CYCLIC TESTING AND ASSESSMENT OF SHAPE MEMORY ALLOY RECENTERING SYSTEMS

CYCLIC TESTING AND ASSESSMENT OF SHAPE MEMORY ALLOY RECENTERING SYSTEMS
CYCLIC TESTING AND ASSESSMENT OF SHAPE MEMORY
ALLOY RECENTERING SYSTEMS
A Thesis
Presented to
The Academic Faculty
by
Matthew S. Speicher
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy in the
School of Civil and Environmental Engineering
Georgia Institute of Technology
May 2010
UMI Number: 3414523
All rights reserved
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CYCLIC TESTING AND ASSESSMENT OF SHAPE MEMORY
ALLOY RECENTERING SYSTEMS
Approved by
Dr. Reginald DesRoches, Advisor
School of Civil and Environmental
Engineering
Georgia Institute of Technology
Dr. James Craig
School of Aerospace Engineering
Georgia Institute of Technology
Dr. Roberto T. Leon, Co-Advisor
School of Civil and Environmental
Engineering
Georgia Institute of Technology
Dr. Yang Wang
School of Civil and Environmental
Engineering
Georgia Institute of Technology
Dr. Laurence Jacobs
School of Civil and Environmental
Engineering
Georgia Institute of Technology
Date Approved: December 7, 2009
Engineering is the art of directing the great sources of power in nature for the use and
convenience of man – Hardy Cross (1952)
ACKNOWLEDGEMENTS
This work would not have been possible without the contribution of many individuals.
The author would like to thank Dr. Reginald DesRoches and Dr. Roberto T. Leon for the
support, guidance, and advice that made this research possible.
The author would like to thank Johnson Matthey for donating the stock NiTi
material for the tension/compression device experiments and Dr. Darel Hodgson for
conceiving and fabricating the tension/compression device and the wire bundles and
providing guidance for this research. The author also thanks Mike Sorenson, Andy Udell,
and Jeremy Mitchell for the support given in the lab.
Tackling a doctoral thesis is very challenging. The author would like to thank all
of the fellow graduate students who made the battle more enjoyable. Specifically, the
author thanks Masahiro Kurata for his continued good spirits and guidance in this
research and his camaraderie during travels to California, Canada, and China. The
author thanks Robert Hurt for getting him into the weight room, helping him develop
research ideas, and continually fixing his car. The author thanks his office mates in
Mason 522a and other colleagues including Ben Kosbab, Walter Yang, Karthik
Ramanathan, Tim Wright, Jieun Hur, Jason McCormick, and Bryant Neilson for making
research more enjoyable with daily banter.
Through the highs and lows of graduate research, the author also thanks his
beautiful wife Lindsay for the constant encouragement and support. The author thanks
his father, mother, brother, and sister for all the support they have given him over the
decade he has been in college.
Additionally, the author would like to thank Elias
iii
Matthew for his constant reminder of what is important as the author finished the work
on this thesis.
Lastly but most importantly, the author would like to thank God and his Son. It is
through the author’s deep faith in the events laid out in the Bible and his personal
experience living in the wake of grace, that the author has unreserved confidence in
God’s infinite power, love, and wisdom and in the redemption brought through his Son.
iv
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................................................................................ III LIST OF TABLES ......................................................................................................... VIII LIST OF FIGURES ......................................................................................................... IX LIST OF SYMBOLS AND ABBREVIATIONS ............................................................... XX SUMMARY…………………………………………………………………………..………… XXII CHAPTER 1
INTRODUCTION ................................................................................. 1 1.1. Problem Description............................................................................................. 1 1.2. Scope of Project................................................................................................... 4 1.3. Thesis Outline ...................................................................................................... 5 CHAPTER 2
LITERATURE REVIEW ....................................................................... 7 2.1. Introduction .......................................................................................................... 7 2.2. Shape Memory Alloys .......................................................................................... 7 2.2.1. SMA overview ............................................................................................... 7 2.2.2. SMA Microstructure ...................................................................................... 8 2.2.3. Shape Memory Alloy: Fundamental Behaviors........................................... 9 2.2.4. NiTi Shape Memory Alloy ........................................................................... 11 2.2.5. Applications of SMAs .................................................................................. 15 2.3. Recentering Systems ......................................................................................... 17 2.3.1. Single Degree-of-Freedom (SDOF) Studies ............................................... 17 2.3.2. Posttensioned Systems .............................................................................. 19 2.3.3. SMA-Based Systems .................................................................................. 22 CHAPTER 3
SINGLE DEGREE OF FREEDOM STUDY ....................................... 26 3.1. Introduction ........................................................................................................ 26 3.2. Approach 26 3.3. Analytical Setup ................................................................................................. 28 3.4. Results and Discussion...................................................................................... 31 3.4.1. General Behavior ........................................................................................ 31 3.4.2. Displacement and Acceleration Demands .................................................. 32 3.4.3. Case Study: SMA4 vs. EP1 vs. PARA1 ..................................................... 37 3.4.4. Summary .................................................................................................... 39 CHAPTER 4
TENSION/COMPRESSION DEVICE ................................................ 40 4.1. Introduction ........................................................................................................ 40 4.2. Background ........................................................................................................ 40 4.3. Device Description ............................................................................................. 41 4.4. Active Element Description ................................................................................ 42 4.4.1. Helical Springs ............................................................................................ 42 4.4.2. Belleville (Spring) Washers ........................................................................ 43 4.5. Experimental Setup............................................................................................ 43 v
4.6. Results and Discussion – Helical Spring Tests .................................................. 45 4.6.1. Results – Hollow Helical Spring .................................................................. 45 4.6.2. Results – Solid Helical Spring .................................................................... 46 4.6.3. Discussion - Helical Spring Tests .............................................................. 48 4.7. Results and Discussion – NiTi Belleville Washer Tests: Phase I ...................... 49 4.7.1. Individual .................................................................................................... 50 4.7.2. Single-Stacked ........................................................................................... 51 4.7.3. Double-Stacked .......................................................................................... 53 4.7.4. Triple-Stacked ............................................................................................ 55 4.7.5. Discussion – Single, Double, and Triple-Stacked Washers........................ 57 4.8. Results and Discussion – NiTi Belleville Washer Tests: Phase II ..................... 59 4.8.1. Individual .................................................................................................... 59 4.8.2. Single-Stacked ........................................................................................... 61 4.9. Conclusions ....................................................................................................... 63 CHAPTER 5
INVESTIGATION OF A RECENTERING BEAM-COLUMN
CONNECTION ................................................................................... 64 5.1. Introduction ........................................................................................................ 64 5.2. Experimental Program ....................................................................................... 65 5.2.1. Component Testing .................................................................................... 65 5.2.2. Loading Scheme ......................................................................................... 67 5.2.3. Instrumentation and Data Acquisition Plan ................................................. 69 5.3. Connection Details ............................................................................................. 71 5.3.1. Beams, Column, and Bracket Elements ..................................................... 71 5.3.2. Shear Tab ................................................................................................... 74 5.3.3. Tendon “Fuse” Elements ............................................................................ 76 5.4. Experimental Results ......................................................................................... 77 5.4.1. Test A – Steel 1 .......................................................................................... 77 5.4.2. Test B – Steel 2 .......................................................................................... 80 5.4.3. Test C – SMA 1 .......................................................................................... 84 5.4.4. Test D – SMA 2 .......................................................................................... 88 5.4.5. Test E – SMA 2 + AL (PARA) ..................................................................... 92 5.5. Discussion of Results ......................................................................................... 96 5.5.1. General Behavior ........................................................................................ 96 5.5.2. Yield Moment and Effective Stiffness ....................................................... 100 5.5.3. Residual Rotation ..................................................................................... 103 5.5.4. Energy Dissipation .................................................................................... 105 5.5.5. Connection Modeling ................................................................................ 108 5.5.6. From Research to Practice: Potential Applications .................................. 115 5.5.7. Analytical Study ........................................................................................ 116 5.6. Summary. ......................................................................................................... 117 CHAPTER 6
INVESTIGATION OF A RECENTERING ARTICULATED
QUADRILATERAL BRACING SYSTEM ........................................ 120 6.1. Introduction ...................................................................................................... 120 6.2. Background ...................................................................................................... 122 6.3. Test Setup........................................................................................................ 123 6.3.1. General AQ ............................................................................................... 123 6.3.2. Cable Assembly ........................................................................................ 125 6.3.3. Test A: SMA-only ..................................................................................... 126 vi
6.3.4. Test B: C-shape-only ............................................................................... 127 6.3.5. Test C: Parallel System (SMA + c-shape) ............................................... 128 6.4. Testing Scheme ............................................................................................... 129 6.4.1. Instrumentation ......................................................................................... 130 6.4.2. Loading Protocol ....................................................................................... 132 6.5. Pretests… ........................................................................................................ 133 6.5.1. Component Test: Wire Bundle ................................................................ 133 6.5.2. Shakedown Test ....................................................................................... 134 6.6. Experimental Results ....................................................................................... 135 6.6.1. Test A ....................................................................................................... 135 6.6.2. Test B ....................................................................................................... 138 6.6.3. Test C ....................................................................................................... 141 6.7. Discussion of Results ....................................................................................... 144 6.7.1. General Behavior ...................................................................................... 144 6.7.2. Effective Stiffness and Yield Moment ....................................................... 152 6.7.3. Residual Drift ............................................................................................ 153 6.7.4. Energy Dissipation .................................................................................... 154 6.8. Analytical Study ............................................................................................... 156 6.8.1. Description and Setup .............................................................................. 156 6.8.2. Results and Discussion ............................................................................ 160 6.9. Summary. ......................................................................................................... 167 CHAPTER 7
SUMMARY, CONCLUSIONS, AND RECOMMENDED FUTURE
RESEARCH ..................................................................................... 169 7.1. Summary and Conclusions .............................................................................. 169 7.2. Recommended Future Research ..................................................................... 173 APPENDIX A LOADING FRAME DETAILS .......................................................... 175 APPENDIX B BEAM-COLUMN CONNECTION: EXPERIMENTAL PROGRAM . 178 APPENDIX C BEAM-COLUMN CONNECTION: DATA REDUCTION................. 191 APPENDIX D BEAM-COLUMN CONNECTION: VALIDATION ........................... 203 APPENDIX E BEAM-COLUMN CONNECTION: DATA ....................................... 209 APPENDIX F BEAM COLUMN CONNECTION: PHOTOGRAPHS ..................... 253 APPENDIX G ARTICULATED QUADRILATERAL CONCEPTION AND
DEVELOPMENT ............................................................................. 257 APPENDIX H SMA-BASED BRACING DESIGN .................................................. 261
REFERENCES…………………………………………………………………………….…. 264 vii
LIST OF TABLES
Table 2-1: Typical properties of NiTi compared with structural steel (table adapted from
Penar (2005)). ................................................................................................................. 13 Table 5-1: Summary of the component mechanical tests. ............................................. 67 Table 5-2: Comparison of the experimental results (Test D) versus the model with
residual accumulation in terms of the maximum concentrated rotation, maximum
moment, residual rotation, and equivalent viscous damping. ....................................... 115 Table 6-1: Tensile load cell calibration values with 10V excitation............................... 131 Table B-1: Instrumentation Schedule for the Beam-Column Tests. ............................. 186 viii
LIST OF FIGURES
Figure 1-1: Qualitative comparison between (a) a traditional system and (b) a SMA
system. .............................................................................................................................. 3 Figure 2-1: 2D representation of the microstructure of SMAs. ......................................... 9 Figure 2-2: 2D microstructure representation of the shape memory effect and
superelasticity. ................................................................................................................ 11 Figure 2-3: Stress-strain relationship for (a) superelastic SMA and (b) shape memory
SMA. ............................................................................................................................... 11 Figure 2-4: Stress-strain curve for superelastic NiTi wire under tension cycling (Tobushi
et al., 1998). .................................................................................................................... 14 Figure 2-5: SMA seismic retrofit in Italy. (Castellano et al., 2001; Indirli et al., 2001). ... 16 Figure 2-6: (a) elastoplastic and (b) recentering systems (Christopoulos et al., 2002a).
