horizontal - +1-2 in. ColBlBH166 Novotechnik Local Column B l - Middle-Vertical-West - +1-2 in. ColBlMVW167 Novotechnik Local Column B l - Middle-Diagonal - +1-2 in. ColBlMD168 Novotechnik Local Column B l- Middle-Vertical-East - +1-2 in. ColBlMVE169 Novotechnik Local Column B l- Top-Horizontal - +1-2 in. ColBlTH170 Novotechnik Local Column B2- Bottom-Horizontal - +1-2 in. ColB2BH171 Novotechnik Local Column B2- Middle-Vertical-West - +1-2 in. ColB2MVW172 Novotechnik Local Column B2- Middle-Diagonal - +1-2 in. ColB2MD173 Novotechnik Local Column B2- Middle-Vertical-East - +1-2 in. ColB2MVE174 Novotechnik Local Column B2- Top-Horizontal - +1-2 in. ColB2TH175 Novotechnik Local Joint A 1- Bottom-Horizontal - +/-1 in. JA1BH176 Novotechnik Local Joint A l- Vertical-West - + /-1 in. JA1VW177 Novotechnik Local Joint A l- Diagonal - + /-1 in. JA1D178 Novotechnik Local Joint A l- Vertical-East - + /-1 in. JA1VE179 Novotechnik Local Joint A l- Top-Horizontal - + /-1 in. JA1TH180 Novotechnik Local Joint A2- Bottom-Horizontal - + /-1 in. JA2BH181 Novotechnik Local Joint B l- Bottom-Horizontal - + /-1 in. JB1BH182 Novotechnik Local Joint B l- Vertical-West - + /-1 in. JB1VW183 Novotechnik Local Joint B l- Diagonal - + /-1 in. JB1D184 Novotechnik Local Joint B l- Vertical-East - + /-1 in. JB1VE185 Novotechnik Local Joint B l- Top-Horizontal - + /-1 in. JB1TH186 Novotechnik Local Joint B2- Bottom-Horizontal - + /-1 in. JB2BH

187 NovotechnikLocal Bar slip Column B l Bottom-Vertical-West- +/-1/2 in. BSB1BVW

188 NovotechnikLocal Bar slip Column Cl Bottom-Vertical-East - +/-1/2 in. BSC1BVE

189 Novotechnik Local Bar slip Column B2 Top-Vertical-West- +/-1/2 in. BSB2TVW190 Novotechnik Local Bar slip Column Cl Top-Vertical-East - +/-1/2 in. BSC1TVE

191 NovotechnikLocal Bar slip Beam AB1 Bottom-Horizontal-East - +!- 1/2 in. BSAB1BHE

192 NovotechnikLocal Bar slip Beam AB1 Bottom-Horizontal-West - +/- 1/2 in. BSAB1BHW

* orientation o f the shaking table used here is not the actual orientation o f the table in the laboratory. North, South, East and West were adjusted to match the East and West directions o f the test frame. Figure A-12 shows the location o f shaking table instruments.A DCDT = Direct Current Displacement Transducer AA Novotechnik = linear position displacement transducers

248


A.5.1 Shaking Table Instruments

The shaking table is instrumented below its surface with 8 accelerometers (four

vertical and four horizontal) and eight displacement potentiometers (four vertical and

four horizontal) that measure the hydraulic jack strokes. The arrangement of these

instruments is shown in Figure A -12.

I f ’- I T -

V4 Accel.\ / A f t G t m L * ^fJV IO Stroke

• V1 Accel.

H40 Stroke

Frame Lpad Cells

H20 Stroke

; V20 Stroke O V 2 Accel.

V3 Accel. ^ V30 Stroke O

Shake-Table Plan View - Instrumentation

Figure A-12: Shaking table instrumentation plan

249


A.5.2 Load Cells

A total of eight identical multi-directional (five component) load cells were used in

this experiment. Each of these load cells is capable of measuring axial loads, as well as

shear forces and bending moments in two orthogonal directions. These load cells were

bolted to the shaking table through a 6 ft wide 2 1/2 in. thick steel plate that ran the entire

length of the table. The test frame was bolted to these load cells through its footings.

Figure A -13 shows a typical connection detail between the shaking table, load cells, and

frame footings.

2 n :

f 7 " i 'i # # 1 ■#---------

21 QH II 1Footing

s y 2 "

* fLoad C

* *Load C

i rSteel Platey

VA/ / Shaking Table

-9^" - 3y 2 "

Figure A-13: Load cell connection detail

A.5.3 Strain Gauges

A total of 40 strain gauges were placed on longitudinal reinforcing bars of Columns

A l, A2, B l, and B2 and Beam AB1. Figure A-14 shows detailed locations of these

gauges. Strain gauges whose readings were recorded during the various tests are listed in

250


Table A-8. Some gauges do not appear in the table as they were damaged prior to testing.

Also, due to data acquisition channel limitations, eight gauges were placed in Beam AB1

but only four were monitored during testing (the gauges monitored during tests are listed

in Table A-8). The purpose of adding additional gauges in Beam AB1 was to make sure

that at least four were operational during testing.

Col A2 8 Gauges4 top and 4 bottom

Col B2 8 Gauges4 top and 4 bottom

1" Typical

Beam AB1 8 gauges total 4 gauges recorded

Col B1 8 Gauges4 top and 4 bottom

Col A1 8 Gauges4 top and 4 bottom

Strain Gauges

North- 6 " — ’ •

Strain Gauges

1" Typical EastWest

South

Typical Gauge Layout

EaslW est

Figure A-14: Strain gauge locations

Strain gauges used in this test were all identical electrical resistance strain gauges

produced by Tokyo Sokki Kenkyujo Co. type YFLA-5 strain gauges with 5 mm gauge

lengths. The nominal limiting strain for the post-yield gauges was 0.1 to 0.2 at room

251


temperature. As per the manufacturer methods and recommendations, strain gauges were

glued to a filed and cleaned bar section approximately 1 in. long. They were subsequently

coated with three different protective agents (for waterproofing and electrical protection).

Gauges were finally wrapped in vinyl mastic to protect them from impacts that may occur

during casting.

A.5.4 Accelerometers

In all, 13 accelerometers were attached to aluminum blocks that were affixed using

epoxy to concrete surfaces of the test specimen at various locations. Figure A -15 shows a

picture o f the accelerometers mounted on Joint A l. Locations and directions o f these

accelerometers are shown in Figure A -16. Care was taken to affix joint accelerometers

just below the top edge of joints in order to avoid diagonal joint shear cracks that may

surface during testing. In addition to these accelerometers, four accelerometers measuring

horizontal accelerations were placed on four separate lead packets. Locations o f these

accelerometers are also shown in Figure A -16.

Figure A-15: Accelerometers at Joint A 1

252


v 2 > H orizontalAccelerometer East

HorizontalAccelerometer.

HorizontalAccelerometer

Vertical andHorizontalAccelerometers


HorizontalAccelerometer 1 1/2" Typical


Vertical andHorizontal___Accelerometers^


HorizontalAccelerometer,


Vertical andHorizontal(Accelerometers

Figure A-16: Accelerometer location drawing

A.5.5 Displacement Transducers

There are three groups of displacement transducers (DTs) attached to the test frame:

1) DTs attached to frame joints for monitoring relative joint displacements (see Figure

A-18 for layout), 2) DTs attached to Columns A l, A2, B l, B2 and Joints A l, B l to

monitor their local deformations (see Figure A -19 for layout), and 3) DTs attached at

beam/joint and column/joint or footing interfaces for monitoring bar slip magnitudes at

those interfaces. All DTs are listed and described in Table A-8.

A.5.5.1 Joint-Location Instrum ents

Two separate triangulation systems were introduced to monitor test frame joint

displacements (Figure A-18): 1) the on-table system in which DTs were attached to

threaded rods embedded at the center of all joints and in all footings on the North side of

253


the frame, and 2) the off-table system in which DTs were attached to a fixed off-table

steel frame and glued to the surface of column axis A joints. Typical connection details

for the DCDTs, Novotechnics and wire pots for these systems are shown in Figure A-17.

The 3/8 in. threaded rods anchored in joints were stiffened with 1 V2 in. diameter

aluminum tube sections that were prestressed to the rods (Figure A-17) approximately %

in. from the surface o f joints so as not prevent joint dilation.

Novotechnik on Aluminum bracket

Aluminum tube stiffener

DCDT on bracket with springs

Aluminum tube stiffener

Jo in t C lJoint A3

Figure A-17: Typical connection details fo r displacement transducers

254


Out

-of-

aiuej-j leejs psxid

CO © , . T— CO $ 2n <0 x ii LL! cu y> <u

r o t ®

CD CD

CD O

RJ W Q)

I t ® .c a> o co > a.

Figure A-18: Joint-location instrument layout

255


A.5.5.2 Column and Jo in t Deformation Instrum ents

Columns A l, A2, B l, B2 and Joint A l, A2 were instrumented with displacement

transducers that measure column and joint flexural and shear deformations. These

instruments were laid out on the North side o f the frame in the pattern shown in Figure

A -19.

WestEast%&' dia. threaded rods anchored in Aluminum plates

for rigid offsetsjoints

Aluminum HSSsections

Wood blocks

1” to 1 3/4”

North Side View

Figure A-19: Column andjoint deformation instrument layout

256


Column instruments monitored translations, rotations and dilations o f two planes 6

in. from each end of columns. These instruments were mounted externally on columns

through aluminum brackets shown in Figure A-20. These brackets were clamped onto

columns using a mechanism that allowed for expansion and contraction o f column

sections through springs. The springs were chosen to provide about 100 to 200 lbs of

clamping force while allowing for at least 1 XA in. of expansion. Contact points between

clamping mechanisms and columns were through two ( l 12 in. x 11/2 in.) wood blocks

(Figure A-20).

Figure A-20: Column instrument bracket detail - A t footing AO

Figure A-21 shows an annotated picture o f column instruments at the base of

Column A l. This figure shows Novotechnik connection details in which the instrument is

mounted on an aluminum bracket with its wire pivoting around a ball-bearing roller. This

arrangement minimizes instrument offset from its anchoring point. Figure A-21 shows

DCDT connection details in which a DCDT is mounted on a resign bracket with stiff

257


springs attached to its measuring rod. These springs keep the connecting wire taught

during dynamic testing. Also on this figure wire pot to footing connection details can be

seen.

Typical Novotechnik connection detail. Wire pivots around roller. DCDT mounted on

bracket with springs

Wire potsNovotechnik on

aluminum bracket

Footing AO out-of-plane wire pot connection

Figure A-21: Typical column instrument connection details — At footing AO

Instruments on joints monitored movements o f joint comers where threaded rods

were imbedded on the inside of joint longitudinal bars. Embedded rods were stiffened by

prestressing 1 % in. diameter aluminum tubes to them. Because o f tight geometry,

aluminum rectangular “rigid” plates were used as offsets to better align joint instruments

with column instmments. Figure A-22 and Figure A-23 shows pictures o f typical joint

instrument connection details.

258


Figure A-22: Typical jo in t instrument connection details - At jo in t A2

Figure A-23: Typical jo in t instrument connection details - At jo in t B l

The complexity o f column and joint instrumentation resulted in non-uniform column

and joint instrument locations across columns and joints. As-built locations of points

2 5 9


between which instruments are measuring deformations were recorded prior to testing

and presented in Figure A-24 and Table A-9. The locations presented in Table A-9 are

given in a coordinate basis centered at the bottom-East comer of Columns A l and B l as

shown in Figure A-24. Also presented in the Table A-9 are coordinates of points whose

movements are o f interest (i.e., joint rod locations and surface points of columns 6 in.

from each end). These coordinates are necessary to obtain horizontal and vertical

displacements o f points o f interest either through virtual work or geometric methods.