........................................................................................................................................ 19 Figure 2-7: (a) Post-tensioned connection with dissipating angles and (b) corresponding
moment-rotation relationship (Ricles et al., 2001) ........................................................... 21 Figure 2-8:
(a) Post-tensioned energy dissipating layout and (b) connection
(Christopoulos et al., 2002b) ........................................................................................... 22 Figure 2-9: SCED device (Christopoulos et al., 2008). .................................................. 22 Figure 2-10: Recentering device with superelastic SMAs (Dolce et al., 2000)............... 24 Figure 2-11: Details of self-centering friction damper with NiTi wires (Zhu and Zhang,
2008). .............................................................................................................................. 25 Figure 2-12: Force deformation of (a) friction only, (b) friction + SMA, (c) SMA only (Zhu
and Zhang, 2008). ........................................................................................................... 25 Figure 3-1: Definition of the SMA and EP force-displacement relationships. ................. 30 Figure 3-2: Force-displacement relationships of the four SMA (SMA1-4) and two EP
(EP1-2) systems. ............................................................................................................. 30 Figure 3-3: Displacement time history of SMA and EP systems for T=0.5 sec. and R=2.
........................................................................................................................................ 32 ix
Figure 3-4: Maxiumum average displacement of SMA divided by the maximum
displacement of EP over a range of periods subjected to LA1-20. Row (a) is SMA1/EP1,
(b) is SMA2/EP1, (c) is SMA3/EP2, and (d) is SMA4/ EP2. ............................................ 35 Figure 3-5: Maxiumum average acceleration of SMA divided by the maximum
acceleration of EP over a range of periods subjected to LA1-20. Row (a) is SMA1/EP1,
(b) is SMA2/EP1, (c) is SMA3/EP1, and (d) is SMA4/ EP2. ............................................ 36 Figure 3-6: Force-deformation of parallel system created for the case study. ............... 38 Figure 3-7: Force-deformation and displacement time histories for SMA4, PARA1, and
EP1 systems. .................................................................................................................. 38 Figure 4-1: Internal view of tension/compression device. .............................................. 42 Figure 4-2: Tension/compression device (a) test machine setup and (b) example loading
protocol. .......................................................................................................................... 45 Figure 4-3: Nitinol spring loaded on center shaft (Test A and B). .................................. 46 Figure 4-4: Force-deformation response of hollow Nitinol spring in device (Test A). ..... 46 Figure 4-5: Force-deformation response solid Nitinol spring in device (Test B)............. 47 Figure 4-6: Helical spring tests (a) equivalent viscous damping and (b) yield forces over
a range of deformations. ................................................................................................. 49 Figure 4-7: Test setup for individual washer test............................................................ 51 Figure 4-8: Response of individual NiTi Belleville washers under compression (Phase I).
........................................................................................................................................ 51 Figure 4-9: Washer configuration for Test C. ................................................................. 52 Figure 4-10: Force-deformation response of single-stacked washer configuration (Test
C). ................................................................................................................................... 53 Figure 4-11: Washer configuration for Test D. ............................................................... 54 Figure 4-12: Force-deformation response of double-stacked washer configuration (Test
D). ................................................................................................................................... 55 Figure 4-13: Washer configuration for Test E. ............................................................... 56 Figure 4-14: Force-deformation response of triple-stacked washer configuration (Test
E). .................................................................................................................................... 56 Figure 4-15: Comparison of equivalent viscous damping ratios for the stacked washer
tests (Phase I). ................................................................................................................ 58 Figure 4-16: Response of individual NiTi Belleville washers under compression (Phase
II). .................................................................................................................................... 60 x
Figure 4-17: Response of individual NiTi Belleville washers (Washer 4 and 5) under
cyclic compression. Plot (a) shows washer 1 cycled three times, (b) shows washer 2
cycled ten times, and (c) shows the first and tenth cycle of Washer 5. .......................... 60 Figure 4-18: Spherical washer used in Test F (McMaster-Carr). ................................... 62 Figure 4-19: Washer configuration for Test F................................................................. 62 Figure 4-20: Force-deformation response of single-stacked washer configuration (Test
F). .................................................................................................................................... 62 Figure 5-1: An overview of the SMA beam-column connection. .................................... 65 Figure 5-2: The (a) stress-strain relationship of the NiTi dogbone and (b) the
corresponding dogbone dimensions (mm). ..................................................................... 66 Figure 5-3: Loading frame schematic. ............................................................................ 68 Figure 5-4: The SAC loading protocol. ........................................................................... 69 Figure 5-5: Instrumentation of specimen connection. Units in mm(in.). ......................... 70 Figure 5-6: Instrumentation of loading frame and specimen. Units in cm. ..................... 70 Figure 5-7: Connection profile view. ............................................................................... 73 Figure 5-8: Connection details and dimensions. Units in mm (in). ................................. 73 Figure 5-9: Connection details with highlighted differences over the progression of
testing.............................................................................................................................. 74 Figure 5-10: Additional connection brackets for Test E. ................................................ 74 Figure 5-11: Tests ran on the connection with the shear tab bolts tightened to various
torque levels per a torque wrench. No tendons were installed. ..................................... 75 Figure 5-12: Tendon details with threads 19.05-0.63 (3/4-16) UNF for the SMA tendon
and 19.05-0.394 (3/4-10) UNC for the steel and aluminum tendons. Units in mm (in.). 77 Figure 5-13: Moment vs. concentrated rotation for the left beam in Test A. .................. 79 Figure 5-14: Residual strain (EXT) in tendons at end of each drift level for Test B. ...... 80 Figure 5-15: Moment vs. concentrated rotation for the left beam in Test B. .................. 83 Figure 5-16: Residual strain (EXT) in tendons at end of each drift level for Test B. ...... 84 Figure 5-17: Moment vs. concentrated rotation for the left beam in Test C. .................. 87 Figure 5-18: Residual strain (EXT) in tendons at end of each drift level for Test C. ...... 88 Figure 5-19: Moment vs. concentrated rotation for the left beam in Test D. .................. 91 xi
Figure 5-20: Residual strain (EXT) in tendons at end of each drift level for Test D. ...... 92 Figure 5-21: Moment vs. concentrated rotation for the left beam in Test E. .................. 95 Figure 5-22: Residual strain (EXT) in tendons at end of each drift level for Test E. ...... 96 Figure 5-23: The averaged connection moment vs. concentrated rotation for Test D. .. 98 Figure 5-24: Example moment-rotation response for Test D. ...................................... 100 Figure 5-25: Straight line approximation of the M-θ response to get My and Ke. .......... 102 Figure 5-26: My over a range of drift levels for Tests B, D, and E. ............................... 103 Figure 5-27: Effective stiffness, Ke, over a range of drift levels for Tests B-E. ............. 103 Figure 5-28: Definition of residual rotation, θres. ........................................................... 104 Figure 5-29: Residual Rotation, θr, over a range of drift levels for Tests B-E............... 105 Figure 5-30: Hysteretic energy dissipated for the first cycle of each drift step vs. drift
level for Test B-E. .......................................................................................................... 107 Figure 5-31: Cumlative hysteretic energy dissipated for the 1st cycle of each drift step
vs. drift level for Test B-E. ............................................................................................. 107 Figure 5-32: Equivalent viscous damping of the first cycle at each drift level for each
test. ............................................................................................................................... 108 Figure 5-33: Equivalent viscous damping of the second cycle at each drift level for each
test. ............................................................................................................................... 108 Figure 5-34:
Modeling details for the prediction analysis of the beam-column
connection. .................................................................................................................... 110 Figure 5-35: (a) Averaged experimental moment-rotation response for Test D vs. (b) the
predicted moment-rotation response using OpenSEES ............................................... 110 Figure 5-36: Experimental vs predicted reponse for Test D with some differences
highlighted. .................................................................................................................... 111 Figure 5-37: Simplified connection model. ................................................................... 113 Figure 5-38: Moment-rotation response of (a) experiment (averaged left and right beam
from Test D), (b) simplified model, (c) simplified model with residual accumulation, and
(d) zoomed view of the simplified model with residual accumulation. ........................... 114 Figure 6-1: (a) Pall friction AQ (Aiken et al., 1993) and (b-c) c-shape dissipator in AQ
(Renzi et al., 2007). ....................................................................................................... 123 Figure 6-2: General articulated quadrilateral (AQ) setup with c-shapes and SMA wire
bundles.......................................................................................................................... 124 xii
Figure 6-3: Dimension of AQ without c-shapes and SMA. Units in mm (in.). .............. 124 Figure 6-4: AQ brace system in loading frame. ............................................................ 125 Figure 6-5: Padeye dimensions for AQ tests. Units in mm (in.). ................................. 126 Figure 6-6: AQ setup for the SMA-only test, Test A. .................................................... 127 Figure 6-7: C-shape dimensions for Test B, t = 12.7 mm (0.5 in.). Units in mm (in.). . 127 Figure 6-8: AQ setup for the c-shape-only test, Test B. ............................................... 128 Figure 6-9: C-shape dimensions for Test C, t = 12.7 mm (0.5 in.). Units in mm [in.]. . 129 Figure 6-10: AQ setup for the c-shape-only test, Test C. ............................................. 129 Figure 6-11: Instrumentation scheme for AQ testing.................................................... 131 Figure 6-12: Instrumation details for (a) the AQ and (b) the cable assembly. ............... 131 Load Cell ....................................................................................................................... 131 Figure 6-13: Close-up view of instrumentation scheme for AQ testing. ....................... 132 Figure 6-14: Cyclic force-strain relationship of 129 mm2 (0.2 in2) SMA wire bundle. ... 134 Figure 6-15: Actuator displacement time history for Test A. ........................................ 136 Figure 6-16: Base shear vs. story drift for Test A. ........................................................ 136 Figure 6-17: Cable force vs. AQ deformation for Test A. ............................................. 137 Figure 6-18: Cable force vs. drift for Test A. ................................................................ 137 Figure 6-19: Actuator displacement time history for Test B. ........................................ 139 Figure 6-20: Base shear vs. story drift for Test B. ........................................................ 139 Figure 6-21: Cable force vs. AQ deformation for Test B. ............................................. 140 Figure 6-22: Cable force vs. drift for Test B. ................................................................ 140 Figure 6-23: C-shape interference at 1.5% drift. .......................................................... 141 Figure 6-24: Actuator displacement time history for Test C. ........................................ 142 Figure 6-25: Base shear vs. story drift for Test C......................................................... 142 Figure 6-26: Cable force vs. AQ deformation for Test C. ............................................. 143 Figure 6-27: Cable force vs. drift for Test C. ................................................................ 143 xiii
Figure 6-28 The resulting force-deformation characteristics of an SMA element
combined in series with an elastic element. .................................................................. 145 Figure 6-29: Contributions of the different brace elements in series for Test A. .......... 146 Figure 6-30: Contributions of the different brace elements in series for Test B. .......... 147 Figure 6-31: Contributions of the different brace elements in series for Test C. .......... 148 Figure 6-32: General response path of braced frame (a) Test A and (b) Test C. ........ 150 Figure 6-33: Discussion of c-shape disspator response for Test B. ............................. 151 Figure 6-34: Straight line approximations of the base shear vs. drift response to obtain
My and Ke. ..................................................................................................................... 152 Figure 6-35: Effective stiffness, Ke, over a range of drift levels for Tests A and C. ...... 153 Figure 6-36: Yield base shear, Vby, over a range of drift levels for Tests A and C. ...... 153 Figure 6-37: Residual drift, Δres, over a range of drift levels in Tests A and B. ............. 154 Figure 6-38: Equivalent viscous damping in the first and second cycle for Tests A and
C. ................................................................................................................................... 155 Figure 6-39: Brace models used in analysis. ............................................................... 157 Figure 6-40: Details of the seven-story braced frame analyzed (FEMA, 2006). .......... 159 Figure 6-41: Deformation response spectrum for LA25 and LA30 with the SCBF and
BRB period shift noted. ................................................................................................. 161 Figure 6-42: (a-d) Base Shear vs. first story drift and (e) first story drift time history for
SCBF,SMA, PARA, and BRB subjected to the LA30 ground motion. ........................... 162 Figure 6-43: (a-d) Base Shear vs. first story drift and (e) first story drift time history for
SCBF, SMA, PARA, , and BRB subjected to the LA25 ground motion. ........................ 163 Figure 6-44: Drift, interstory dift, and residual drift for the first story of the SCBF, SMA,
PARA, and BRB. Braces A-D (mean = black circles and line, data point = red circles).
...................................................................................................................................... 166 Figure A-1: Loading frame test bed. ............................................................................. 176 Figure A-2: Column pins with shim plates installed. ..................................................... 177 Figure B-1: The 810 MTS Universal Testing Machine. ................................................. 179 Figure B-2: Stress-strain relationship of the beam coupons. ....................................... 180 Figure B-3: Cyclic loading protocol for the mechanical testing..................................... 181 xiv
Figure B-4: Dogbone mechanical test specimen dimensions ( units in mm)................ 182 Figure B-5: Stress-strain of the steel threaded bar for Test A. ..................................... 182 Figure B-6: Stress-strain of A36 steel bar for Test B (data from Penar, 2005). .......... 183 Figure B-7: Stress-strain of the NiTi dogbone. ............................................................. 184 Figure B-8: Stress-strain for the annealed aluminum bar............................................. 185 Figure B-9: Instrumentation of specimen connection (units in cm). ............................. 188 Figure B-10: Instrumentation of frame and specimen (units in cm).............................. 189 Figure C-1: Sign convention for the M-θ plots. ............................................................. 191 Figure C-2: Strain gauge rosette orientation for principle strain calculations. .............. 194 Figure C-3: Schematic defining parameters in order to calculate the drift from beam and
column flexure. .............................................................................................................. 196 Figure C-4: Schematic defining parameters in order to calculate the drift per the left
beam instrumentation. ................................................................................................... 201 Figure C-5: Schematic defining parameters in order to calculate the drift per the right
beam instrumentation. ................................................................................................... 202 Figure D-1: Strain time history of top-mid SG on left beam for each test. .................... 205 Figure D-2: Principle strain time history at center of the panel zone for each test. ...... 206 Figure D-3: Description of the drift contributions. ........................................................ 207 Figure D-4: Drift time histories as calculated by the (1) sum of the drift contributions, (2)
the SP sensor, and (3) the difference these two values. ............................................... 208 Figure E-1: Actuator displacement time history for Test A. .......................................... 209 Figure E-2: Actuator force-displacement for Test A. .................................................... 210 Figure E-3: M-θ at the column face of the left beam for Test A. ................................... 210 Figure E-4: M-θ at the column face of the right beam for Test A. ................................ 211 Figure E-5: M-θ at outside L-shape for column per top strain gauges for Test A. ....... 211 Figure E-7: Displacements at the top of the column vs. at the actuator for Test A. ..... 212 Figure E-8: Gap openings (LVDT) vs. top of column displacement for Test A............. 213 Figure E-9: Average gap opening (LVDT) vs. top of column displacement for Test A. 213 xv
Figure E-10: Strain in the top-front tendon vs. Mbeam,avg for Test A. .............................. 214 Figure E-11: Strain of the top-back tendon vs. Mbeam,avg for Test A. ............................. 214 Figure E-12: Strain of the bottom-front tendon vs. Mbeam,avg for Test A. ....................... 215 Figure E-13: Strain in the bottom-back tendon vs. Mbeam,avg for Test A. ....................... 215 Figure E-14: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
A. ................................................................................................................................... 216 Figure E-15: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test A. ........................................................................................................... 217 Figure E-16: Actuator displacement time history for Test B. ........................................ 218 Figure E-17: Actuator force-displacement for Test B. .................................................. 219 Figure E-18: M-θ at the column face of the left beam for Test B. ................................. 219 Figure E-19: M-θ at the column face of the right beam for Test B. .............................. 220 Figure E-20: M-θ at outside of the HSS for column per top strain gauges for Test B. . 220 Figure E-21: M-θ at outside of the HSS for column per bottom strain gauges for Test B.
...................................................................................................................................... 221 Figure E-22: Displacements at the top of the column vs. at the actuator for Test B. ... 221 Figure E-23: Gap openings (LVDT) vs. top of column displacement for Test B........... 222 Figure E-24: Average gap opening (LVDT) vs. top of column displacement for Test B.
...................................................................................................................................... 222 Figure E-25: Strain in the top-front tendon vs. Mbeam,avg for Test B. .............................. 223 Figure E-26: Strain in the top-back tendon vs. Mbeam,avg for Test B. ............................. 223 Figure E-27: Strain in the bottom-front tendon vs. Mbeam,avg for Test B. ........................ 224 Figure E-28: Strain in the bottom-back tendon vs. Mbeam,avg for Test B. ....................... 224 Figure E-29: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
B. ................................................................................................................................... 225 Figure E-30: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test B. ........................................................................................................... 226 xvi
Figure E-31: Actuator displacement time history for Test C. ........................................ 227 Figure E-32: Actuator force-displacement for Test C. .................................................. 228 Figure E-33: M-θ at the column face of the left beam for Test C. ................................ 228 Figure E-34: M-θ at the column face of the right beam for Test C. .............................. 229 Figure E-35: M-θ at outside of the HSS for column per top strain gauges for Test C. . 229 Figure E-36: M-θ at outside of the HSS for column per bottom strain gauges for Test C.
...................................................................................................................................... 230 Figure E-37: Displacements at the top of the column vs. at the actuator for Test C. ... 230 Figure E-38: Gap openings (LVDT) vs. top of column displacement for Test C .......... 231 Figure E-39: Average gap opening (LVDT) vs. top of column displacement for Test C
...................................................................................................................................... 231 Figure E-40: Strain in the top-front tendon vs. Mbeam,avg for Test C .............................. 232 Figure E-41: Strain in the top-back tendon vs. Mbeam,avg for Test C .............................. 232 Figure E-42: Strain in the bottom-front tendon vs. Mbeam,avg for Test C ........................ 233 Figure E-43: Strain in the bottom-back tendon vs. Mbeam,avg for Test C ........................ 233 Figure E-44: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
C. ................................................................................................................................... 234 Figure E-45: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test C. ........................................................................................................... 235 Figure E-46: Actuator displacement time history for Test D. ........................................ 236 Figure E-47: Actuator force-displacement for Test D. .................................................. 237 Figure E-48: M-θ at the column face of the left beam for Test D. ................................ 237 Figure E-49: M-θ at the column face of the right beam for Test D. .............................. 238 Figure E-50: M-θ at outside of the HSS for column per top strain gauges for Test D. . 238 Figure E-51: M-θ at outside of the HSS for column per bottom strain gauges for Test D.
...................................................................................................................................... 239 Figure E-52: Displacements at the top of the column vs. at the actuator for Test D. ... 239 xvii
Figure E-53: Gap openings (LVDT) vs. top of column displacement for Test D. ......... 240 Figure E-54: Average gap opening (LVDT) vs. top of column displacement for Test D.
...................................................................................................................................... 240 Figure E-55: Strain in the top-front tendon vs. Mbeam,avg for Test D. ............................. 241 Figure E-56: Strain in the top-back tendon vs. Mbeam,avg for Test D. ............................. 241 Figure E-57: Strain (EXT) in the bottom-front tendon vs. Mbeam,avg for Test D. ............. 242 Figure E-58: Strain (EXT) in the bottom-back tendon vs. Mbeam,avg for Test D. ............. 242 Figure E-59: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
D. ................................................................................................................................... 243 Figure E-60: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test D. ........................................................................................................... 244 Figure E-61: Actuator displacement time history for Test E. ........................................ 245 Figure E-62: Actuator force-displacement for Test E. .................................................. 246 Figure E-63: M-θ at the column face of the left beam for Test E. ................................. 246 Figure E-64: M-θ at the column face of the right beam for Test E. .............................. 247 Figure E-65: M-θ at outside of the HSS for column per top strain gauges for Test E. . 247 Figure E-66: M-θ at outside of the HSS for column per bottom strain gauges for Test E.