Table A-9: Column andjoint instrument coordinates

Node#

Column Axis A Column Axis B

X Coordinate inches

Y Coordinate inches

X Coordinate inches

Y Coordinate inches

1 -1.75 0.00 6.75 0.002 8.40 0.00 -2.53 0.003 -1.75 0.50 6.75 0.854 2.72 3.59 3.14 3.535 8.40 0.50 -2.53 0.856 8.40 3.75 -2.53 3.157 6.00 6.00 0.00 6.008 -1.75 3.50 6.75 2.959 7.65 5.25 -1.15 6.0010 -2.75 5.25 7.75 5.2511 0.00 6.00 6.00 6.0012 -2.04 5.75 7.04 5.7713 7.58 32.53 -1.60 32.5214 8.15 6.00 -1.13 6.7015 8.50 33.00 -2.50 33.0016 6.00 33.00 0.00 33.0017 -1.25 7.25 7.75 8.3018 -1.00 33.00 7.00 33.0019 7.75 33.75 -1.75 33.7520 -1.75 33.50 7.75 33.5021 0.00 33.00 6.00 33.0022 2.19 37.00 5.05 35.0723 4.70 40.35 1.66 39.8424 6.75 36.50 -0.84 34.7525 6.75 40.75 -1.13 40.2526 5.00 40.75 1.38 40.2527 -0.75 35.00 6.71 35.25

260


28 -0.75 40.50 6.63 40.5029 5.00 40.00 1.38 39.7530 2.25 40.00 4.88 39.7531 2.25 40.50 4.88 40.5032 1.56 40.79 5.56 40.8033 5.00 49.13 1.93 49.3034 4.25 40.75 2.13 40.2535 4.50 46.38 1.63 46.8036 5.00 46.38 1.13 46.8037 1.75 40.50 4.38 40.5038 1.50 46.25 4.13 46.6339 5.00 47.13 1.13 47.5540 2.25 46.75 4.88 47.1341 2.25 46.25 4.88 46.6342 2.50 46.69 4.58 47.0343 4.56 50.34 1.12 51.7644 6.75 46.38 -1.25 46.8045 6.75 51.25 -0.91 51.7646 6.00 54.00 0.00 54.0047 -0.75 46.25 6.13 46.6348 -0.75 50.75 6.50 51.0149 6.75 54.00 -1.75 53.5050 -1.75 53.25 7.75 53.2551 0.00 54.00 6.00 54.0052 -1.04 53.77 7.02 53.8253 7.60 80.52 0.00 82.0054 7.75 54.50 -2.25 54.0055 8.50 81.00 -2.50 81.0056 6.00 81.00 0.00 81.0057 -1.75 55.25 7.25 54.0058 -1.00 81.00 7.00 81.0059 7.75 80.25 -1.75 80.2560 -1.75 80.50 7.75 80.5061 0.00 81.00 6.00 81.0062 0.19 82.11 5.48 82.7263 4.47 88.58 1.43 87.9864 6.75 83.75 -0.50 83.9965 6.00 89.00 -0.13 88.3866 4.75 89.00 1.13 88.3867 -0.75 83.50 6.75 84.5068 -0.75 88.75 6.75 88.1369 4.75 88.25 1.13 87.6370 2.13 88.00 4.75 87.6371 2.13 88.75 4.75 88.13

* Coordinates for the nodes are measured from the bottom-East comer of Columns Al and Bl (see Figure A-24)

261


Join t A2 Join t B2

6 8 p , 6 3 , ,6869

6060

'/C olum n A2 j Column B2

57 46149 54 ■44650 \ X ,

45 '45 f4843,48 '33i

47

Join t A1 Joint B1

25. n28

2 4

■•♦16

Colum n B1 i! Colum n A1i

j Colum n A1 | i l

7 4 -^4 1 4

UDrigin (0,0) ]

LEGEND

Rigid offset from a ttach em en t point Instrum ent m easuring wire

Footing A0

I \lColum n B1

Origin (0,0) j 'tS

Footing B0

Figure A-24: Column andjoint instrument location drawings with node numbering scheme

262


A.5.5.3 B ar Slip Instrum ents

In total, six displacement transducers were affixed using epoxy to the South surface

o f test frame Beam AB1 and Columns B l, B2 and C l. These instruments were placed at

the joint or footing interface in the manner shown in Figure A-25. Locations of these

instruments are described in Table A-8. These instruments were aligned with longitudinal

reinforcing bars and placed 2 in. away from footing interfaces or 3A in. on either side of a

column-joint or beam-joint interface.

Figure A-25: Bar slip instruments - detail pictures

263


Appendix B: Joint Subassembly Test

Details and Results

To assess the shear strength of test frame joints without transverse reinforcement,

cyclic tests were performed on two subassemblies replicating exterior joints of the test

frame without transverse steel. The difference in the two subassembly tests was in the

axial load imposed on the columns. In Test 1, columns were under no axial load, while in

Test 2 columns were prestressed using two pneumatic jacks (Figure B -l) to a

compressive force o f 20 kips. A picture of the test setup can be seen in Figure B -l. In this

figure, columns are seen to be positioned horizontally and held by a “pin” device on the

West side and rest on a “roller” device on the East side. Both devices were attached a

distance equal to half clear column height from beams faces. The hydraulic jack that

imparted cyclic forces to the beams was connected a distance equal to half clear span

from column faces.

Concrete mix design for these tests was the same as that used in the test frame. At

the time of casting, standard cylinders 6 in. in diameter by 12 in. in height were cast

according to ASTM C31 requirements. The cylinders were kept in the same environment

as the test specimens, and were stripped on the same day the forms were removed. The

cylinders were capped with high-strength sulfur mortar and tested to determine concrete

compressive strength according to ASTM C39. Concrete stress-strain curves obtained

from these tests are plotted in Figure B-2 in which concrete ultimate compressive stress is

observed to be about 4 ksi.

264


Figure B - l : Joint subassembly test setup picture

Figure B-2:

Strain 3x 10

Joint subassembly concrete cylinder stress-strain results

2 65


0Q .

TDCDO

_ l

~ o0

" 5 .Q .<ECD0

CO

10

5

0

5

TEST 1 - No Axial Load TEST 2 - 20 Kips Axial Load10

-5 -3 -2 -1 0 1 2 3 4 5Beam Displacement (in.)

Figure B-3: Joint subassembly applied beam force vs. displacement - Tests 1 & 2

in

O

000

-I— *

COCD0

_CCO■ a0

_N

'C DEo

TEST 1 - No Axial LoadTEST 2 - 20 Kips Axial Load:^ . . t 1 , r T l - r r r r ..|- r t ^ f T ,

-4 -3 -2 -1 0 1 2 3 4 5Beam Displacement (in.)

Figure B-4: Joint subassembly normalizedjoint shear stress vs. beam displacement (psi units) — Tests 1 & 2

266


Key results from the joints tests are presented in Figure B-3 and Figure B-4. Figure

B-3 plots the force versus displacement readings at beam loading points for both tests

while Figure B-4 plots normalized joint shear stresses versu beam loading point

displacement for both tests. As can be seen in the latter figure, the joint subjected to 20

kips of axial load (Test 2) was slightly stronger in shear and stiffer than the one without

axial load. Maximum normalized shear stress values for these tests were (18.9 f ' c (psi))

for Test 2 and (16.7 Jf ' c (psi)) for Test 1. The joint under axial load also exhibited a

steeper degradation in shear strength than the joint without axial load.

Figure B-5 shows a picture of the failed joint at the end of Test 2. This picture

clearly shows the failure of the joint prior to any significant degradation in the columns.

Figure B-5: Joint subassembly failure picture - Test 2

267


Appendix C: Data Reduction and

Verification

C .l Shaking Table Input vs. Output Ground .Motion

Comparison

Figure C-l compares shaking table input versus output ground motion response

spectra (5% damping) recorded during Dynamic Test 1. The output ground motion

acceleration histories were recorded on the footing below column B 1. This figure shows

fairly good agreement between input and output motions except for a discrepancy at a

period of approximately 0.09 sec.

Input Motion, Chile Valparaiso 1985, Llolleo Comp. 100 X 4.06 Shaking Table Output Motion _________________________D)

CD 4

Q.

0.2 0.4 0.6 Period (sec)

0.8

Figure C -l: Shaking table input vs. output motion acceleration response spectra

268


C.2 Data Reduction

C.2.1 Data Filtering

Frequency filtering was applied to all instrument channels to eliminate high

frequency noise content of instrumentation outputs. Large frequency-domain spikes at 60

and 20 hz, which are - generated by electric current interference, were of particular

nuisance. The built-in Matlab 7.0 [Mathworks (2004)] filtering function “filtfilt” was

used with a Butterworth 10th order low-pass filter design. More information on this

command can be found in the Matlab 7.0 [Mathworks (2004)] software help.

Vertical accelerometers and vertical shaking table displacement potentiometer were

filtered using the method described above with a cut-off frequency of 50 hz. This high

cut-off frequency was used for vertical accelerations because of the naturally occurring

high-frequency content of these responses. To verify the existence of this high-frequency

content, a crude column axial natural-period calculation is presented. Axial natural

frequency of a column is defined by:

/ = axial natural frequency of column

m = mass above column -> for Column A l, m = 112701b/386.4 = 29.17 lb

k= column axial stiffness = AE/L = 6*6*2750*1000/39 = 2.54e6 lb/in.

■ * /= 46.95 hz

Thus a 50 hz cut-off frequency will capture most o f the first floor column vertical

acceleration responses. A higher cut-off frequency was impractical due to the very high

electric current interference at 60 hz (see Figure C-2). Displacement potentiometers

269


measuring column axial deformations were filtered along with the rest o f the instruments

at a much lower cut-off frequency as these instruments are not sensitive to high

frequencies. Figure C-2 plots the filtered versus non-filtered Fourier Transforms (FT) for

the vertical accelerometer at Joint A l during the Half-Yield Test. This plot shows the

high-frequency content of this response as well as the high electrical interference at 60hz.

The filtered response in this figure is seen to be identical to the non-filtered one until

about 45 hz and gradually diminishes to zero at around 55 hz. This filtering scheme

retains most of the high frequency response without running into the 60 hz interference.

12

10

8q

"OZ 5

i 6E<

4

2

°0 20 40 60 80F requency Hz

Figure C-2: Filtered vs. non-filtered FT plots for vertical accelerometer at Joint A l -H alf-Yield Test

All other instruments were filtered using the method described above with a cut-off

frequency of 18 hz. This value was chosen to avoid electric current interference at 20 hz

270

N on-FilteredFiltered


and to be far enough from the “elastic” third mode period o f the structure which was

estimated at 14.5 hz.

Figure C-3 plots the ratio o f filtered over non-filtered FT for the horizontal

accelerometer at Joint D1 during the Half-Yield Test. This plot confirms that the filtered

Fourier amplitudes are identical to the non-filtered ones up to about 14 hz and diminish

gradually to almost zero amplitude at approximately 22 hz. Figure C-4 plots the filtered

and non-filtered FT for the horizontal accelerometers at Joints D l, D2 and D3 during the

Half-Yield Test. This plot shows almost no difference between the filtered and non-

filtered responses. Low FT amplitudes are observed in Figure C-4 above 14 hz, which

indicates little loss o f energy in the filtering process.

0 . 8

0.4

0 . 2

2 0 2 5Frequency Hz

Figure C-3: Ratio o f filtered to non-filtered FTfor horizontal accelerometer at Joint D l-H a lf-Y ie ld Test

271


FFT Filtered vs. Non-Filtered for Horiz. Accel. D3 - Half-Yield T est1 0 0 ,----- ,------------ 1------------ i------------ .------------

a>•o3

a.E<

2 0 25F requency Hz

FFT Filtered vs. Non-Filtered for Horiz. Accel. D2 - Half-Yield T est 1 0 0

80

5 6 0

"5.I 40

2 0

°0 5 10 15 20 25Frequency Hz

FFT Filtered vs. Non-Filtered for Horiz. Accel. D1 - Half-Yield T est 1 0 0

80

5 60 3-t—»

"q.I 40

2 0

°0 5 10 15 20 25Frequency Hz

Figure C-4: Filtered vs. non-filtered FT plots for horizontal accelerometers atJoints D l, D2, andD3 - Half-Yield Test

272

— Non-Filtered — Filtered

1 •

1 1

1 1 1 1i

1

1 !

I :I I i

J V J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


C.2.2 Modal Property Calculations

Modal properties o f the test frame were extracted from snap-back tests, periods o f

free-vibration at the end o f each dynamic test, and a white-noise dynamic test. This

section presents methods used to extract these modal properties. In all tests, horizontal

accelerometer responses were used for dynamic property evaluation as accelerometers

have high resolution at low amplitudes.

C.2.2.1 Calculation Methods

Methods used to extract test frame modal properties are split in two categories: time

domain methods and frequency domain methods. Time domain methods use filtered floor

acceleration history responses to extract test frame modal periods and damping ratios.