...................................................................................................................................... 248 Figure E-67: Displacements at the top of the column vs. at the actuator for Test E. ... 248 Figure E-68: Gap openings (LVDT) vs. top of column displacement for Test E........... 249 Figure E-69: Average gap opening (LVDT) vs. top of column displacement for Test E.
...................................................................................................................................... 249 Figure E-74: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outter face of the column
flange for Test E. ........................................................................................................... 252 Figure F-1: Deformation of HSS transfer elements after the completion of Test A. ..... 253 Figure F-2: Experimental test setup with beam-column installed. ................................ 254 Figure F-3: Profile view of Test A. ................................................................................ 254 Figure F-4: Profile view of Test B. ................................................................................ 255 xviii
Figure F-5: Profile view of Test C. ................................................................................ 255 Figure F-6: Profile view of Test D. ................................................................................ 256 Figure F-7: Profile view of Test E. ................................................................................ 256 Figure G-1: (a) AQ with SMA bundles and c-shape dissipaters, (b) 3D view of SMA
attachment, and (c) c-shape dimension variation for constant thickness, stiffness, and
yield force. ..................................................................................................................... 260 Figure G-2: C-shape kinematic behavior assuming the center of c-shape is axially
inextensible and the arms are completely rigid. ............................................................ 260 Figure H-1: The resulting force-deformation characteristics of an SMA element
combined in series with an elastic element. .................................................................. 263 xix
LIST OF SYMBOLS AND ABBREVIATIONS
SYMBOLS
Af
Austenite finish temperature
As
Austenite start temperature
Cd
Deflection amplification factor
K
Stiffness
Ke
Effective Stiffness
M
Moment
Mf
Martensite finish temperature
Ms
Martensite start temperature
Mw
Moment magnitude
R
Strength reduction factor (i.e. Response modification coefficient)
Vby
Yield base shear
ζ
Equivalent viscous damping
θ
Rotation
Δ
Deformation (CHAPTER 4), Drift (CHAPTER 5 and 6)
Δres
Residual drift (CHAPTER 6)
Δmax
Test-target maximum deformation (CHAPTER 4)
Ωo
System overstrength factor
ABBREVIATIONS
AQ
Articulated quadrilateral
BRB
Buckling restrained brace
DAQ
Data acquisition system
xx
EP
Elastoplastic
EXT
Extensometer
LC
Load Cell
LVDT
Linear variable displacement transducer
MANSIDE
Memory Alloys for New Seismic Isolation and Energy Dissipation Devices
NEHRP
National Earthquake Hazards Reduction Program
NiTi
Nickel-titanium
PARA
Parallel
PR
Partially restrained
PT
Post-tensioned
SDOF
Single-degree-of-freedom
SE
Superelastic effect
SMA
Shape memory alloy
SME
Shape memory effect
SG
Strain gauge
SP
String Potentiometer
xxi
SUMMARY
In an effort to mitigate damage caused by earthquakes to the built environment, civil
engineers have been commissioned to research, design, and build increasingly robust
and resilient structural systems.
Innovative means to accomplish this task have
emerged, such as integrating Shape Memory Alloys (SMAs) into structural systems.
SMAs are a unique class of materials that have the ability to spontaneously recover
strain of up to 8%. With proper placement in a structural system, SMAs can act as
superelastic “structural fuses”, absorbing large deformations, dissipating energy, and
recentering the structure after a loading event. Though few applications have made it
into practice, the potential for widespread use has never been better due to
improvements in material behavior and reductions in cost.
In this research, a single degree-of-freedom study was first conducted in order to
investigate the benefits of recentering compared to energy dissipation. Through this
study the following fundamental observation was made:
enhanced performance, in
terms of maximum displacements, can be obtained from a recentering system by
maximizing the hysteretic loop, thus increasing the energy dissipation. This observation,
coupled with previous work that has shown that recentering systems are capable of
meeting or exceeding the performance level obtained from other advanced systems, has
further motivated the experimental work conducted herein.
For the experimental portion of this research, three different structural
applications were developed and tested.
The first was a tension/compression damper
that utilized either nickel titanium (NiTi) helical springs or Belleville washers. These new
forms of NiTi were previously untested; therefore the properties were largely unknown.
xxii
Nonetheless, the results indicated that unique applications may be possible with both
forms. For the second part of the experimental work, a SMA-based partially-restrained
interior beam-column connection utilizing NiTi tendons was investigated.
The
connection was designed to concentrate all of the inelastic deformation into the SMA
tendons and then recenter due to the superelasticity of these tendons. The connection
proved to have good recentering and ductility even after it was cycled to 5% drift.
Finally, for the last part of the experimental work, a special bracing system was
developed using an articulated quadrilateral (AQ) arrangement. The AQ arrangement
allowed SMA wire bundles to be put in parallel with c-shaped dampers, thus enabling the
designer to tailor the amount of damping in the flag-shaped hysteresis. The braced
frame experimental results demonstrated that a maximized hysteresis can indeed be
obtained while the analytical results demonstrated that one can obtain more evenly
distributed deformation demands for an SMA-based system than compared traditional
system.
This exploratory experimental work highlights the potential for SMA-based
structural applications to enhance seismic structural performance and community
resilience.
xxiii
CHAPTER 1
INTRODUCTION
1.1.
Problem Description
In 1994 the Northridge earthquake struck Southern California causing $40 billion in
direct damage
(Eguchi et al., 1998) and exposing previously unknown vulnerabilies of
welded moment connections in hundreds of buildings. In 1995 the Kobe earthquake
shook central Japan, collapsing elevated highways, destroying numerous buildings,
killing over 5000 people, and causing over $130 billion in direct damage (Scawthorn and
Yanev, 1995). More recently, on March 12, 2008, a Mw 7.9 earthquake struck Sichuan
Province in China killing tens-of-thousands of people, quickly becoming a grim reminder
of the consequences of what happens when vulnerable structures are subjected to
strong ground shaking.
In an effort to mitigate damage to the built environment caused by earthquakes,
civil engineers have been commissioned to research, design, and build increasingly
robust and resilient structural systems. Innovative means to accomplish this task have
emerged and can be broken down into three basic categories: base isolation, active (and
semiactive) control, and passive control. These three categories, combined with new
code requirements, promise to enhance modern structures’ earthquake performance.
Base Isolation has received considerable attention from the research community
over the years and has established itself as the most mature of the three mitigation
techniques. Numerous buildings across the world have been designed and/or retrofitted
with base isolators (e.g. Istanbul International Airport, San Francisco City Hall, and
Oakland City Hall). Base isolators effectively decouple the motion of the ground from
1
that of the structure and thus greatly reduce damage. However, even with widespread
use and excellent performance, base isolation is not always possible or appropriate due
to the high premium for such a system. Therefore, other techniques must be explored.
As an alternative to base isolation, active and passive control both deal with
inserting special elements within the building in order to modify the response. Active
and semi-active control techniques modify response through a combination of energy
dissipation and externally-powered force-delivery devices that respond to real-time
stimuli. In contrast, passive control techniques modify the response through passively
dissipating energy in predetermined elements which, if designed correctly, can eliminate
unwanted inelastic behavior in the remainder of the structure and help distribute the
deformation demand more evenly over the height of the structure. A variety of structures
have been built or retrofitted with passive control techniques, such as the San Francisco
State Office Building, Coronado Bay Bridge, and the West Los Angeles Federal Building.
Passive control has become a mainstay in the structural engineering toolbox.
In the category of passive control, recentering systems have recently emerged as
a viable way to enhance a structure’s response.
Rather than focusing on energy
dissipation, as in typical passive control systems, recentering systems sacrifice damping
for the ability to reduce residual deformations after a seismic event.
A comparison
between an elastoplastic (traditional) system and a recentering (shape memory alloy or
SMA) system is shown in Figure 1-1. Recentering can be achieved by using posttensioned devices/connections (Ricles et al., 2001; Tremblay et al., 2008) or by using
superelastic shape memory alloys (Leon et al., 2001; Dolce et al., 2001; McCormick et
al., 2007; Sepulveda et al., 2008). Several studies have shown improved structural
performance, in terms of maximum and residual drifts, when comparing recentering
systems to traditional passive energy dissipation systems (Ricles et al., 2001;
Christopoulos and Filiatrault, 2002; Christopoulos et al. 2008; Zhu and Zhang, 2008).
2
Recently, Eatherton et al. (2009) have begun working on vertically post-tensioned
rocking frame systems that incorporate both recentering and energy dissipation
elements.
With the increasing body of experimental and analytical work being
conducted on recentering systems, the balance between recentering and energy
dissipation still needs further investigation.
Additionally, more practical methods of
employing recentering need to be explored.
Figure 1-1: Qualitative comparison between (a) a traditional system and (b) a SMA
system.
In this research, superelastic nickel-titanium (NiTi) shape memory alloys (SMAs)
are investigated as means to accomplish recentering. NiTi SMAs have the distinct ability
to spontaneously recover up to 8% strain upon the removal of stress, yet have found
limited applications in the civil engineering industry since their discovery over four
decades ago. The potential to both provide recentering and supplemental damping is
the hallmark of SMAs behavior. It is hypothesized that optimized structural performance
can be obtained by appropriately balancing recentering and damping, thus limiting
maximum displacements while also reducing residual displacements. To investigate this
fundamental idea, a single-degree-of-freedom analytical study is first investigated. Next,
3
three different SMA-based systems are developed and tested under cyclic loads. With
such great potential, the goal of this research is to assess the ability of these new
systems to enhance structural performance in order to mitigate earthquake losses.
1.2.
Scope of Project
To accomplish the objective of this research, the following tasks were undertaken:
ƒ
TASK 1: Conduct a preliminary study of a single degree-of-freedom oscillator
comparing recentering systems to traditional damped systems.
This study
examined the response over a range of periods and excitations in order to
understand how to best enhance structural performance.
ƒ
TASK 2: Conduct an exploratory investigation on a novel l tension/compression
device. This device subjects new forms of SMAs to compression loading and
has potential to be implemented into a bracing system to provide unique forcedeformation properties.
ƒ
TASK 3: Develop and test a recentering beam-column connection using modified
and improved detailing from that used by Penar (2005). Modifications included
special provisions for preventing local buckling, bolted components to enable
interchanging and variation, improved tendon superelasticity, and implementation
of SMAs with aluminum in parallel configurations. The ability of a simple finite
element model to capture the behavior of the beam-column connection was also
assessed.
ƒ
TASK 4: Develop and test a new type of recentering bracing system based on
an articulated quadrilateral (AQ) configuration. This AQ configuration enables
SMA wire bundles to be combined in parallel with energy dissipating elements,
4
thus allowing the engineer to adjust the amount of damping and recentering of
the system. The experimental results were used to conduct a case-study on the
effectiveness of a SMA braced frame in comparison to traditional and buckling
restrained braced frames.
ƒ
TASK 5: Synthesis and recommendations in order to obtain practice-ready
applications of SMA-based systems.