Frequency domain methods utilize Fourier Transforms (FT) or transfer functions o f

accelerometer responses to obtain test frame modal periods. Table C -l gives an overview

o f the various dynamic tests used to evaluate test frame modal properties at various

damage states and gives the modal extraction methods used in each o f the tests. The

following sections describe in more detail the two dynamic extraction methods.

273


Table C -l: Dynamic modal property extraction overview

Frame State Test Type Series Details Extraction MethodInitial“uncracked”state

Snap-Back

Four tests using 1 0 0 0 1 b pull-back

force at 3rd floor level

Time domainElapsed time between peaks of filtered

history response (for periods) Logarithmic decay on filtered history

response (for damping)Frequency domain

FT peaks (for periods)Three test using.1 0 0 0 1 b pull-back

force at 1 st floor level


history response (for periods) Logarithmic decay on filtered history

response (for damping)Frequency domain

FT peaks (for periods)“Cracked” after Half- Yield Test

Free-vibration

Free vibration at end of test

Frequency domainFT Peaks (for periods)

White-Noise

Low amplitude white-noise test with

peak ground acceleration = 0.015g

Frequency domainFT peaks (for periods)

Damaged after Dynamic Test 1

Free-vibration


Frequency domainFT peaks (for periods)

Snap-Back

Two tests using 1 0 0 0 1 b pull-back

force at 3rd floor level


response (for periods)Frequency domain

FT peaks (for periods)Three tests using

5001b pull-back force at 3rd floor level

Time domain Elapsed time between peaks of filtered


FT peaks (for periods)

Damaged after Dynamic Test 2

Free-vibration




FT peaks (for periods)

274


C.2.2.1.1 Time Domain Methods

In the time domain, free-vibration horizontal acceleration responses o f the test frame

(as measured by seven horizontal accelerometers on the test frame) were filtered in

frequency ranges around the first three modal frequencies producing history responses

dominated by the mode under investigation. The filtering method used here is the same as

the one used to filter out noise from all instrument responses (see Section C.2.1).

Frequency ranges used in this process are as follows:

1. For elastic snap-backs:

o 1st mode lowpass f < 5hz

o 2nd mode bandpass 7 < f < 11.5hz

o 3rd mode bandpass 12.5 < f < 18hz

2. For Half-Yield Test free vibration:

o 1st mode lowpass f < 3.7hz

o 2nd mode bandpass 7.4 < f < 9.2hz

o 3rd mode bandpass 10.5 < f < 15hz

3. For Dynamic Test 1 free vibration:


o 2nd mode bandpass 3.2 < f < 6 hz

o 3rd mode bandpass 6 < f < 12hz

4. For damaged state snap-backs after Dynamic Test 1:




275


5. For Dynamic Test 2 free vibration:




Modal properties were evaluated from filtered acceleration history responses as

follows:

1. For each o f the first three modes, peaks at maximum acceleration in the

filtered acceleration histories are located as well as peaks n cycles after that.

The value o f n varies for each test and is equal to ten for elastic snap-back

tests and Half-Yield Test free-vibration period, and equal to seven for other

tests where hysteretic damping was high.

2. The modal period is then calculated by taking the time difference between

these two peaks and dividing by the number o f cycles separating them.

3. The modal damping ratio is calculated here by applying the well known

logarithmic decay method [Chopra (2000)] to the two peaks obtained

previously.

Figure C-5 illustrates the filtering process applied to readings o f the horizontal

accelerometer at Joint B2 during a typical first-floor elastic snap-back test.

276


Filt

ered

H

oriz

. A

ccel

, (g

) Fi

lter

ed

Hor

iz.

Acc

el,

(g)

Filt

ered

H

oriz

. A

ccel

. (<

2.51— N o n - F i l te r e d

— 1 s t M o d e F i l t e r e d

— 2 n d M o d e F i l t e r e d

— 3 rd M o d e F i l t e r e d

Q .

0.5

Frequency Hz

0.01

— Non-Filtered — Filtered

- 0.01

- 0.021 2 3 4 5 6 7 8

T im e ( s e c )

2n d M ode

T im e ( s e c )

1 st M ode

0.01

0

-0.01

-0 .02b.1

-JS

T

4 5T im e ( s e c )

A)

B)Figure C-5: Typical horizontal acceleration response filtering around the first three

modes. A) FT plot illustrating the frequency filtering around the first three modes, B) the corresponding history plots o f the filtered response fo r all three modes - (Joint B2, First Floor Elastic Snap-Back Test)

During the free-vibration periods at the end o f each dynamic test, the floating o f the

shaking table produced significant noise in free-vibration responses which forced a

277


narrower filtering band around modal frequencies and prevented accurate damping ratio

evaluation using this method.

C.2.2.1.2 Frequency Domain Methods

Fourier Transforms o f accelerometer responses were used to estimate test frame

modal periods from snap-back tests and free-vibration tests. Smoothed transfer functions

o f accelerometer response histories were used to evaluate test frame modal periods during

the white-noise test. A transfer function is defined as the ratio o f the acceleration Fourier

Transform (FT) recoded at footing level to the FT o f accelerations recorded at floor

levels. Test frame modal periods were obtained by locating peaks o f smoothed transfer

functions or Fourier Transforms.

C.2.2.2 Initial “Undamaged” State Snap-Back Tests

This section describes the initial snap-back tests performed on the test frame prior to

any dynamic testing and presents the modal properties calculated from these tests.

At the onset o f the testing program, four snap-back tests were conducted at the third

floor level o f the frame and three at the first floor level with an applied pull-back force o f

approximately 1 kip. The first floor snap-back tests were performed as a means o f

exciting higher modes o f the structure. Figure C- 6 shows a picture o f the snap-back setup

for a third floor snap-back test. Figure C-7 plots the Fourier Transforms o f the horizontal

accelerometer responses for the accelerometers attached to Joints D l, D2, and D3 for all

snap-back tests. Figure C- 8 and Figure C-9 plot typical displacement histories at all three

floor levels for first and third floor snap-backs.

278


Figure C-6 : Snap-back setup at thirdfloor

279

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission

FFT

Am

plitu

de

FFT

Am

plitu

de

Third Floor Elastic Snap-Back - Accelerometers 3rd floor accel. a t D3

25Frequency Hz

2nd floor accel. a t D2

Frequency Hz

4

1

0,2 0

1st floor accel. atD12

1.5Q.

1

0,

First Floor Elastic Snap-Back - Accelerometers 3rd floor accel. a t D3

l i-

2 5Frequency Hz

Frequency Hz 1st floor accel. a t D1

2nd floor accel. a t D24

3

Q .E<I— LL. L L

2

1

0,

t 0.5L L

25Frequency HzFrequency Hz

Figure C-7: Fourier transform plots for the elastic snap-back tests - Accelerometers

280


-3x 10

3rd Floor Displ.-— 2nd Floor Displ. 1st F loor Displ.

dQ_WQN

OXoo

LL

Time (sec)

Figure C-8 : First floor snap-back: typical displacement histories o f all three floors

3rd Floor Displ.--- 2nd Floor Displ. 1st F loor Displ.0 . 0 2

0 . 0 1

Q_tnQn 01_O

X

j2 -0.01

-0 . 0 2

0 1 2 3 4 5Time (sec)

Figure C-9: Third Floor snap-back: typical displacement histories o f all three floors

281


The initial “undamaged” state modal properties o f the frame were extracted from

these snap-back tests using readings from all seven horizontal accelerometers distributed

at all three floor levels o f the frame. Both time and frequency domain modal property

extraction methods described in previous sections were applied to all seven accelerometer

data. First mode dynamic period and damping ratio was calculated by averaging the

results from the 3rd floor snap-back tests and 2nd and 3rd mode properties were calculated

by averaging the results from the 1st floor snap-back tests. The reason for this split is

evident in Figure C-7 which shows that the 1st floor snap-back tests excite the 2nd and 3rd

modes far more than the 3rd floor snap-back-tests and similarly the 1st mode is excited

more intensely by the 3rd floor snap-back tests. Table C-2 summarizes mean test frame

modal properties obtained from these snap-back tests.

Table C-2: Frame modal properties - initial “undamaged" state snap-back tests

1st mode 2nd mode 3rd mode

FrequencyDomainMethods

Period (sec)Std. Deviation / # of pts

0.3030.003 / 28

0 . 1 0 1

0.0004/210.069

0.0002/21FrequencyStd. Deviation I # of pts

3.300.031/28

9.850.016/21

14.470.038/21

TimeDomainMethods


0.306 0.0003 / 28

0 . 1 0 1

0.0003/210.069

0.0004/21FrequencyStd. Deviation / # of pts

3.270.004 / 28

9.790.025/21

14.390.073/21

Damping Ratio % Std. Deviation / # of pts

1.930.105/28

1.850.057/21

2.130.116/21

In addition to test frame elastic modal properties presented in Table C-2 the snap-

back tests allowed the evaluation o f 1st and 3rd floor frame stiffnesses. During the 1st floor

snap-back tests the frame was pulled at the 1 st floor level with a force o f 1 kip that was

inclined from the horizontal at an angle o f 13.6 degrees. A mean horizontal displacement

at that level was then measured to be 0.0057 in.. Thus the 1st floor stiffness could be

282


calculated as K i=l*cos(13.6)/0.0057 = 170.5 kip/in.. Similarly from the 3rd floor snap-

back tests we obtain the 3rd floor stiffness to be K3 = l*cos(30.7)/0.023 = 37.4 kip/in..

C.2.2.3 End of Half-Yield Test Free-Vibration

At the end o f the Half-Yield Test, the frame was left to vibrate freely for a few

seconds and its free-vibration responses were recorded. This allowed the extraction o f the

test frame modal properties using the methods described in previous sections. Table C-3

presents the mean modal properties obtained from the seven horizontal accelerometers on

the frame along with their sample standard deviations and sample sizes. During the free-

vibration period, the floating o f the shaking table produced significant noise in free-

vibration responses which forced a narrower filtering band around modal frequencies and

prevented accurate damping ratio evaluation using this method.

Table C-3: Frame modal properties - free-vibration post Flalf-Yield Test


Frequency Period (sec) 0.341 0 . 1 2 0 0.081Domain Std. Deviation / # of pts 0 .0 /7 0 .0 /4 0.0 / 7Methods Frequency 2.93 8.32 12.33

Std. Deviation / # of pts 0 .0 /7 0 .0 /4 0 .0 /7

Time Period (sec) 0.347 0 . 1 2 0 0.082Domain Std. Deviation / # of pts 0.0003 / 7 0.0006 / 7 0.003 / 7Methods Frequency 2 . 8 8 8.32 1 2 . 2 1

Std. Deviation / # of pts 0.002 / 7 0.039 / 7 0.406 / 7

We can note from Table C-3 that the frame has “softened” after the Half-Yield Test

as seen in the lengthening o f all three modal periods. This is attributed to the flexural

cracking that was observed during the Half-Yield Test.

C.2.2.4 White-Noise Dynamic Test

Following the Half-Yield Dynamic Test, a low-amplitude (with maximum peak

ground acceleration = 0 .015g) white-noise dynamic test was performed on the structure

283


in order to determine “cracked” dynamic properties. Only the frequency domain method

described previously is used to extract modal properties o f the frame in this test. Due to

jaggedness (see Figure C-10) o f the transfer functions derived from this test, a 15-point

moving average smoothing scheme was applied to them before frequencies could be read.

. 9 2 0

Q_

< 1 0

Freq. (Hz)

Figure C-10: Typical transfer function (accelerometer at Joint A l)

Table C-4 presents the extracted modal periods and frequencies for this test as well

as their sample sizes and standard deviations. Modal properties in Table C-4 match

closely those obtained from the end-of-test free-vibration period following the Half-Yield

Test (Table C-3).

Table C-4: Frame modal properties - white-noise test

1st mode 2nd mode 3rd mode 1

Frequency Period (sec) 0.350 0.115 0.080Domain Std. Deviation / # of pts 0 .0 /7 0.002 / 7 0.0002 / 7Methods Frequency 2.85 8.67 12.53

Std. Deviation / # of pts 0 .0 /7 0.134/7 0.039 / 7

284


C.2.2.5 End of Dynamic Test 1 Free-V ibration

At the end o f the Dynamic Test 1, the frame was left to vibrate freely for a few

seconds and its free-vibration responses were recorded. This allowed the extraction o f the

test frame modal properties using the methods described in previous sections. Table C-5

presents the mean modal properties obtained from the seven horizontal accelerometers on

the frame, along with their sample standard deviations and sample sizes. We can see from

Table C-5 that the frame has “softened” significantly during this test as seen in the

lengthening o f all three modal periods.