1.3.
Thesis Outline
The content of this thesis is organized into the following chapters:
ƒ
CHAPTER 2: Shape memory alloys are first introduced and their fundamental
behavior is reviewed.
Next,
background on recentering systems is given,
including experimental work done on post-tensioned and SMA recentering
systems. This review is given to set the context for the rest of the research.
ƒ
CHAPTER 3: A single degree-of-freedom oscillator is investigated to explore the
differences in performance of an elastoplastic system (damping) and a flagshaped hysteretic system (recentering).
Additionally, the balance between
recentering and damping is investigated by combining an elastoplastic system in
parallel with a recentering system.
ƒ
CHAPTER 4: Cyclic tests are performed on a tension/compression device that
utilizes two new forms of SMAs: helical springs and Belleville washers.
Additionally, an investigation into the individual performance of a Belleville
washer is presented and potential applications are noted.
ƒ
CHAPTER 5: Cyclic tests are performed on a half-scale interior beam-column
connection that implements SMA tendons. The test results are analyzed in terms
5
of strength, stiffness, residual drift, and damping. The experimental results are
then compared with a simple model implemented into OpenSEES.
ƒ
CHAPTER 6: An articulated quadrilateral bracing system that utilizes SMA wire
bundles in parallel with c-shape dissipators is conceived, developed, tested, and
assessed. An analytical study is then conducted to assess the response of a
seven-story braced frame that implements SMA-bracing elements.
ƒ
CHAPTER 7: Overall conclusions are presented with respect to each SMAbased system explored in this work. Recommendations for needed areas of
future work and the need for practice-ready applications is discussed.
6
CHAPTER 2
LITERATURE REVIEW
2.1.
Introduction
This chapter presents a summary of the literature relevant to the overall scope of this
research.
First, a review of shape memory alloys is conducted to provide a better
understanding of its behavior.
Next, background research on recentering systems
(created by post-tensioning or using shape memory alloys) is summarized to support the
motivation for this work.
Additional background information is given, as necessary, in
each subsequent chapter.
2.2.
2.2.1.
Shape Memory Alloys
SMA overview
Shape memory alloys are a class of metallic alloys with several distinct and
advantageous properties. The property that has drawn the most interest is the material’s
ability to return to its original shape after stress is removed (pseudo- or superelastic
effect or SE) or after heat has been applied (shape memory effect or SME). The first
recorded observation of the SME was the AuCd alloy in 1932 by Chang and Reid
(Otsuka and Wayman, 1998).
In 1962, an equal-atomic composition of nickel and
titanium was observed to exhibit shape memory characteristics at the U.S. Naval
Ordinance Lab, resulting in the name NiTiNOL (Jackson et al., 1972).
Several
characteristics have made the NiTi alloy the preferred SMA for application in the
medical, aerospace, and civil engineering fields. These characteristics include its high
7
corrosion and fatigue resistance, biocompatibility, stable hysteretic behavior, and large
recentering capability (recovers strain of up 8%). Because of these characteristics, NiTi
was the alloy used throughout this research.
Even with good promise, applications of SMAs in structural engineering have
been limited. This is in part due to the lack of knowledge transfer between the material
scientist community developing the SMAs and the civil engineering community trying to
implement them (Tyber et al., 2007). It also can be credited to the lack of knowledge of
the large-scale performance of the SMAs (McCormick et al., 2007b) and the difficulty in
implementing large size SMA elements due to poor machining characteristics (Weinert
and Petzoldt, 2004). Despite these challenges, in the last decade knowledge of SMAs’
mechanical and material properties has grown dramatically and its potential for
applications has never been better.
With the call for more resilient, robust, and
sustainable structural systems, the use of SMAs in recentering systems needs further
investigation to enable implementation of real world applications.
2.2.2.
SMA Microstructure
The SMA microstructure is made up of two basic ordered atomic phases which
enable it to possess its unique shape memory properties.
These two phases are
austenite and martensite and their 2D representation is illustrated in Figure 2-1.
Austenite is stable at high temperatures and low stresses, is highly symmetric, and has a
B2 body-centered atomic structure. Martensite is stable at low temperatures and high
stresses, possesses a B19’ rhombic geometry, and exists with either twin variants
(Figure 2-1b) or a single favored variant (Figure 2-1c) (Wayman and Duerig, 1990).
Martensite is softer and has lower strength than its austenite counterpart.
occurrence of the two variant orientations will be explained in the next two sections.
8
The
Further detailed information about the microstructure and crystallography of
SMAs is readily available in the literature (Duerig et al., 1990; Gall et al., 1999c; Gall et
al., 1999d; Hane and Shield, 1999; Otsuka and Shimizu, 1986; Otsuka and Wayman,
1998; Perkins, 1981; Tadaki et al., 1988). Of particular note, Frick et al. (2005) and
Tyber et al. (2007) provide a detailed review of the basic material microstructural
characterization of NiTi SMAs, the effect of the presence of precipitates in relation to
mechanical properties, and an explanation of the role of subphases (R-phase) during the
martensitic transformation.
Figure 2-1: 2D representation of the microstructure of SMAs.
2.2.3.
Shape Memory Alloy: Fundamental Behaviors
As stated previously, shape memory alloys have two fundamental behaviors: shape
memory and superelasticity.
These behaviors are dependent on the following
characteristic temperatures of the SMA: Ms (temperature at which martensite begins
forming), Mf (temperature at which martensite ends forming), As (temperature at which
austenite begins forming), and Af (temperature at which austenite ends forming).
2.2.3.1. Shape Memory Effect
The shape memory effect (SME) occurs when the SMA starts in the martensitic phase.
The SME behavior is illustrated in a portion of Figure 2-2.
Additionally, the typical
mechanical behavior is shown in Figure 2-3. The SME begins with martensitic SMA in a
twinned orientation.
When stress is applied to the material, the twinned structure
9
reorients into a detwinned single variant in order to accommodate the resulting strains
(in traditional metals the strain is accommodated by slip). Upon the removal of the
stress, the detwinned structure remains deformed as shown in the bottom right of Figure
2-3. To recover its shape, the metal is heated above its Af and then cooled back below
the Mf. This sequence of heating and cooling causes the martensite crystal structure to
revert back into the low symmetry twinned orientation; therefore the shape is fully
recovered and the SME is complete.
2.2.3.2. Superelastic Effect
Shape memory alloys exhibit superelastic behavior above the austenite finish
temperature, Af (i.e. austenitic SMA). The top of Figure 2-2 and left side of Figure 2-3
give the qualitative microstructural changes and mechanical behavior. When the SMA is
loaded to a certain stress level, the austinite accommodates the strain by transforming
into detwinned martensite, creating a loading plateau.
After the loading plateau is
crossed, the austenite has been fully transformed into stress-induced detwinned
martensite.
If the load continues to increase, the SMA will eventually sustain permanent
deformations because of the formation of slip planes (as in typical metals). However, if
the load is released, the stress will decrease until an unloading plateau is reached,
where the detwinned martensite will revert back into austinite and thus full shape
recovery will be obtained. The resulting hysteresis gives superelastic SMAs inherent
energy dissipation.
10
Figure 2-2: 2D microstructure representation of the shape memory effect and
superelasticity.
Figure 2-3: Stress-strain relationship for (a) superelastic SMA and (b) shape memory
SMA.
2.2.4.
NiTi Shape Memory Alloy
NiTi has been established as the alloy of choice for applications in civil engineering
because of its fatigue and corrosion resistance, stable hysteresis, and large strain
11
recoverability. For these reasons, NiTi was the SMA chosen for this research. The
following subsections give a review of the state-of-the-knowledge of NiTi.
2.2.4.1. General Properties of NiTi
The mechanical behavior of NiTi has been the subject of numerous studies in the past
several decades. Bars, wires, and plates have been tested in multiple shapes and forms.
Wires and bars are both of importance to this research because the envisioned
applications implement these forms.
To better understand the range of behaviors
observed in NiTi, a list of NiTi and steel properties are compared in Table 2-1.
Several studies have found that SMA bars have inferior superelastic properties
when compared to wires (Dolce and Marnetto, 1999; MANSIDE, 1998).
However,
recent work has investigated this difference and demonstrated good superelastic
(recentering) properties can be obtained from both bars and wires with appropriate
chemical composition, heat treatment, and deformation processing (Tyber (McCormick
et al., 2007b; Tyber et al., 2007).
Nevertheless, there are still some differences in the properties between bars and
wires, some of which come from the additional cold working that wires undergo. One
significant difference that has been shown is the equivalent viscous damping (2-4% for
bars, 4-8% for wires) (DesRoches et al., 2004). Though the level of equivalent viscous
damping in superelastic NiTi does not justify using it for pure damping purposes, it is
desirable to maximize performance by balancing the damping and recentering
properties.
In this research, the difference between the equivalent viscous damping in
bars and wires is marginalized by combining other elements in parallel with the SMA
elements, thus increasing the overall system damping.
12
Table 2-1: Typical properties of NiTi compared with structural steel (table adapted from
Penar (2005)).
NiTi
Austenite
Structural Steel
Martensite
Physical Properties
Melting Point
Density
Thermal conductivity
Thermal Expansion
1240-1310°C
3
6.45 g/cm
0.28 W/cm °C
0.14 W/cm °C
-6
-6
11.3 x 10 /°C
6.6 x 10 /°C
1500°C
3
7.85 g/cm
0.65 W/cm °C
-6
11.7 x 10 /°C
Mechanical Properties
Recoverable Elongation
Young’s Modulus
Yield Strength
Ultimate tensile strength
Elongation at Failure
Poisson’s Ratio
Hot Workability
Cold Workability
Machinability
Hardness
Weldability
up to 8%
21-41 GPa
70-140 MPa
895-1900 MPa
5-50% (typically ~25%)
0.33
Quite good
Difficult due to rapid work hardening
Difficult, abrasive techniques preferred
30-60 Rc
Quite good
0.2%
200 GPa
248-517 MPa
448-827 MPa
~20%
0.27-0.30
Good
Good
Good
Varies
Very good
Excellent
Fair
30-83 GPa
195-690 MPa
Chemical Properties
Corrosion performance
2.2.4.2. Cyclic Loading and Fatigue
Since earthquakes induce cyclic loads on a structure, it is clear that there needs to be a
firm understanding of NiTi’s cyclic behavior. Numerous cyclic tests on superelastic NiTi
have been carried out to study the effects of repeated loading and fatigue.
These
studies have shown cyclic loading causes increased residual strain, decreased loading
plateaus, and decreased hysteretic loops (DesRoches et al., 2004; Dolce and Cardone,
2001; Gong et al., 2002; Kawaguchi et al., 1991; Miyazaki et al., 1986; Strnadel et al.,
1995a; Strnadel et al., 1995b). To mitigate these trends, several researches have looked
at the possibility of training NiTi elements to achieve stabilization. Training generally
results in a stabilized hysteresis and enhanced recentering (decreased residuals)
(MANSIDE, 1998; McCormick and DesRoches, 2006; Miyazaki et al., 1986; Strnadel et
al., 1995a; Wang et al., 2003). An example of this stabilization is shown in Figure 2-4
from a study by Tobushi et al. (1998).
13
Figure 2-4: Stress-strain curve for superelastic NiTi wire under tension cycling (Tobushi
et al., 1998).
2.2.4.3. Thermal Processing
The effects of thermal processing (annealing) also influence the mechanical behavior of
NiTi. Annealing causes precipitation of Ni3Ti4 within the microstructure which aids in
suppressing slip. Suppression of slip results in a suppression of unwanted permanent
deformations (Tyber et al., 2007). Additionally, annealing causes a good distributing of
dislocations that are introduced if the material is cold worked.
The optimum aging temperature is around 400 °C (Miyazaki, 1990). A protocol
for thermal processing of superelastic NiTi is outlined by McCormick et al. (2007b). This
protocol was used in the processing of the superelastic NiTi bars for the beam-column
connection tested as part of this research.
The wires bundles, helical springs, and
Belleville washers used in the other parts of this research were processed and heat
treated using proprietary knowledge by Nitinol Technology, Inc.
2.2.4.4. Loading Rate
The mechanical behavior of NiTi is influenced by the rate of loading seen in typical civil
engineering applications. In general, the dominant frequency range of an earthquake is
14
0.2 Hz to 4.0 Hz. For NiTi, when the loading frequency (and thus the strain rate) is
increased, the loading plateau increases and the amount of hysteretic damping
decreases (DesRoches et al., 2004; Dolce and Cardone, 2001; Tobushi et al., 1998).
Wu et al. (1996) noted that the true nature of strain rate effects is due to the inability to
dissipate heat rather than any internal time dependant phenomena. They conducted
cyclic strain rate tests in a liquid environment and found that the increase in loading
plateau stress and decrease in unloading plateau stress is a function of self-heating and
self-cooling of the specimen rather than strain rate. Thus, larger diameter bars will
generally have increased strain rate dependence, though the effect of this on a structural
system needs further study. The tests conducted in this research were quasi-static, thus
the effects of loading rate were not considered.
2.2.4.5. Deformation Processing
Most NiTi is cold-worked to produce the desired shape.
In metals, cold working
generally produces higher strength and fatigue resistance due to increased dislocation
densities (Callister, 2000). Since dislocations, on average, are repulsive, and increased
dislocation density helps stop plastic flow and results in a stronger and, in the case of
NiTi, a more superelastic material. However, hot-rolled NiTi has also recently been
shown to have good superelasticity. This is due to the presence of Ti3Ni4 precipitates
which hinder plastic flow (Frick et al., 2005; McCormick et al., 2007b; Tyber et al., 2007).
Since hot-rolled NiTi costs only a fraction of its cold-worked counterpart, hot-rolled NiTi
is an attractive option for bars.
2.2.5.
Applications of SMAs
2.2.5.1. Non-Structural Applications
Shape memory alloys have been used in a wide range of non-structural applications.
The majority of these applications are in the medical, commercial, and aerospace fields.
15
Applications in the medical field include arterial stents, catheters, orthodontic braces,
and orthopedic prostheses (Duerig et al., 1990). Commercial applications have taken
advantage of the superelastic properties of SMAs and include eyeglass frames, cellular
telephone antennas, golf clubs, and brasserie underwires (Asai and Suzuki, 2000; Hsu
et al., 2000).
Additionally, the aerospace industry has looked at SMAs in adaptive
aircraft wings and smart helicopter blades in order to reduce noise and vibrations
(Beauchamp et al., 1992; Chandra, 2001).
2.2.5.2. Structural Applications
The unique mechanical behavior of SMAs has continued to drive an interest in
investigating potential applications in structural systems (discussed further in Section
2.3.3). Though applications are not widespread, several historic structures in Italy have
been seismically retrofitted with SMA devices.
These buildings include the St. Giorgio
Church bell tower in Rio, St. Feliciano Cathedral in Foligno, and St. Frances Basilica in
Assisi (Castellano et al., 2001; Indirli et al., 2001).
a) St. Giorgio
(b) St. Feliciano
(d) St. Frances
Figure 2-5: SMA seismic retrofit in Italy. (Castellano et al., 2001; Indirli et al., 2001).
16
2.3.
Recentering Systems
Recentering systems are a form of passive control that enables a structure to eliminate
(full recentering) or greatly reduce (partial recentering) residual deformations after a
loading event. Recentering is accomplished through the application of a recentering
force originating from a mechanism (post-tensioning) or a material property (SMA).
Recentering can result in enhanced structural performance, as has been shown in
recent studies (Christopoulos et al., 2002a; Wang and Filiatrault, 2008). In contrast to
recentering, traditional passive control schemes focus on energy dissipation as the
means of improving structural response. The following section gives a brief summary of
the current state-of-knowledge of recentering systems (as they apply to structural
engineering).
2.3.1.
Single Degree-of-Freedom (SDOF) Studies
The study of a simple single degree-of-freedom (SDOF) oscillator can be a useful tool in
gaining a better understanding of the governing characteristics of a recentering system.
Several researchers have taken this approach and investigated the response of a SDOF
system with recentering behavior. Christopoulos et al. (2002a) looked at the response of
a system with self centering flag-shaped hysteretic behavior modeled after a posttensioned (PT) energy dissipating connection. The recentering response was compared
to traditional elastoplastic (EP) systems as shown in Figure 2-6. The SDOF oscillator
was subjected to a suite of ground motions from California with a probability of
exceedance of 10% in 50 years. The study showed the following:
ƒ
For every EP system there is at least one flag-shaped recentering system with
similar period and strength that resulted in smaller or equal maximum
displacements.
17
ƒ
Maximum accelerations were similar for small flag-shaped loading plateau
slopes.
ƒ
Dissipated energy is generally much larger for the EP system.
ƒ
Increasing the slope of the flag-shaped loading plateau for short period and low
strength systems was most effective at decreasing the displacement demand.
ƒ
Conversely, for long period systems with high strength, increasing the hysteretic
area is more effective then increasing the slope of the loading plateau
This study provides a broad overview of how a SDOF system is affected by a PT-based
recentering behavior.
One of the main highlights of such a system is the ability to
eliminate residual deformations.
Following up on this research, Wang and Filiatrault (2008) undertook an even
more rigorous investigation into the behavior of a SDOF recentering system. Their work,
published in an extensive MCEER technical report, investigated a SDOF recentering
system over a variety of parameters and over an expanded set of ground motions.
Numerous charts were produced with the purpose of providing a direct design aid for
recentering systems. The findings affirmed and expanded on the study by Christopoulos
et al. (2002a), including the observation that a recentering system can be used to reduce
maximum and residual displacements. Furthermore, the design charts provide a tool for
developing a methodology for the design of a recentering system (discussed further in
the next section).
In contrast to PT-based systems, other studies have investigated the response of
SMA-based SDOF recentering systems. Duval et al. (2000) used random vibrations to
analyze the response of a helical SMA spring. Masuda et al. (2002) investigated the
effect that the shape of the hysteretic loop has on the dynamic performance.
Additionally, Seelecke (2000) investigated the response of a rigid mass suspended by a
tube and subjected to torsional loadings. None of these studies, which used SMA as the
18
backbone of the recentering model, evaluated the performance of the SDOF oscillator
subjected to earthquake ground motions. Additionally, they did not present the trends
over a range of periods and other structural properties, which would be useful in
assessing the applicability of SMA-based devices in earthquake applications. For this
reason, a brief SDOF study was conducted in the next chapter of this research to see if
additional insight can be gleaned.
Figure 2-6: (a) elastoplastic and (b) recentering systems (Christopoulos et al., 2002a).
2.3.2.
Posttensioned Systems
Several researches have experimentally and analytically investigated PT recentering
framing systems. Choek and Lew (1990; 1991) and Cheok et al. (1993) experimentally
investigated one-third-scale post-tensioned (PT) precast concrete connections. They
found that the PT assemblies, in comparison to cast-in-place monolithic assemblages,
increased ductility, decreased damage, and decreased residual drift.
Priestley and
MacRae (1996) tested PT concrete connections and a 60% scale five-story building as
part of the Precast Seismic Structural Systems (PRESSS) initiative.
Excellent
performance was again reported for the system.
Ricles et al. (2001) expanded the idea of PT connections by investigating their
use in steel moment-resisting frames. The connection investigated is shown in Figure
19
2-6a. The qualitative flag-shaped recentering moment-rotation relationship is shown in
Figure 2-6b.
This flag-shaped recentering behavior is produced from the synergy
between the post-tensioning and the dissipating angles.
In parallel with Ricles’ work, Christopoulos et al. (2002b) also extended the posttensioning concept with several studies. A typical layout of the recentering connection
scheme and the details of the PT connection are shown in Figure 2-7a-b, respectively.
Energy dissipating bars are used in lieu of angles to create improved damping behavior.
The connection was investigated analytically and experimentally. The results showed
that the connection had a large amount of ductility, good damping, and excellent
recentering.
As a continuation of the SDOF study mentioned in the previous section, Wang
and Filiatrault (2008) reported on the shaketable testing of a three-story PT steel frame.
A detailed design procedure was outlined for the design of the multi-degree-of-freedom
(MDOF) recentering system approximated as a SDOF system.
The design procedure
used a set of SDOF charts that plot a performance index versus structural period over
varying levels of strength factors (yield strength/weight of structure), post-yield
stiffnesses, and hysteretic energy dissipation levels. The analytical and experimental
results demonstrated that improved performance can be reached with a recentering
system.
Yet another system using PT elements has been recently proposed and
experimentally evaluated by Christopoulos et al. (2008).
Instead of creating a
recentering beam-column connection, a self-centering energy dissipating (SCED)
bracing system was conceived.
This special brace has post-tensioned elements
combined with friction energy dissipators in order to produce flag-shaped recentering
behavior. The device consists of a HSS tube sliding inside of another HSS tube with a
20
series of aramid tensioning elements providing a PT force and friction pads creating
energy dissipation. Schematics of the SCED system are shown in Figure 2-9.
Tremblay et al. (2008) performed an analytical study of a 2-, 4-, 8-, 12-, and 16story braced steel frames to further investigate the potential of the SCED device. The
SCED braces were compared to buckling restrained braces (BRB) over three suites of
ground motions. The SCED system performed very well in comparison to the BRB
system; reducing peak story drifts and eliminating residual deformations. However, the
analysis did indicate higher maximum accelerations for the SCED system, which was in
agreement with the findings of the recentering SDOF studies (Wang and Filiatrault,
2008).