Table C-5: Frame modal properties - free-vibration post Dynamic Test 1


Frequency Period (sec) 0.81 0.38 0.13Domain Std. Deviation / # of pts 0 .0 /7 0.008/4 0 .0 /7Methods Frequency 1.23 2.64 7.85

Std. Deviation / # of pts 0 .0 /7 0.06 / 4 0.0/ 6

C.2.2.6 Damaged-State Snap-Back Tests

After Dynamic Test 1, in which the frame sustained significant damage, a series o f

snap-back tests were performed to assess test frame damaged-state modal properties. This

was done after all lead weights were re-attached properly to the frame. Due to the non-

linearity in test frame behavior, two levels o f snap-back tests were performed. The first

series o f snap-backs had a pull back force o f 1 kip and the second 0.5 kips. All snap-back

tests were performed at the third floor level. Due to time constraints first floor snap-back

tests were not performed at this stage. Figure C-l 1 plots displacement time histories o f all

three floors o f the frame for the first 1 kip snap-back test. We note in this figure that the

floor oscillations are not centered at zero due to the permanent drifts incurred during

Dynamic Test 1.

285


The dynamic properties obtained from both snap-back test series were very similar

and their results are summarized in Table C-6 . Both time domain and frequency domain

methods described previously were used here to evaluate the dynamic properties o f the

frame.

— 3 rd F lo o r D isp l. " '— 2 n d F lo o r D isp l. 1 s t F lo o r D isp l.

S--0 . 1

n -0 . 2

-0.3

-0.4

-0.5

60 1 2 3 4 5 7Time (sec)

Figure C - ll: Displacement histories o f all floors at column axis A - First 1 kip snap- back test after Dynamic Test 1

Table C-6 : Frame modal properties — damaged-state snap-back tests


Fourier

Transform

Method


0.824 0.033 / 35

0.2540.018/34

0.1500.0062 / 23

FrequencyStd. Deviation / # of pts

1 . 2 1

0.051/353.93

0.298 / 346.67

0.286/23Damping (%)Std. Deviation / # of pts

13.42 0.56 / 35

N/A N/A

Response

History

Method


0.717 0.022 / 35

N/A N/A

FrequencyStd. Deviation / # of pts

1.39 0.043 / 35

N/A N/A

286


C.2.2.7 End of Dynamic Test 2 Free-Vibration

At the end o f Dynamic Test 2, the frame was left to vibrate freely for a few seconds

and its free-vibration responses were recorded. This allowed the extraction o f the modal

properties o f the frame at the end o f the test using the methods described earlier. Table

C-7 presents the mean modal properties across the seven horizontal accelerometers on the

frame along with their sample standard deviations and sample sizes. We can see from

Table C-7 that the frame has further “softened” during this test as seen in the lengthening

o f all three modal periods.

Table C-7: Frame modal properties - free-vibration post Dynamic Test 2

1st mode 2nd mode 3rd mode 1

Frequency Period (sec) 0.93 0.33 o .nDomain Std. Deviation / # of pts 0 .0 /7 0.017/7 0 .016/7Methods Frequency 1.08 3.00 5.79

Std. Deviation / # of pts 0 .0 /7 0 .17 /7 0 .5 5 /6 I

C.2.3 Initial Assumed Gravity-Load-State of the Frame

This section presents the pertinent response values for the initial gravity-load-state o f

the frame as obtained from the analytical model described in Chapter 3. Response values

presented in Table C-8 are those obtained form the analytical model that have

corresponding experimentally recorded counterparts.

Initial gravity-load-state bending moment and shear force diagrams for the entire

structure as obtained from the analytical model are presented in Figure C-12 through

Figure C-15. Gravity-load deformed shape o f the frame is also presented in Figure C-16

(deformations scaled 500 times).

287


Table C-8: Summary o f initial gravity-load-state forces and deformations

First Floor Column Forces *Axial Force

(kips)Shear Force

(kips)Bending Moment Bottom (kip-in.)

Column A1 -10.38 0.42 -4.59Column B 1 -21.72 -0 . 1 1 1.31Column Cl -20.30 0.04 -0.38Column D l -9.35 -0.35 4.14Strains in Column and Ilearn Longitudinal Steel (microstrains) (+ve=extension)

Bottom East Bottom West Top East Top WestColumn A1 -113 -59 - 2 0 -150Column A2 -139 29 2 1 -129Column B 1 -174 -190 -197 -164Column B2 -97 -136 -128 -103Beam AB1 -30 -84 34 8 8

Joint Global Horizontal/Vertical Translations (in.) **Axis D Axis C Axis B Axis A

Third Floor -0.00083/-0.0067

-0 .0 0 1 1 /-0.015

-0.0014/-0.014

-0.0017/-0.0066

Second Floor -0.00097/-0.0056

-0.00092/-0 . 0 1 2

-0.00088/-0 . 0 1 2

-0.00087/-0.0056

First Floor -0.00048/-0.0033

-0.00039/-0.0074

-0.00029/-0.0073

-0.00019/-0.0034

Columns A l, A2, B l, B2 Top and Bottom Critical Section Rotations ***Bottom Sect. Rotation (rad) Top Sect. Rotation (rad)

Column A l 4.5e-5 -10.4e-5Column A2 14.3e-5 -11.4e-5Column B l -1.3e-5 2.7e-5Column B2 -3.3e-5 1.8e-5

*: for force sign convention see Figure C-17**: Positive global displacement is from West to East***: for critical section rotation sign convention see Figure C-20

288


± 20

-20

-4020 40

Beam CD3 X coord

20

S -20

-40.20 40

Beam BC3 X coord

5 20

-20

-4020 40

Beam AB3 X coord

20 40Beam CD2 X coord

40

20

0

-20

-40

r h

f \

\ — ------N. - - - - - -

J i

ii

20 40 60Beam BC2 X coord

40

~ 20

§ -20

-4020 40

Beam AB2 X coord

40 40

2 -20

-40

g -20

-400 20

Beam CD1 X coord40 60 20

Beam BC1 X coord40

40

2 -20

-400 20 40 60

Beam AB1 X coord

Figure C-12: Frame initial gravity-load-state — Beam bending moment diagrams

o 20 40 60

w 2 9-

S 0a)m -2

-4

4

S. 2k<6 0 ffl

-2

Beam CD3 X coord

I------- I—

20 40Beam CD2 X coord

60

-4k_-------i-------- i---------r-0 20 40 60

Beam CD1 X coord

w -2

j60 0 20 40 60

Beam BC3 X coord

4

in oo .kto 0 o>fh - 2

-4!0 20 40

Beam BC2 X coord60

Beam BC1 X coord

Beam AB3 X coord

20 40Beam AB2 X coord

60

co -2

20 40 60 0 20 40 60Beam AB1 X coord

Figure C-13: Frame initial gravity-load-state — Beam shear force diagrams

289


-10 0 10 Moment K.in


ooo>-COOcE3Oo

-10M oment K.in

30

20

10


30

20

10

-no 0 10Moment K.in


10 0 10 Moment K.in

"2ooo>CEOO

-10Moment K.in


■po8 30 >-ocEoO

-10Moment K.in

8 30 >5 20

§ 1 0oo „

-10u 0 10M oment K.in

>-<

oO

30

10

0-10 0 100 0 10

Moment K.in

Figure C-14: Frame initial gravity-load-state - Column bending moment diagrams

o 30[

q 20

| 10

-0.5 0 0.5S h ear Kips

3 0 -

2 0 -

10 -

oo-0.5 0 0.5

S h ear Kips

3 0 -

2 0 -

10r



3 0 -

2 0 -

1 0 -

O

o8 3 0 - >5 20

1 0 -

cE3Oo


-0.5 0 0.5S hear Kips

8 30h

o8 30 -

O 20C | 10 O° o

-0.5 0 0.5S h ear Kips S h ear Kips

I.5 0 0.S hear Kips




Figure C-15: Frame initial gravity-load-state - Column shear force diagrams

290


Figure C-16: Frame initial gravity-load-state - Frame deformed shape

C.2.4 First Story Column Force Calculations

Moments, shears, and axial forces o f the first story columns were calculated from

each test using moment, shear, and axial load readings o f load cells. Figure C-17 shows a

typical first story column and load cell layout, and a schematic representation o f column

and load cell forces with sign conventions. From basic equilibrium, the following

equations were obtained that relate column forces to load cell readings:

Column Axial Loads (Units: kips')

Ab = Ax + A2 + Wf (-ve = compression), see Figure C-17 for illustration o f terms

At = A h + Wc

Ab = bottom o f column axial load (this is the axial load presented in all figures)

A i and A2 = load cell axial load readings

Wf= footing weight = 3.18 kips / 4 (see Appendix A .3)291


At = top o f column axial load

Wc = weight o f column

Note: contribution o f footing vertical acceleration was minimal and thus not included in

column axial load calculations. At footing BO where the maximum recorded vertical

acceleration was approximately 0 .2 g, the maximum error in column axial load due to

footing acceleration omission is e=3.18/4*0.2=0.16 kips (which is on the order o f 1% of

column axial loads).

Column Bottom and Top Shear Forces (Units: kips, inches)

Vb = V\ + V2 - mf * Accelf , see Figure C-17 for illustration o f terms

Vt =Vb - ^ A c c e l f - ^ A c c e l ls!

Vb = bottom o f column shear force (this is the shear force presented in all figures)

Vi and V2 = load cell shear force readings

mf= footing mass = 3.18 kips 1 4 1 386.4 (see Appendix A.3)

Accelf= footing horizontal acceleration (accelerometer at footing BO values used for all)

Vt = top o f column shear force

mcoi = mass o f column (clear between footing and beams)

Accelist = first floor horizontal acceleration (accelerometer at Joint B l used for all as it

sustained least damage throughout dynamic tests)

Column Bottom and Top Moments (Units: kips, inches!

M b = - M x- M 2 +(Vx + F2)*18.5 + ( 4 - A 2) * \ 6 . 5 / 2 + mf * Accel f * 6

^39^if)M, =Vb *39 + M b - A bS + ^ t Accel

f3 9 * 3 ^ m\ - 2 L A cceL\ y I

Mb = bottom o f column moment

292


Mi and M2 = load cell moment readings

Mt = top o f column moment

<5 = horizontal displacement o f the first floor joint above each column

Note: in these equations rotational inertia is ignored

v-t

v t

lco l/2*A ccellst

3'-3B

lco l/2 # A cce lf

Mb

ib.MbVb

2' - 8'

VIPM2

Load CellsVl

Figure C-17: Typical first story column schematic forces and sign conventions

293


C.2.5 Story Shear Force Calculations

Second and third story shears were calculated in all tests using acceleration readings

o f horizontal accelerometers glued at various joints o f the frame. Given the excellent

agreement between first story shear forces calculated using floor inertias and load cell

readings (see section C.3.1), first story shear forces derived from load cells and floor

inertias could be used interchangeably with little loss o f accuracy. First story shears

presented in Chapter 5 were taken from load cell readings rather than by summing floor

inertia forces to have first story shears consistent with individual first story column

shears. The floor shears were thus calculated:

V storyx = Y j V u ,_ s to r y C o lu m n s » (see Section C.2.4 for 1st story column shear calculations)

readings)

A/7oor3 = Joint D3 horizontal accelerometer readings

Mfooting = mass o f footings including half column weights above floor level = 3.44/4 =

0.795 kips *

~Mfloor2 = second floor mass including half columns weights above and below floor level =

20.45 kips *

M.fl0or3 = third floor mass including half columns weights below floor level = 19.71 kips *

^ story2 ( / . ^ f l o o r ! / . ^ ' f l o o r Z ^ f l o o r Z

ystoryu v , 2 , Vstory3 = first through third strory shears

V ist stoty coiu/nnss = first story column shear forces

A footing = Footing BO horizontal accelerometer readings

A/7oor2 = Joint B2 horizontal accelerometer readings (2nd floor accelerometer with cleanest

294


*: see Appendix A .3 for values

C.2.6 Joint Displacement Calculations

Horizontal and vertical displacements o f all joints were monitored by a series o f

displacement potentiometers (wire-pots, DCDTs, and LVDTs) which recorded axial

extension and compression along the axes presented in Appendix A. 5.