Figure 2-7: (a) Post-tensioned connection with dissipating angles and (b) corresponding
moment-rotation relationship (Ricles et al., 2001)
21
Figure 2-8:
(a) Post-tensioned energy dissipating layout and (b) connection
(Christopoulos et al., 2002b)
Figure 2-9: SCED device (Christopoulos et al., 2008).
2.3.3.
SMA-Based Systems
SMAs have drawn considerable attention in the civil engineering community over the
past two decades because of their unique stress-strain behavior. In the 1990’s the
European Commission launched a research initiative, known as the MANSIDE (Memory
Alloy for New Structural Isolation Devises) project to investigate and implement SMAs
22
into civil engineering structures (MANSIDE, 1998). From this project, several retrofit
schemes were investigated and/or developed using SMA wires and bars (Dolce and
Cardone, 2006; Dolce et al., 2000; 2001; 2004; 2005; Dolce and Marnetto, 1999). The
functioning scheme of one such recentering device is shown in Figure 2-10. The device
showed good energy dissipation and excellent recentering. The self-centering friction
damped brace (SFDB) developed by Zhu and Zhang (2008) is another SMA-base
recentering device. This device is very similar in response to the SCED described in the
last section, with the recentering driven by NiTi wires rather aramid fibers (schematic
shown in Figure 2-11. The energy dissipation is derived from the sliding friction between
the adjacent steel members. A typical force-deformation response for the device is
shown in Figure 2-12. Three- and six-story braced frames were used to compare the
SFDB vs. BRB vs. SFDB-frictionless.
The results show that the SFDB effectively
eliminates residual deformations and, on average, reduces maximum inter-story drifts
when compared to the BRB.
SMA beam-column connections have also been investigated in the literature.
Ocel et al. (2004) investigated the use of SMAs in an exterior connection. They used
martensitic (SME) NiTi tendons as the primary moment-resisting elements. In order to
recover shape spontaneously, Penar (2005) investigated the use of superelastic NiTi
tendons in an interior connection. However, due to unwanted local buckling and poor
superelasticity in the NiTi tendons, the connection displayed very little recentering ability.
Analytical work has also been done on SMA beam-column connections. Taftali
(2007) presented an extensive study on the probabilistic seismic demand of SMA
connections in steel frames. Superelastic SMA connections were shown to be most
beneficial in reducing or eliminating residual deformations. This study demonstrated that
neither recentering nor energy dissipation produces the optimal response over a range
of hazard levels. Rather, Taftali concluded that it may be beneficial to incorporate both
23
recentering and energy dissipation elements into the same system to optimize the
performance while understanding that increased recentering results in reduced system
residual deformations.
Recently, Sepulveda et al. (2008) tested a beam-column connection with
superelastic CuAlBe SMAs. CuAlBe is a much more cost-effective form of SMA, but has
been shown to have inferior (only superelastic until 2.3% strain) behavior when
compared to NiTi.
Their initial evaluation showed that the SMA connection did not
improve the response due to poor performance of the CuAlBe material.
Various other SMA-based systems have been investigated analytically and
experimentally. This includes investigations of NiTi bracing systems or devices (Aiken et
al., 1993; Cardone and Dolce, 2009; Clark et al., 1995; Dolce et al., 2005; Higashino et
al., 1996; Lafortune et al., 2007; McCormick et al., 2007a; Yan et al., 2007; Zhang and
Zhu, 2008), investigations of NiTi bridge restrainers (Adachi and Unjoh, 1999; Andrawes
and DesRoches, 2005; DesRoches and Delemont, 2002), and investigations of NiTi
base isolators for both bridges (Wilde, 2000) and buildings (Dolce et al., 2001; Graesser
and Cozzarelli, 1991). Additionally, strategies for seismic retrofit are outlined in work
done by Di Sarno and Elnashai (2003).
Figure 2-10: Recentering device with superelastic SMAs (Dolce et al., 2000).
24
Figure 2-11: Details of self-centering friction damper with NiTi wires (Zhu and Zhang,
2008).
Figure 2-12: Force deformation of (a) friction only, (b) friction + SMA, (c) SMA only (Zhu
and Zhang, 2008).
25
CHAPTER 3
SINGLE DEGREE OF FREEDOM STUDY
3.1.
Introduction
This chapter investigates the influence of the superelastic hysteresis on the response of
a single degree-of- freedom (SDOF) oscillator. In general, buildings have at least 80%
of their modal participation coming from the first mode. Therefore, it is reasonable to
approximate a structure as a SDOF oscillator in order to investigate overall response.
Several SDOF studies investigating the effects of recentering systems have been
conducted by other researchers (as mentioned in Chapter 2). This study approaches
the topic from a slightly different angle by doing the following:
ƒ
Modeling the flag-shaped hysteresis after NiTi mechanical behavior
ƒ
Conducting the analysis over a range of strength reduction factors
ƒ
Comparing elements with the same initial stiffness and yield strength
ƒ
Varying the flag-shaped hysteresis based on optimum parallel system behavior
The parameters of this SDOF study were selected to help determine the important
factors that govern a SMA-based recentering system’s response, which in-turn
motivated the experimental portion of this research.
3.2.
Approach
With SMA’s ability to recover large strains, the effects of this unique stress-strain
behavior on displacement and acceleration demands were investigated under code-level
earthquakes. This was done in the following ways:
26
ƒ
First, the differences in the response (displacement and acceleration) of a normal
elastoplastic (EP) and a generic recentering (SMA) system were investigated.
Both of these systems were given zero post-yield (or transformation for the SMA)
stiffness.
ƒ
Second, the level of hysteretic damping in the recentering system was increased
to determine if improved behavior could be obtained. Previous research has
noted that SMAs have varying hysteretic damping properties depending on
thermomechanical processing and physical dimensions (DesRoches et al.,
2004). An SMA system was given nearly optimum energy dissipation and then
the performance was compared to the other systems.
ƒ
Third, the effect of the loading plateau stiffness was investigated by comparing
two new SMA and EP systems with equivalent loading plateau stiffnesses. Since
the mechanical behavior of large-scale SMA specimens generally show
moderate loading plateau stiffnesses, this is a more realistic approximation.
ƒ
Fourth, the effect of including the stress-induced martensite’s stiffness was
investigated. Since SMAs begin to stiffen at 6-8% strain, a true SMA-based
system would have this inherent stiffening effect. Once the plateau is crossed, it
is expected that improved behavior will be observed.
ƒ
Finally, a case study was investigated in order to study the effects of using a
parallel system consisting of an SMA and an EP element. The parallel system
was created as a practical way to increase the energy dissipation of the
superelastic hysteretic loop while still maintaining a high level of recentering.
Though it depends on the exact system composition, in this example, adding an
EP element in parallel with an SMA element increased the energy dissipation by
approximately 300% (compared to the equivalent SMA-only system).
27
3.3.
Analytical Setup
The SDOF system was idealized as a mass, m, attached to a spring with stiffness, k,
and a dashpot with damping coefficient, c. In all of the analysis, c was held constant by
defining ζ, the damping ratio, to be 5%. This value is commonly assumed in analytical
studies and should not be construed as a property of these recentering systems. The
damping coefficient is defined as:
c = 2mωnζ
(3.1)
The general force-displacement relationships for the SMA and EP systems are shown in
the top of Figure 3-1. The parameters that define the SMA system are γ1-4 (normalized
force levels of SMA hysteresis), β (loading plateau width), and k (stiffness).
The
parameters that define the EP system are γ1 (normalized yield force), α (hardening
value), and k (stiffness).
A total of six different systems were created (SMA1-4, EP1-2) as shown in Figure
3-2.
These systems were compared to investigate the effects of loading plateau
stiffness (strain hardening for EP), recentering, and energy dissipation.
SMA1 was
modeled after an idealized SMA response with zero transformation plateau stiffness and
no deformation limit to this plateau. SMA2 was modeled the same as SMA1 but with a
larger hysteretic loop. SMA3 was modeled after SMA experimental test response with a
typical stress plateau slope (DesRoches et al., 2004).
The deformation limit of the
plateau was again extended to prevent the stiffening effect that occurs in the martensite
phase. SMA4 was modeled after SMA experimental test response with a normal-sloped
loading plateau and the martensite stiffening included (this is intended to be the most
realistic model in this study). For the non-recentering systems, EP1 and EP2 were
modeled after an elastic-perfectly-plastic system and an elastic-plastic system with strain
hardening (equivalent to the loading plateau slope in the SMA3-4 models), respectively.
28
The finite element program used for analysis was OpenSEES (McKenna and
Fenves, 2004).
The SMA constitutive model used was a modified one-dimensional
model (Fugazza, 2003) first proposed by Auricchio and Sacco (1997). This behavior is
shown in the left part of Figure 3-1 with two trigger-lines controlling the behavior around
the hysteretic loop. The model implicitly assumed the SMA has no strength degradation
and no residual strain accumulation. This is a reasonable assumption when SMAs are
mechanically trained (McCormick et al., 2005) and was determined sufficient for this
study.
One suite of ground motions from the Los Angeles (LA) area was taken from the
FEMA/SAC building study (Somerville et al., 1997). The suite consisted of 20 records
with a 10% probability of exceedance in 50 years (LA1-20). In order to assist in the
comparison of results, each ground motion record was scaled to the suite’s average
spectral acceleration at the corresponding period that was being analyzed.
The analysis was run over a range of periods and strength reduction factors from
0.1 to 2.1 sec. at an interval of 0.2 sec. This period range covers the typical range
expected for single-story through small high-rise buildings.
The strength reduction
factor, R, was assigned to be 2, 4, or 8. Since it is generally desirable to have larger
strength reduction factors (in order to decrease the forces and resulting member sizes in
a structure), special attention was paid to the structures with the higher strength
reduction factor.
The fundamental issue investigated in this study was whether there are any
noticeable trends in which recentering was more advantageous then damping. In order
to probe this question, the performance parameters that were assessed are the
maximum displacement (a measure of structural damage) and maximum acceleration (a
measure of serviceability). The residual displacement was not considered during the
majority of this study because the SMA-based systems all have zero residual (by
29
definition).
However, a brief case study at the end of this chapter highlights the
difference in residual displacement, which is arguably the most important benefit of using
a recentering system.
EP
γ2
γ3
γ1
γ4
two horizontal
trigger-lines
k
F / Fy
F / Fy
SMA
β
αk
γ1
k
u / uy
u / uy
Figure 3-1: Definition of the SMA and EP force-displacement relationships.