Two separate and partially redundant systems o f potentiometers were used to

determine joint displacements during testing. The first system is only attached to the

frame itself and is used to determine relative joint movements with respect to the

footings; this system is termed the on-table joint triangulation system. The second system

measures the absolute displacements o f the joints and footings with respect to a fixed

reference frame that is located off the shaking table; this system is termed the off-table

joint triangulation system.

C.2.6.1 On-Table Joint Triangulation Displacement Calculations

This triangulation system measures in-plane vertical and horizontal joint

displacements with respect to footings. In the following calculations, footings are

assumed to move as one rigid body since the load cells on which they are placed can be

considered ’’infinitely” stiff with respect to test frame columns.

To determine joint displacements using the on-frame triangulation system, two sub

systems illustrated in Figure C-18 are solved at each time step in the following sequence:

1. Displacements o f Joints B l, C l, and D l are first solved using sub-system 1 with

footing displacements taken to be zero. Displacements o f these three joints are thus

calculated independently from each other.

295


2. Displacements o f Joint A1 are solved using sub-system 2 and previously calculated

displacements o f joint B1 and displacements o f footing AO which are assumed to be

zero.

3. Steps 1 and 2 are repeated for the second and third floors.

rxd

ry+dryrd+drd

Y aYOdYOy

-'X O d.

Sub-System 1

rx+drx

YOx

ry+dry

Y a

YOy

Sub-System 2

Figure C-18: Joint displacement triangulation sub-systems

296


The non-linear sets o f equations that are solved for each sub-system are presented

next. These sets o f equations account for large displacements and are formed o f two non

linear equations which contain only two unknowns: the horizontal (X) and vertical (Y)

displacements o f the joint under consideration. These equations are solved using the

Matlab 7.0 [Mathworks (2004)] non-linear equation solver function “fsolve”.

Sub-system 1:

\(rd + drd)2 = (rxd + XQd - X ) 2 + (ryd - YOd + Y) 2

{ (ry + dry)2 = ( X O y - X ) 2 + ( r y - Y O y + Y)2

Sub-system 2:

Urx + drx)2 = ( r x - X 0 x + X ) 2 + (-70jc + 7 ) 2

{ (ry + dry)2 = (XOy - X ) 2 + ( r y - YOy + Y)2

Definition o f terms:

rd = initial un-deformed diagonal potentiometer length

drd = diagonal potentiometer change in length (+ve for extension)

rxd = initial un-deformed diagonal potentiometer X-axis projection length

ryd= initial un-deformed diagonal potentiometer Y-axis projection length

XOd - horizontal (X-axis) displacement o f lower joint (or footing) attached to the

diagonal potentiometer

Y0d= vertical (Y-axis) displacement o f lower joint (or footing) attached to the diagonal

potentiometer

ry = initial un-deformed vertical potentiometer length

dry = vertical potentiometer change in length (+ve for extension)

XOy — horizontal (X-axis) displacement o f lower joint (or footing) attached to the vertical

potentiometer

297


YOy = vertical (Y-axis) displacement o f lower joint (or footing) attached to the vertical

potentiometer

X = horizontal (X-axis) displacement o f joint under consideration

Y= vertical (Y-axis) displacement o f joint under consideration

rx = initial un-deformed horizontal potentiometer length

drx = horizontal potentiometer change in length (+ve for extension)

XOx = horizontal (X-axis) displacement o f lower joint (or footing) attached to the

horizontal potentiometer

YOx = vertical (Y-axis) displacement o f lower joint (or footing) attached to the horizontal

potentiometer

C.2.6.2 Off-Table Joint Triangulation Displacement Calculations

Off-table joint triangulation was performed in a similar manner to that o f that o f the

on-table instruments described in the previous section. The only difference was the

addition o f the third dimension at Footing AO and Joint A3, which had potentiometers

placed perpendicularly to the test frame plane. The out-of-plane movement o f Joints A1

and A2 were linearly interpolated between the out-of-plane deformations o f Footing AO

and Joint A3. The following non-linear equations were solved to triangulate Footing AO

and Joints A l, A2 and A3:

Joint A3-

Joint AO

(ryd + dry)2 = (ryx - X ) 2 + (ryy + Y)2 + ( z ) 2 (rx + drx)2 = (rx - X ) 2 + ( Y) 2 + ( z f

(rzd + d rz ) 2 = (rzx — X ) 2 + (Y ) 2 + (rzz — Z )2

(rx + drx)2 = ( r x - X ) 2 + (Y)2 + ( z ) 2

Y = (TableYSE + TableYm ) / 2

(rzd + drz)2 = (rzx - X ) 2 + (Y)2 + (rzz — Z f

298


Joint A lorA l

(ryd + dry)2 = (ryx - X ) 2 + (ryy + Y )2 + ( z )2 (rx + drx)2 = ( r x - X ) 2 + ( Y f + ( z )2

z = ( z - Z ) ^ 2n^ \ A 3 AO J

Definition o f terms:

ryd = initial un-deformed diagonal potentiometer length

dry = diagonal potentiometer change in length (+ve for extension)

ryx = initial un-deformed diagonal potentiometer X-axis projection length

X = horizontal (X-axis) displacement o f joint under consideration

ryy = initial un-deformed diagonal potentiometer Y-axis projection length

Y= vertical (Y-axis) displacement o f joint under consideration

Z = out-of-plane (Z-axis) displacement o f joint under consideration

rx = initial un-deformed horizontal potentiometer length

drx = horizontal potentiometer change in length (+ve for extension)

rzd = initial un-deformed out-of-plane diagonal potentiometer length

drz = out-of-plane diagonal potentiometer change in length (+ve for extension)

rzx = initial un-deformed out-of-plane diagonal potentiometer X-axis projection length

rzz = initial un-deformed out-of-plane diagonal potentiometer Z-axis projection length

TableYsE and Table Yne = vertical displacement o f shaking table at South-East and North-

East comers

I12/1 and hs = height from Footing AO potentiometer anchor to Joint A1 or A2 and A3

ZA3 and ZA3 = out-of-plane movement o f Footing AO and JointA3

299


Once the global displacements o f Footing AO and Joints A l, A2, and A3 were

determined from basic triangulation, rigid body rotational displacements generated by

shaking table rotations were subtracted from these values. Translations o f Footing AO

were also subtracted to obtain joint movements relative to Footing AO. These

transformations are illustrated in Figure C-19 for in-plane adjustments.

O ns

"f , A3

I ! A0

Figure C-19: Off-Table triangulation adjustments

The following relations were used to evaluate shaking table rotations:

Gns = tan -1y dvSE + dvNE dvSW + dvNW

204"

300


9 e w = tan 1 •/ dvNW + dvNE \ ( dvSW + dvSE x

204"

where:

0ns = shaking table rotation angle about the North-South axis (see Appendix A.5 for

layout)

Oe w = shaking table rotation angle about the East-West axis (see Appendix A.5 for

layout)

dvNE, dvNW, dvSE, dvSW= vertical displacements recorded by vertical potentiometers at

four comers o f shaking table (see Appendix A.5 for layout)

Using these rotations, the horizontal (DX), vertical (DY) and out-of-plane (DZ) rigid

body adjustments (illustrated in Figure C-19) for each o f Joints A l, A2, and A3 were

calculated using the following equations:

D X = -d x + h sin(#vs)

D Y = -d y + h( 1 - cos(0NS)) + h( 1 - cos(0EW ))

DZ = -d z + h sin(0EW)

where:

h = height at which the joint displacement potentiometers are attached to the frame

measured from to the center o f rotation. In this case the center o f rotation is taken at

Footing AO instrumentation (see Figure C-19). For Joint A l, h=49 in., for Joint A2, h=91

in., and for Joint A3, h=145 in..

dx, dy, dz = footing AO horizontal and vertical and out-of-plane translations

C.2.7 Column Critical-Section Rotations

The non-seismically detailed columns at axes A and B were instrumented locally

with displacement potentiometers covering the first two stories and recorded column

301


shear and flexural deformations (see instrumentation Appendix A.5 for details). O f

greatest interest in these measurements were column rotations at their critical sections

(i.e., top and bottom 6 in.). Calculating these rotations was done in a straightforward

manner by taking the difference in the vertical deformations measured on either side o f

the column critical end sections (over a height h o f 6 in.) and dividing it by the distance

between the two instruments. When vertical instruments were not placed plumb vertically

(see Appendix A.5 for exact locations) due to test setup constraints, their readings were

adjusted by the cosine o f the angle separating them from vertical. These adjustment

angles were relatively small. The equation used for the rotation calculations was thus:

[dh\ cos(a l) - dh l co s(a 2 ))U — ------------------------------------------------------_______________ w____________

Figure C-20 illustrates the deformations measured and defines the terms in the

previous equation. It is useful to note here that rotations obtained thus are total rotations

which include rotation contribution o f bar slip within footings and joints.

rr =r-

Xw "/

Figure C-20: Column rotations

302


C.3 Result Checks and Balances

C.3.1 Base Shear Checks

This section compares test frame base shear results calculated from load cells or

floor horizontal inertia forces (see Section C.2.5). Figure C-21 compares the results

during the period o f most intense shaking for a typical elastic snap-back test, the Half-

Yield Test, a typical damaged-state snap-back test, and Dynamic Test 2. As can be seen

from Figure C-21, base shear results derived from load cells and floor inertias are almost

identical during the elastic snap-back test and the Half-Yield Test giving strong

confidence in both results. During the damaged state snap-back tests and Dynamic Test 2

there are some very minor discrepancies between the two methods o f evaluating base

shear whereby accelerometer base shear values contain higher frequency oscillations

about mean load cell values. These discrepancies are only minor in scale and could be

attributed to the high level o f damage and spalling that was observed in test frame joints

to which accelerometers were attached.

Dynamic Test 1 comparisons are treated in Chapter 5 because some lead weights

decoupled during that test.

303


Elastic Snap-Back Half-Yield T est

S o u rce : A cce lerom eters S ou rce : Load-C ells0.6

0.4tng .is:CDCD

. n- v f

WCD(DCDmcd -o 2cn

-0.4

-10

41.5 2 2.5 3 3.5 20 22 24 26 28 30Time (sec)

D am aged-S tate Snap-BackTime (sec)

Dynamic T est 2

0.4

? 0.2

-0.2

-0.4

-0.61 1.5 2 2.5 3 3.5 4

I- -

CDa .kCDCD.CcoCDCDCDm

-10

-15

20 22 24 26 28 30Time (sec t Time fse c l

Figure C-21: Base shear comparison between load cells and accelerometers —Typical elastic snap-back, Half-Yield Test, typical damaged-state snap-back test and Dynamic Test 2

C.3.2 Overturning Moment Checks

Similarly to base shear checks, the base overturning moment was evaluated during

snap-backs tests both from load cell axial and moment data as well as from horizontal

and vertical inertia data. Vertical inertia effects were taken into account by assuming

rigid body motion o f the frame in the vertical direction and interpolating vertical

accelerations that were recorded at the four comers o f the shaking table. This assumption

is a cmde simplification for the purposes o f this check, especially since the test frame is

not rigid vertically. Figure C-22 plots the results o f this comparison for global frame

moments evaluated about the vertical centerline o f the frame (middle o f beams BC) and

304


horizontal center o f the load cells and for a typical elastic snap-back test. Figure C-23 and

Figure C-24 do the same during periods o f high intensity shaking for Dynamic Tests 1

and 2. Figure C-22 shows very close agreement between the two calculation methods

giving strong confidence in load cell moment and axial load readings. Figure C-23 and

Figure C-24 show that the overturning moments calculated using the inertia forces follow

the trend o f load cell values fairly closely but showed significant oscillations around

them. This check thus suggests that the load cell readings were accurate during the

dynamic tests with discrepancies between them and inertia force estimates being

attributed to the crude nature o f this check.

300 S o u rce : Load Cells S o u rce : A cce lerom eters

250

< 200

-S 150

100

-50.2.5

T im e ( s e c )3.5

Figure C-22: Overturning moment about centerline o f frame: comparison between load cells and accelerometers - Typical elastic snap-back test

305


Bas

e O

vert

urni

ng

Mom

ent

abou

t Fr

ame

Cen

ter

(Kip

.in)

4 000 — S o u rce : Load C ells — S o u rce : A cce lerom eters

3000 j

2000

1000

-1000

-2000

-3000

21 21.5 22 22.5 23 23.5 24T im e ( s e c )

Figure C-23: Overturning moment about centerline o f frame: comparison between load cells and accelerometers - Dynamic Test 1

— Source: Load Cells j— Source: Accelerometers < -2500

.9- 2000

1500

1000

500

o -500

E -1000

> -1500

ra -2000

-2500

21 21.5 22 22.5 23 23.5 24Time (sec)

Figure C-24: Overturning moment about centerline o f frame: comparison between load cells and accelerometers — Dynamic Test 2

306


C.3.3 Lead-Weight Accelerometer Check

Following Dynamic Test 1, horizontal accelerometers were placed on four lead

packets to monitor their movement with respect to the frame. Accelerometers were

placed on the bottom most and inner most lead packets o f beams AB1, CD1, AB3 and

CD3. Figure C-25 and Figure C-26 plot the Fourier Transforms (FT) o f lead

accelerometer readings versus those o f test frame joint accelerometers during both

Dynamic Test 2 and 3. As well, these figures plot the histories o f these accelerometer

readings for the period o f most intense shaking. With the exception o f the accelerometer

at lead weight AB3 during Dynamic Test 3, these figures show very good agreement

between lead weight and joint accelerations at both the first and third floor levels. It is

thus concluded that lead weight attachment devices performed adequately during the last

two dynamic tests and minimal slip occurred between the frame and lead weights.

FFT - 3rd Floor Joint Accel, vs. Lead Accel.

L ead A ccel. A B3| L ead A ccel.C D 3 1 Jo in tD 3 A ccel.

History - 3rd Floor Joint Accel, vs. Lead Accel.

1 2 3 4 5 6Freq (hz)

FFT - 1st Floor Joint Accel, vs. Lead Accel.

— L ead A ccel. A B 1 !— L ead A ccel.C D 1 ,

Jo in tB I A ccel, i

0.5

o0)oo<

-0.5

24Time (sec)

History -1 st Floor Joint Accel, vs. Lead Accel.

2 150

3 4 5Freq (hz)

0.5

0d>OO<

-0.5

14 15 16Time (sec)

17 18

Figure C-25: Lead weight horizontal accelerations. v.s\ frame accelerations — Dynamic Test 2

307


FFT - 3rd Floor Joint Accel, vs. Lead Accel. History - 3rd Floor Joint Accel, vs. Lead Accel.

— L e a d A c c e l. A B 3— L e a d A c c e l.C D 3— Jo in tD 3 A c ce l.

Freq (hz)FFT - 1st Floor Joint Accel, vs. Lead Accel.

0.6

0.4

0.2

O -0.2

-0.4

-0.6

12 13 14 15 16 17Time (sec)

History - 1st Floor Joint Accel, vs. Lead Accel.

— L e a d A c c e l. AB1 — L e a d A c ce l.C D 1 — J o in tB I A c ce l.

Freq (hz)

0.6

0.4

0.2

o -0.2

-0.4

-0.6

12 13 14 15 16 17Time (sec)

Figure C-26: Lead weight horizontal accelerations, vs. frame accelerations —Dynamic Test 3

C.3.4 On-Table versus off-Table Instrument Displacement Comparison

The partial redundancy between the on-table and off-table joint displacement

measurements (see Section C.2.6), makes it is possible to compare the horizontal and

vertical displacements derived from both sets o f instruments for Joints A l, A2 and A3.

An important point to observe here is that the on-table triangulation instruments were

attached to threaded rods imbedded in the center o f the joints while the off-table

triangulation instruments were attached to targets that were glues on the outside (East)

edge o f the joints. This should generate a discrepancy between the two measurement

methods that should only be minor.

Figure C-27 through Figure C-30 compare horizontal drift ratio histories o f the first

and third floors o f the frame evaluated using the on-table and off-table instruments during

308


the Half-Yield Test and Dynamic Test 1. The “raw” curves presented in these figures are

obtained directly (without any modifications) from off-table horizontal wire pots at the

first and third floor levels. This addition serves as a check on the computations used to

obtain drift values from other instruments.

The first floor horizontal drift ratio are evaluated by dividing the first floor horizontal

displacements by the column clear height (= 39in.). The third floor horizontal drifts are

evaluated by dividing the third floor horizontal displacements by the third floor height

measured from top o f the footings to center o f third floor beam (= 139.5in.).

Both Figure C-28 and Figure C-30 show a very close agreement between drifts

obtained form all on-table instruments and off-table instruments. This gives good

confidence in third floor drift calculations. Figure C-27 and Figure C-29 show slight

offsets between first floor drifts evaluated using on-table and off-table instruments. These

offsets are not seen at the third floor level. Thus since on-table joint drifts are evaluated

independently and match each other well for both first third floors, it is concluded that the

on-table instruments provide the more accurate drift measurements. Also o f interest to

note here is that Joint D1 drifts are slightly offset from the other joints in a direction

consistent with beam CD1 lengthening during testing.

309


— R a w o ff-T a b le A1— A d ju s te d off-T able A1 — o n -T ab le A1— o n -T a b le B1 — o n -T ab le C1

o n -T ab le D1

0 . 6

0.4

' 5 -0 . 2

■N -0.4

-0 . 6

23 262 2 24 25 27Time (sec)

Figure C-27: First floor horizontal drift history comparison between on-table and off-table instrument measurements — Half-Yield Test

0.5I — R aw off-T able A3— A d ju s ted off-T able A3— o n -T ab le A3— o n -T ab le B3— o n -T ab le C 3

o n -T ab le D3O03QL

QCO+JcoNi_oX-t—Ic'o -:>

-0 .27

Time (sec)

Figure C-28: Thirdfloor horizontal drift history comparison between on-table and off-table instrument measurements — Half-Yield Test

310


R aw off-T able A1 A d ju s ted off-T able A1

— o n -T ab le A1 o n -T ab le B1 o n -T ab le C1 o n -T ab le D1

24 25Time (sec)

Figure C-29: First floor horizontal drift history comparison between on-table and off-table instrument measurements - Dynamic Test 1

R aw off-T able A3 A d ju s te d off-T able A 3 o n -T a b le A 3 o n -T a b le B3 o n -T ab le C 3 o n -T ab le D3

24 25Time (sec)

Figure C-30: Thirdfloor horizontal drift history comparison between on-table and off-table instrument measurements - Dynamic Test 1

311


C.3.5 Out-of-Plane Displacements of Frame

Out-of-plane displacements o f the frame were recorded with horizontal wire pots

attached to Footing AO and Joint A3 and connected to a fixed frame o ff the shaking table.

Relative out-of-plane displacement o f the frame is calculated by triangulation which

removes shaking table rigid body motions from the measurements (see Section C.2.6.2).

Figure C-31 plots the out-of-plane horizontal drift ratio histories o f Joint A3 for Dynamic

Tests 1, 2, and 3. The third floor horizontal drift ratios are evaluated by dividing the third

floor relative horizontal displacements (relative to those o f Joint AO) by the third floor

height measured from the top o f the footings to center o f third floor beam (= 139.5in.).

Figure C -31 shows that out-of-plane drift levels are relatively small considering that

frame columns can be considered as cantilevers in the out-of-plane direction. The

maximum drift ratio o f about 0.5-0.7% that the frame sustained in the out-of-plane

direction correspond roughly to the maximum first story in-plane drift ratios sustained

during the Half-Yield Test. Considering that the first story columns reached stress levels

in the range o f half their yield stresses at that in-plane drift level, the out-of-plane drifts

recorded would then correspond to a stress state much lower than half-yield since in the

out-of-plane direction the columns act as cantilevers with fixed-free end conditions. As

well, comparing the in-plane drift level that the frame columns sustained during the high

intensity dynamic tests (in excess o f 5%) to those out-of-plane movements (order o f

0.5%) they can be considered relatively small.

312


D y n am ic T e s t 1

a:0

110 20

i30

i40

T im e ( s e c ) D y n am ic T e s t 2

i50 60

i70 80

!_1 , ! 1 1 11_ ......1 I

HM-**

40T im e ( s e c )

D y n am ic T E s t 3

50 60 70 8 0

c'o^ 0 .5

-0 .5

0 2 4 6 8 10 12 14 16 18 20T im e ( s e c )

Figure C-31: Joint A3 out-of-plane horizontal drift ratio - Dynamic Tests 1, 2, and 3

C.4 Strain-Gauge Readings

C.4.1 Half-Yield Dynamic Test

Figure C-32 and Figure C-33 plot longitudinal bar strains recorded in Columns A l

and B1 versus end moments measured in these columns. In these figures, flexural

softening due to cracking is evident as the moment versus strain relations are seen to shift

from linear prior to cracking to bi-linear after cracking.

Figure C-34 through Figure C-36 plot the strain histories for Columns A l, A2, B l,

B2, and Beam AB1 for the Half-Yield Test. As with all data presented in this section,

these figures include the gravity-load offset as calculated from analysis and discussed in

Chapter 5. These plots show that the maximum tension strain did not exceed 1500 micro-313


strains in the first story columns and did not exceed 1 0 0 0 micro-strains in the second

story columns. Beam AB1 maximum strain exceeded 1000 micro-strains only by a slight

margin. Longitudinal bar material tests (Appendix A .l) give a yield strain for test frame

#3 longitudinal bars o f approximately 2300 micro-strains. Thus longitudinal bar strains in

Columns A l, A2, B l, B2, and Beam AB1 only reached about half yield strain during the

Half-Yield Test.

It is interesting to note here that all strain gauge readings showed a tension shift in

between the beginning and the end o f the test. This may be due to the fact that flexural

cracks in the concrete did not close completely at the end o f test.

Column A1 Top (West) Column A1 Top (East)1 0 0 1 0 0

£i

Q. CL

C03Eo — South Side Gauge

— North Side Gauge-50

- 1 0 0 - 1 0 0i 500 Micro-Strain

1 0 0 0 1500-500 -500 I 500 Micro-Strain

1 0 0 0 1500

Column A1 Bottom (West) Column A1 Bottom (East)1 0 01 0 0

Q.

-50 -50

- 1 0 0 - 1 0 0-500 I 500 Micro-Strain

1 0 0 0 1500 -500 I 500 Micro-Strain

1 0 0 0 1500

Figure C-32: Column A l longitudinal bar strains vs. moments — Half-Yield Test

314


Note on Figure C-32: The strain gauge at the South side, top o f Column A l was

defective and its strain readings were zeroed prior to adding the initial gravity load strains

to them. Thus its response is shown as a vertical line at the original gravity load offset.

Column B1 Top (West) Column B1 Top (East)

Micro-Strain Column B1 Bottom (West)

500

— South Side Gauge — North Side Gauge

0 500 1000 1500Micro-Strain

Column B1 Bottom (East)1 0 0 1 0 0

50CL

-50 -50

- 1 0 0 - 1 0 0-500 I 500 Micro-Strain

1 0 0 0 1500 -500 I 500 Micro-Strain

1 0 0 0 1500

Figure C-33: Column B1 longitudinal bar strains vs. moments - Half-Yield Test

Note on Figure C-33: The strain gauge at the South side, bottom o f Column B1 was

defective and its strain readings were zeroed prior to adding the initial gravity load strains

to them. Thus its response is shown as a vertical line at the original gravity load offset.

315


Micr

o-St

rain

Mi

cro-

Stra

in

Micr

o-St

rain

M

icro

-Stra

in

Colum n A2 T op (W est)1500 1500

1 0 0 0 1 0 0 0

500 500

-500 -500

1 0 2 0 30 40 50

Colum n A2 T op (E ast)

Time (sec)Column A2 Bottom (West)

Time (sec)

Column A1 Top (West)

20 30 40Time (sec)

Column A1 Bottom (West)

1500 1500

1 0 0 0 1 0 0 0

500 500

-500 -500

1 0 2 0 30 40 50

1500 1500

1 0 0 0 1 0 0 0

500 500

-500 -500

1 0 2 0 30 40 50

1 0

-----— South Side Gauge — North Side Gauge _

Ill

Hinmm r ||R n ii it 1 ------------ 1------------ 1------------

10 20 30 40Time (sec)

Column A2 Bottom (East)

50

20 30Time (sec)

Column A1 Top (East)' — 1------------ 1-----------— South Side Gauge

— North Side Gauge

Hll '

.Mi --------■— i—

4020 30Time (sec)


50

Time (sec)20 30

Time (sec)

Figure C-34: Columns A1 & A2 longitudinal bar strain histories — Half-Yield Test

316


Micr

o-St

rain

Mi

cro-

Stra

in

Micr

o-St

rain

M

icro

-Stra

in

Colum n B2 T op (W est)1500 1500

1 0 0 0 1 0 0 0

500 500

-500 -500

1 0 2 0 30 40 50

Colum n B2 T op (E ast)

South Side Gauge North Side Gauge

Time (sec)Column B2 Bottom (West)

20 30 . 40Time (sec)

Column B2 Bottom (East)

1 0 0 0

20 30Time (sec)

Column B1 Top (West)1500

1 0 0 0

500

-500

1 0 2 0 30 40 50

20 30 40Time (sec)

Column B1 Top (East)1500

— South Side Gauge North Side Gauge

Time (sec)Column B1 Bottom (West)

1500 1500

1 0 0 0 1 0 0 0

500 500

-500 -500

1 0 2 0 30 40 50

20 30 40Time (sec)


Time (sec)20 30 40

Time (sec)

Figure C-35: Columns B l & B2 longitudinal bar strain histories - Half-Yield Test

317


Note for Figure C-34 and Figure C-35: defective strain gauge readings were zeroed

prior to adding the initial gravity load strains to them. Thus their responses are shown as

horizontal lines at the original gravity load offset.

Beam AB1 Top (West)15001500

1 0 0 01 0 0 0CCO

500500WI£o

-500 -500

2 0 30 40 501 0Time (sec)

Beam AB1 Bottom (West)

Beam AB1 Top (East)

1 0 4020 30Time (sec)

Beam AB1 Bottom (East)

20 30Time (sec) Time (sec)

50

Figure C-36: Beam AB1 longitudinal bar strain histories - Half-Yield Test

318


B eam AB1 T op (W est) B eam AB1 T op (E ast)

55

-0.4 -0.2 0 0.2 0.4 0.6Drift (%)


-0.4 -0.2 0 0.2 0.4 0.6Drift (%)

Beam AB1 Bottom (East)1500

1 0 0 0

500

0

500

-0.4 -0.2 0 0.2 0.4Drift (%)

0.4 -0.2 0 0.2 0.4 0.6Drift (%)

Figure C-37: Beam AB1 longitudinal bar strain vs. first story drift ratio -Half-Yield Test

C.4.2 Dynamic Test 1

The same figures as those presented for the Half-Yield Test are presented in this

section. Beyond Dynamic Test 1, Strain gauge readings are not reported as they ceased

being reliable.

319


Colum n A1 T op (W est) Colum n A1 T op (E ast)

c 100

2 -100

-5000 0 5000 10000 15000Micro-Strain

Column A1 Bottom (West)

-5000

i — South Side Gauge f — North Side Gauge]

0 5000 10000 15000Micro-Strain

Column A1 Bottom (East)200

c 100Q_

4—>c0Eo

2100

■200■5000 0 5000 10000 15000

200

c 100I

Q.

C0E° -100

■2005000 10000 15000■5000 0

Micro-Strain Micro-Strain

Figure C-38: Column A l longitudinal bar strains vs. moments - Dynamic Test 1

Column B1 Top (West) Column B1 Top (East)200

7 100

0

Q.

C (DE° - 1 0 0

-200

V-Vd — South Side Gauge [r — North Side Gauge :{:

200

7 100tQ_

~ oc0E° -100

-200

, , , , ,

±j:

. i i r r f “ fcB'ii'iiM M — ■ J ------ -

■TT'j'T’TT'i*—rrr r? -

” '' ......... V \ ' ..L. TT-rrirrI f f f i l t17777*

-5000 0 5000 10000 15000Micro-Strain

Column B1 Bottom (West)

-5000 0 5000 10000 15000Micro-Strain

Column B1 Bottom (East)200

100

100

0 5000 10000 15000

200

c 100I

q .

c0Eo2

100

0 5000 10000 15000Micro-Strain Micro-Strain

Figure C-39: Column B1 longitudinal bar strains vs. moments - Dynamic Test 1

320


Micr

o-St

rain

Mi

cro-

Stra

in

Micr

o-St

rain

M

icro

-Stra

in

Colum n A2 T op (W est) Colum n A2 T op (E ast)10000

8000

6000

4000

2000

0

-2000

I

: k i

10000

8000

c 6000(0-4—JCO 4000oo 20002

0

-200020 6040

Time (sec)Column A2 Bottom (West)

80

South Side Gauge North Side Gauge

40Time (sec)

Column A2 Bottom (East)10000

8000

WHW-2000

10000

8000

c 6000CO

55 4000oO 2000

2

0

-200040

Time (sec) Column A1 Top (West)

20 40 60Time (sec)

Column A1 Top (East)

80

— South Side Gauge — North Side Gauge

-200040 60Time (sec)

Column A1 Bottom (West) x 10

40 60Time (sec)


100

15000

10000

-5000 40 60Time (sec)

40 60Time (sec)

80 100

Figure C-40: Columns A1 & A2 longitudinal bar strain histories - Dynamic Test 1

321


Micr

o-St

rain

Mi

cro-

Stra

in

Mic

ro-S

train

10000

8000

6000

4000

2000

0

-2000

Colum n B2 T op (W est) Colum n B2 T op (E ast)

10000

8000

6000

4000

2000

0

- 2000.

r “ i

. _ _hkJT

___________

J

J r N t

20 6040Time (sec)


40Time (sec)

Column B1 Top (West)

0

-x 10

20 40 60Time (sec)


80

10000

8000

c 6000CD

■4—*CO 4000oo 2000

2

0

-2000

80

10000 10000

8000

c 6000roW 4000oo 20002

0

-2000

!I

|i__j__;iiii

i. . * i i i i

”1

----1

i i

- Mi

______

I ;1 0 0

15000

10000

5000

0

-5000,

20000

15000

10000

-500040 60Time (sec)

— South Side Gauge— North Side Gauge

flnn*w 'riT— n

20 40 60Time (sec)


80

1 ii ii i

i i

. . . A

i i *20 40 60

Time (sec)Column B1 Top (East)

80

! f— South Side Gauge — North Side Gauge

r l

i i 1 :0 20 40 60 80

Time (sec)Column B1 Bottom (East)

100

1 1 :

— ..

1 F :20 40 60

Time (sec)80 1 0 0

Figure C-41: Columns B l & B2 longitudinal bar strain histories - Dynamic Test 1

3 2 2


Beam AB1 Top (W est) Beam AB1 Top (East)250015000

2000

•S 10000 « 1500

o 1 0 0 0

5000 500

L M

Time (sec)

2000

c us55E -2000

-4000


40Time (sec)

Beam AB1 Bottom (East)

Ii

2000

c 1500<0CO 1000oo 5002

0

-50020 40

Time (sec)60 80 20 40

Time (sec)60 80

Figure C-42: Beam AB1 longitudinal bar strain histories - Dynamic Test 1

Beam AB1 Top (West) Beam AB1 Top (East)

raWob

20000 3000

15000 2000cCD10000

1000o .—5000 o

-5000 -1000-1 0 5 -1 0

Drift (%) Drift (%)Beam AB1 Bottom (West) Beam AB1 Bottom (East)

c255io

4000 3000

2000 2000c2

1000-2000 o

-4000

-6000 -1 0 0 0-1 0 5 -10

Drift (%) Drift (%)

Figure C-43: Beam AB1 longitudinal bar strain vs. fis t story drift ratio - Dynamic Test 1

323


Appendix D: OpenSEES Modeling

D .l Material Properties

This section presents the uni-axial material model properties used in the analytical

model o f the test frame presented in Chapter6 . Table D -l summarizes these material

properties.

The OpenSEES uni-axial concrete02 material model was used for confined and

unconfined concrete fibers in columns and beams. Analytical concrete material was

calibrated to the concrete material stress-strain curves obtained from concrete cylinder

tests (see Appendix A). Confinement effects on core concrete were estimated from the

model proposed by Mander et al. (1988). Longitudinal steel was modeled using the

OpenSEES uni-axial material steel02. Longitudinal steel yield stress values were

increased by 25% from experimental coupon results to account for strain-rate effects.

Other steel material properties were matched to coupon test results as presented in

Appendix A.

Sample calculation details for bar-slip steel fiber material properties are presented for

#3 longitudinal bars, which have material properties: fy=80 ksi, Es=27300 ksi, b=0.01,

fu=100 ksi (fy=yield stress, Es=steel modulus o f elasticity, b=ratio o f hardening slope to

elastic slope, and fu=ultimate stress).

From Equations (2-7) and (2-8) we have:

slipy= 0.0153 in. (bar-slip at yield)

slipu = 0.398 in. (bar-slip at ultimate)

evaluated with:

324


ue = 1 2 /7 'c (psi) (elastic bond stress)

Up = 3.24yjf 'c (psi) (imposed plastic bond stress resulting from ue value and b=0.01)

This leads to bar-slip steel02 material parameters: fy=80 ksi, Ebs=5220 ksi and

b=0.01. Bar-slip concrete material strains are thus multiplied by the ratio o f E s / E b s = 5.23

to maintain the same material stiffness ratio with bar-slip steel as that o f frame-element

concrete with longitudinal steel.

The calibration process is performed similarly for #2 longitudinal bars and all bar-

slip fiber-section steel and concrete material properties are presented in Table D -l.

Table D - l : Uni-axial material modelsMaterial

DescriptionOpenSEES

UniaxialMaterial

Material Model Description

Parameters Reference

Concrete cover All elements

Concrete02 Kent-Scott-Park concrete material with degraded

linear unloading/reloading stiffness according to

Karsan-Jirsa

f c = 3.57 ksi £c = 0.0026 f’u = f’c/3

F = 3?°U ->Oc

f,= 7 . 5 V / ' c *

Et = E0“ / 5

Scott et al. (1982)

Concrete Core Flexure-shear-

critical columns and beams

Concrete02 (Same as above) f c = 3.90 ksi sc = 0.0028 f u = 0.9 f c

£u 3ec

ft= 7 . 5 V / ’c

Et = E0 / 5

(Same as above)

Confinement effects based on Mander et

al. (1988)

Concrete Core Ductile columns

Concrete02 (Same as above) f c = 7.50 ksi £c = 0.0055 f u = 0.98 f c

£u 3ec

ft= 7 . 5 V / ' c

E, = E0 / 5

(Same as above)

Longitudinal Steel

#3 bars

Steel02 Giuffre-Menegotto-Pinto steel material with

isotropic strain hardening.

fy = 80.0 ksi Es = 27300 ksi

b = 0.01 (all other values

default OpenSEES

Menegotto and Pinto

(1973)

325


Longitudinal Steel

#2 bars



fy = 87.5 ksi Es = 26500 ksi


default OpenSEES)

Menegotto and Pinto

(1973)

Concrete cover Bar-Slip

All elements



Karsan-Jirsa

F c = 3.57 ksi sc = 0.0136f’u = f’c/3 £u 3ec

ft = 7 . 5 V / 'cEt = E0 / 5

Scott et al. (1982)

Concrete core Bar-Slip

Flexure-shear- critical columns

and beams



Karsan-Jirsa

f c = 3.90 ksi £c = 0.0146 f „ = 0.9 f c

£y 3EC

5 = 7 . 5 V / 'cE, = E0/ 5

(Same as above)

Confinement effects based on Mander et

al. (1988)

Concrete core Bar-Slip

Ductile columns



Karsan-Jirsa

f c = 7.50 ksi £c = 0.0288 f „ = 0.98 f c

£u 3£c

ft= 7.5-y/ f ' c Et = E0 / 5

(Same as above)

Bar-Slip steel #3 bars



fy = 80.0 ksi Es = 5220 ksi


default OpenSEES)

Menegotto and Pinto

(1973)

Bar-Slip steel #2 bars



fy = 87.5 ksi Es = 5067 ksi


default OpenSEES)

Menegotto and Pinto

(1973)

*: as per ACI 318-05 [American Concrete Institute (ACI) Committee 318 (2005)] recommendations ** : E0 = tangent stiffness of concrete material at zero load given by (2*f J sc) in the concrete02 material

D.2 Moment-Curvature Sectional Analyses

Moment-curvature sectional analyses were performed on ductile and flexure-shear-

critical column sections with various axial loads. Material properties presented in the

previous section are used for these moment-curvature analyses. The difference in flexural

strength between analyses based on static yield stress o f steel bars and those taking 1.25

326


times yield stress (for dynamic effects) are highlighted in Figure D -l. The yield moment

can be compared with the experimental results presented in Chapter 6 .

Ductile Column - fy = 64 Ksi Non-Ductile Column - fy = 64 Ksi140 2 0 0

120

150. 100

c 100 P=5 kips P=0 kips— ~P=-10 kips P=-20 kips P=-30 kips

4050

5Curvature 1/in.

Ductile Column - fy = 80 KsiCurvature 1/in.

Non-Ductile Column - fy = 80 Ksi-3 -3

x 1 0 x 1 0

140 200

120

150. 100

c 100

50

5Curvature 1/in. C urvature 1/in.-3 -3

x 1 0 x 1 0

Figure D -l: Ductile and non-ductile column moment curvature analyses

D.3 Shear and Axial LimitState Material Properties

Defining shear and axial LimitState [Elwood (2002)] material properties is a two

step process. First, parameters for the failure envelopes are defined (Table D-3 and Table

D-4) and second the tri-linear hysteretic material models (Table D-5) are defined for the

initial state o f the springs prior to shear and axial failures. Based on the recommendations

o f Elwood (2002) the LimitState shear and axial material properties listed in Table D-2

are used to model flexure-shear-critical column shear and axial failures.

327


Table D-2: LimitState materials - input parameters

limitCurve Shear $curveTag SeleTag $rho $fc $b $h $d $Fsw $Kdeg $Fres SdefType $for Type <$ndl $ndJ $dof SperpDirn $delta>

limitCurve Shear $curveTag $eleTag 0.0015 3.57 6 6 5.15 (0.0368*95*5.15/4) 111.33 2 0 $ndl $ndJ 1 2 0.0__________________________________________________

limitCurve Axial ScurveTag $Fsw $Kdeg SFres SdefType SforType <$ndl $ndJ $dof $perpDirn $delta>

limitCurve Axial $curveTag (0.0368*95*5.15/4) -30.0 5.0 2 2 $ndl $ndJ 1 2 0.0

uniaxialMaterial LimitState $matTag $slp $elp $s2p $e2p $s3p $e3p $sln $eln $s2n $e2n $s3n $e3n SpinchX SpinchY Sdamagel $damage2 $beta ScurveTag ScurveType

ShearuniaxialMaterial LimitState SmatTag 25.0 2.5e-4 30.0 3e-4 35.0 3.5e-4 -25.0 -2.5e-4 -30.0 -3e-4 -35.0 -3.5e-4 0.5 0.4 0.0 0.0 0.4 ScurveTag 2 0

AxialuniaxialMaterial LimitState SmatTag 65.0 6.5e-4 75.0 7.5e-4 85.0 8.5e-4 -65.0 -6.5e-4 -75.0 -7.5e-4 -85.0 -8.5e-4 0.5 0.5 0.0 0.0 0.0 ScurveTag 1

328


Table D-3: Shear Limit Curve (from Elwood (2002))

Shear Limit CurveThis command is used to construct a shear limit curve object that is used to define the point of shear failure for a LimitStateMaterial object. Point of shear failure based on empirical drift capacity mode! from Chapter 2.

limitCurve Shear ScurveTag SeleTag $rho $fc $b $h $d $Fsw $Kdeg _______$Fres SdefType SforType <$ndl $ndJ $dof SperpDirn $delta>.

ScurveTagSeleTag

$rho$fcSbSh

$dSFsw

SKdeg

SFres

SdefType

SforType

Sndl

SndJ

SdofSperpDIrn

Sdelta

329

unique limit curve object integer taginteger element tag for the associated beam-column elementtransverse reinforcement ratio (/Wbh) concrete compressive strength (psi) column width (in.) full column depth (in.) effective column depth (in.)floating point value describing the amount of transverse reinforcement (F*» = A^d,/®)If positive: unloading stiffness of beam-column element (Kurioad from Figure 4-8)if negative: slope of third branch of post-failure backbone (see Figure 4-6)floating point value for the residual force capacity of the post-failure backbone (see Figure 4-6)Integer flag for type of deformation defining the abscissa of the limit curve

1 = maximum beam-column chord rotations2 = drift based on displacment of nodes ndl and ndd

Integer flag for type of force defining the ordinate of the limit curve

0 = force in associated limit state material1 == shear in beam-column element

integer node tag for the first associated node (normally node i of SeleTag beam-column element)integer node tag for the second associated node (normally node J of SeleTag beam-column element)nodal degree of freedom to monitor for driftperpendicular global direction from which length is determined to compute driftdrift {floating point value) used to shift shear limit curve


Table D-4: Axial Limit Curve (from Elwood (2002))

Axial Limit CurveThis command is used to construct an axial limit curve object that is used to define the point of axial failure for a UmitStateMateria] object. Point of axial failure based on model from Chapter 3. After axial failure response of LlmitStateMaterial is forced to follow axial limit curve.

limitCurve Axial ScurveTag SeleTag SFsw $Kdeg $Fres SdefType SforType <$ndl $ndJ $dof SperpDirn $delta>.

ScurveTagSeleTag

SFsw

SKdeg

SFres

$defType

SforType

Sndl

SndJ

SdofSperpDirn

Sdelta

unique limit curve object integer taginteger element tag for the associated beam-column elementfloating point value describing the amount of transverse reinforcement (Fa* = A*(fjtdo/8)floating point value for the slope of the third branch in the post-failure backbone, assumed to be negative (see Figure 4-6)floating point value for the residual force capacity of the post-failure backbone (see Figure 4-6)integer flag for type of deformation defining the abscissa of toe limit curve

1 = maximum beam-column chord rotations2 = drift based on displacment of nodes ndl and ndJ

integer flag for type of force defining the ordinate of the limit curve*

0 = force in associated limit state material1 = shear in beam-column element2 = axial load in beam-column element

integer node tag for toe first associated node (normally node I of SeleTag beam-column element)integer node tag for the second associated node (normally node J of SeleTag beam-column element)nodal degree of freedom to monitor for drift**perpendicular global direction from which length Is determined to compute drift**drift (floating point value) used to shift axial limit curve

NOTE: * Options 1 and 2 assume no member loads. ** 1 = X, 2 = Y. 3 = Z

330


Table D-5: Tri-linear hysteretic material fo r shear and axial springs (from Elwood(2002))

Limit Stats MaterialThis command Is used to construct a unfaxlal hysteretic material object with pinching of torce and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility. Failure of the material is defined by the associated limit curve.

uniaxialMaterial LimitState SmatTag $s1p Se1p $s2p $e2p $s3p $e3p $s1n $e1n Ss2n $e2n $s3n $e3n SpinchX SpinchY

_______$damage1 $damage2 Sbeta ScurveTag ScurveType.______

SmatTag unique material object integer tag$s1p $e1p stress and strain (or force & deformation) at first point of

fie envelope in the positive direction$s2p S@2p stress and strain (or force & deformation) at second point

of the envelope in the positive directionSs3p $e3p stress and strain (or force & deformation) at third point of

the envelope in the positive direction (optional)$81 n Se1n stress and strain (or force & deformation) at first point of

the envelope in the negative direction*Ss2n Se2n stress and strain (or force & deformation) at second point

of the envelope in the negative direction*Ss3n Se3n stress and strain (or force & deformation) at third point of

the envelope in the negative direction (optional)*SpinchX pinching factor for strain (or deformation) during reloadingSplnchY pinching factor for stress (or force) during reloadingSdamagel damage due to ductility: Di(p*1)Sdamage2 damage due to energy: D2(E/Eutt)Sbeta power used to determine the degraded unloading stiffness

based on ductility, p* (optional, defauit=0.0)ScurveTag an integer tag for the LimitCurve defining the limit surfaceScurveType an integer defining the type of LimitCurve (0 = no curve,

1 = axial curve, all other curves can be any other integer)

• N O T E : negative backbone points should be entered as negative numeric values

331


Appendix E: Frame Component Pictures at

Various Damage States

This appendix presents pictures of test frame joints and elements after each of the

main dynamic tests.

E .l Column A l Base

Figure E -l: Column A 1 Base - Post Half- Yield Test

332


Figure E-2: Column A l Base, v ide vieu, - P o s, D ynam ic Tes, 1

333

a * ™ * * w#h pemissi0„ of the copyriflht owner puriher reproduc(ion ^ ^ ^

Figure E-3: Column A l Base, wide view - Post Dynamic Test 2

334


Figure E-4:

Figure E-5:

Column A l Base, South detail — Post Dynamic Test 2

Column A l Base, North detail - Post Dynamic Test 2

335


Figure E-6: Column A l Base, wide view - Post Dynamic Test 3

336


E.2 Joint A l

Figure E-7: Joint A l — Post Half- Yield Test

Figure E-8: Joint A l - Post Dynamic Test 1

337


Figure E-9: Joint A 1 - Post Dynamic Test 2

E.3 Joint A2

Figure E-10: Joint A2 - Post Half-Yield Test

338


Figure E-l 1: Joint A2 - Post Dynamic Test 1

Figure E-12: Joint A2 - Post Dynamic Test 2

339



E.4 Joint A3

Figure E-14: Joint A3 - Post Half-Yield Test

340


Figure E-15: Joint AS - Post Dynamic Test 1


341


£.5 Column B1 Base

Figure E-17: Column B1 Base - Post Half-Yield Test

Figure E-18: Column B l Base, wide view - Post Dynamic Test 1

342


Note: brackets were loosened after each of Dynamic Tests 1 and 2 at the base of

Column B 1.

Figure E-19: Column B1 Base — Post Dynamic Test 2

Figure E-20: Column B1 Base - Post Dynamic Test 3

343


E.6 Joint B1

Figure E-21: Joint B1 - Post Half-Yield Test

Figure E-22: Joint B l - Post Dynamic Test 1


Figure E-23: Joint B1 - Post Dynamic Test 2

liiiififi


345


E.7 Joint B2

iiiiilllll

Figure E-25: Joint B2 - Post Half-Yield Test


346

R e p r o d u c e d w ith p e r m is s io n o f th e c o p y r ig h t o w n e r . F u rth er r ep ro d u c tio n p ro h ib ited w ith o u t p e r m is s io n .


E.8 Joint B3

Figure E-28: Joint B3 — Post Half-Yield Test

347

R e p r o d u c e d w ith p e r m is s io n o f th e c o p y r ig h t o w n e r . F u rth er r ep ro d u c tio n p ro h ib ited w ith o u t p e r m is s io n

Figure E-30: Joint B3 — Post Dynamic Test 3

348

R e p r o d u c e d w ith p e r m is s io n o f th e c o p y r ig h t o w n e r . F u rth er r ep ro d u c tio n p ro h ib ited w ith o u t p e r m is s io n

E.9 Column C l Base

Figure E-31: Column C l Base - Post Half-Yield Test

Figure E-32: Column C l Base - Post Dynamic Test 1

349


Figure E-33: Column Cl Base — Post Dynamic Test 2

Figure E-34: Column C l Base - Post Dynamic Test 3

350


E.10 Joint C l

Figure E-35: Joint C l - Post Half-Yield Test

vf|___

*m

V'%" 'jS$®££ '.Cl

\L

f ;'v}-' ' |I yk N

■ .10 y r e i ;(/■' I

i s;> ■' __ *

\N

-1111 V

tfmmmgmV > t t

■ f

(

.

m/ ■

mw—

Figure E-36: Joint C l — Post Dynamic Test 1

351


Figure E-37: Joint C l - Post Dynamic Test 3

E .ll Joint C2

Figure E-38: Joint C2 - Post Half-Yield Test

352


Figure E-39: Joint C2 - Post Dynamic Test 1


353


E.12 Joint C3

JKBHHHUB*

Figure E-41: Joint C3 - Post Half- Yield Test



Figure E-43: Joint C3 — Post Dynamic Test 3

Figure E-44: Joint C3, top view - Post Dynamic Test 3

355


E.13 Column D1 Base

Figure E-45: Column D1 Base - Post Half-Yield Test

Figure E-46: Column D1 Base — Post Dynamic Test 1

356


Figure E-47: Column D1 Base - Post Dynamic Test 2

Figure E-48: Column D1 Base, bar fracture - Post Dynamic Test 3

357


E.14 Joint D1

Figure E-49: Joint D1 - Post Half-Yield Test

Figure E-50: Joint D1 - Post Dynamic Test 1

358



E.15 Joint D2


359




360


E.16 Joint D3



361



362


Documents

Experimental and Analytical Dynamic Collapse Study of a Reinforced Concrete Frame with Light