SMA1
SMA2
β = large (1500 uy)
SMA3
SMA4
β = large (1500 uy)
γ1
γ2
γ3
γ4
γ1
γ2
γ3
γ4
1
1
5/8 4/8
1
1
2/8 1/8
γ1
β = large (1500 uy)
γ2
γ3
γ4
1 241fy 240fy 4/8
EP1
β = 7/3
γ1
γ2
1 11/8
γ3
γ4
1
4/8
EP2
γ1
α
γ1
α
1
0
1
13/80
Figure 3-2: Force-displacement relationships of the four SMA (SMA1-4) and two EP
(EP1-2) systems.
30
3.4.
3.4.1.
Results and Discussion
General Behavior
To illustrate the general trends seen in this study, an example displacement-time-history
and force-displacement responses are shown in Figure 3-3. These results were from
systems with a period of 0.5 sec. and strength reduction factor of 2 subjected to the LA1
record. In general, the SMA-based systems had larger maximum displacements than
the equivalent EP system.
However, the residual displacements of the SMA-based
system were always zero compared to varying levels of residual in the EP systems. The
larger maximum displacements can be attributed to the SMA system not dissipating as
much energy compared to its EP counterpart. This undissipated energy resulted in the
SMA system incurring larger displacement demands.
For the entire range of results, the performance of the recentering system was
assessed by dividing the SMA system by the EP system. This term will be referred to as
the normalized displacement. A normalized displacement less than unity indicates that
the SMA system outperformed the EP system. Conversely, a normalized displacement
greater than unity indicates the EP system outperformed the SMA system. Additionally,
error bars of plus/minus one standard deviation were plotted to give a representation of
the data spread.
31
3
SMA
1
2
0
-1
F/Fy
u/uy
1
0
EP
1
-1
0
SMA
EP
-2
-1
-3
0
10
20
30
40
-3
-2
-1
0
1
2
3
u/uy
time (sec.)
Figure 3-3: Displacement time history of SMA and EP systems for T=0.5 sec. and R=2.
3.4.2.
Displacement and Acceleration Demands
3.4.2.1. SMA1 vs. EP1
SMA1 and EP1 were the first two systems compared. Both of these systems have zero
load plateau stiffnesses and unlimited ductility (β = large (1500uy) for the SMA). By
comparing these two systems, the benefits of damping were being weighed against that
of recentering.
The results of this comparison are shown in row (a) of Figure 3-4
(displacement) and Figure 3-5 (acceleration).
In general, the maximum displacement of the SMA approached that of the EP
system for increasing period and decreasing R. An exception to this trend was seen at
small periods (T < 0.5 sec.) where increasing R results in improved SMA performance.
However, in this same small period range, the behavior of SMA was poor in comparison
to the EP system. These results support the idea that recentering systems (which, by
definition, have less hysteretic damping than an EP system) generally perform better for
longer (larger) period systems.
Conversely, for shorter (smaller) period systems,
damping was expected to be more effective. This explains why the EP system was
greatly outperforming the SMA system at shorter periods.
32
In terms of the acceleration demands, the performance of the SMA system
approached that of the EP system as the period increased. For periods greater than 1.0
sec., the difference in acceleration demand between the two systems was negligible.
Additionally, the acceleration demands did not seem to be sensitive to a change in R,
especially at longer periods (T > 1.0 sec.).
3.4.2.2. SMA2 vs. EP1
In order to investigate the benefit of increased damping in a recentering system, the
SMA2 system was compared to the EP1 system. SMA2 had approximately 50% more
energy dissipation in its hysteresis in comparison to SMA1. The results of this increase
are shown in row (b) of Figure 3-4 (displacement) and Figure 3-5 (acceleration).
The trends observed in this comparison were nearly identical to that seen in the
previous comparison (SMA1 vs. EP1) for both maximum displacement and acceleration
demand. However, when comparing the results of SMA1 to SMA2 (row (a) to row (b)),
there was a clear improvement of behavior in the SMA2 system. The displacement
demand for the SMA2 system was reduced across the entire range of T and R.
However, the EP system still consistently outperformed the SMA system with regards to
displacement demand. In contrast, the SMA system’s acceleration demand was nearly
equivalent to that of the EP system for medium to long period levels, which was
consistent with the SMA1 performance.
3.4.2.3. SMA3 vs. EP2
For SMA3 and EP2, stiffness was introduced into the loading plateaus. SMA3 and EP2
both had the same loading plateau slopes (slope = 0.16). The slope was determined
from mechanical test results of a 12.7 mm (0.5 in.) diameter NiTi bar (McCormick and
DesRoches, 2004). The results of this comparison are shown in row (c) of Figure 3-4
(displacement) and Figure 3-5 (acceleration).
33
The displacement demands were similar to that seen in the comparison between
SMA1 vs. EP1. An exception to this similarity was seen in the short period range, where
SMA3 (with loading plateau stiffness) performed better then SMA1 (without loading
plateau stiffness). In terms of acceleration demands, no significant differences were
observed between SMA1 and SMA3, indicating little sensitivity to the loading plateau
stiffness.
3.4.2.4. SMA4 vs. EP2
In order to investigate the effect of the stiffening seen in SMA after the loading plateau
has been crossed, SMA4 was compared with EP2. The loading plateau length was set
to 7/3 uy (an approximation from mechanical tests by DesRoches et al. (2004)). The
results of this comparison are shown in row (d) of Figure 3-4 (displacement) and Figure
3-5 (acceleration).
In terms of displacement demand at short periods, SMA4 dramatically reduced
the response in comparison to SMA3. Additionally, SMA4 had improved performance
vs. EP1 as the R increased, with a dramatic improvement observed at short periods.
The improved performance was the direct result of SMA4’s stiffness after the loading
plateau, preventing further displacements at the expense of attracting increased loads.
This effect was especially dominant at short periods and larger R values. The resulting
effect on a MDOF system is anticipated to be positive because this behavior will help
prevent the formation of soft-stories and force a more uniform drift demand along the
entire height of a structure.
In terms of acceleration demand, SMA4’s response was essentially identical for
the R of 2. However, acceleration demands increased for R values of 4 and 8, with the
most significant increase in the period range of 0.3 to 1.1 sec. This result indicates that
acceleration demands will be increased in a real SMA-based system due to the stiffness
increase after the SMA has been fully transformed from austenite to martensite.
34
R=2
R=4
R=8
SMA1/EP1
4
(a)
3
2
1
0
SMA2/EP1
4
(b)
3
um,SMA / um,EP
2
1
0
SMA3/EP2
4
(c)
3
2
1
0
SMA4/EP2
4
(d)
3
2
1
0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
T (sec.)
Figure 3-4: Maxiumum average displacement of SMA divided by the maximum
displacement of EP over a range of periods subjected to LA1-20. Row (a) is SMA1/EP1,
(b) is SMA2/EP1, (c) is SMA3/EP2, and (d) is SMA4/ EP2.
35
R=2
R=4
R=8
SMA1/EP1
3
(a)
2
1
0
SMA2/EP1
3
(b)
2
am,SMA / am,EP
1
0
SMA3/EP2
3
(c)
2
1
0
SMA4/EP2
3
(d)
2
1
0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
T (sec.)
Figure 3-5: Maxiumum average acceleration of SMA divided by the maximum
acceleration of EP over a range of periods subjected to LA1-20. Row (a) is SMA1/EP1,
(b) is SMA2/EP1, (c) is SMA3/EP1, and (d) is SMA4/ EP2.
36
3.4.3.
Case Study: SMA4 vs. EP1 vs. PARA1
The beneficial effects of increased hysteretic damping and post-plateau stiffness were
shown in the previous sections. In order to create a system with maximized energy
dissipation and minimized residual accumulation, PARA1 system was created with SMA
and EP elements in parallel. The system selected has the force-deformation as show in
Figure 3-6, where T=1.1 sec. and R=4. The hysteretic damping is 3.4 times that found in
an SMA-only system. The SMA4 was used as the SMA model.
The PARA system was subjected to the scaled LA1 ground motion.
The
resulting force-deformation responses and displacement time histories are shown in
Figure 3-7. The normalized maximum and residual displacements (um/uy, ur/uy) for the
SMA4, PARA1, and EP1 systems were (5.9, 0.0), (5.6, 0.1), and (6.4, 4.7), respectively.
The PARA1 and SMA4 system have 5-10% smaller displacement demands compared to
the EP1 system in this case, giving these systems a slight advantage. However, there is
a clear advantage when comparing the residual deformations, in which the PARA1
system returned to approximately 1.8% of its maximum deformation compared to the EP
system returning to 73% of its maximum deformation. This indicated there is potential in
the improved damping provided by a parallel-type system, as was supported by the
investigation of the increased damping system of SMA2. If the SMA’s restoring force is
properly balanced with the yielding force of the EP element to ensure a good balance of
energy dissipation and recentering ability, the response can be improved while
simultaneously limiting unwanted residual damage.
37
2
1
F/Fy
PARA1
SMA portion
EP portion
0
-1
-1
0
1
2
3
4
u/uy
Figure 3-6: Force-deformation of parallel system created for the case study.
SMA4
PARA1
EP1
4
F/Fy
2
0
-2
-4
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
u/uy
u/uy
6
4
2
0
-2
-4
-6
5.9
5.6
0.1
4.7
6.4
0
20
40
60
0
20
40
60
0
20
40
60
time (sec.)
Figure 3-7: Force-deformation and displacement time histories for SMA4, PARA1, and
EP1 systems.
38
3.4.4.
Summary
A new look was taken into the performance of a superelastic SDOF system when
subjected to a suite of ground motions. This was specifically done in the light of NiTi
SMA characteristics that have been documented in numerous studies. In general, SMAs
become more effective in reducing the response of a system in the longer period range
when compared to traditional elastoplastic systems.
However, unlike elastoplastic
systems, SDOF systems with SMAs have limited residual deformations. The effect of
increasing the size of the recentering hysteretic loop was examined.
The results showed that the increased hysteretic loop adds a positive effect on
the performance, reducing displacements without noticeably affecting acceleration
demands and residual displacements. Additionally, the benefit of accounting for the
post-plateau stiffness in an SMA was demonstrated. This post-plateau stiffness reduced
displacement demands over a broad range of periods, though the side-effect was an
increase in force demands.
However, it is expected that this behavior will have a
beneficial effect on a multiple degree-of-freedom system, spreading ductility demand
more uniformly throughout the system. Lastly, a practical way to increase the hysteretic
damping was proposed by using a parallel system. A case study showed a parallel
system can moderately decrease displacement demands when compared with a SMAonly system while maintaining small residual displacements when compared with an
elastoplastic system.
In summary, it should be noted that this was a preliminary study into the wide
range of parameters that affect a SDOF recentering system. Though some information
was gleaned, further analysis need to be conducted to understand the circumstances
(e.g. period range, ground motion characteristics) in which damping, recentering, or a
mix of both is most effective in reducing structural response parameters.
39
CHAPTER 4
TENSION/COMPRESSION DEVICE
4.1.
Introduction
Engineers continue to look for creative new ways to use SMAs in hopes of enhancing
structural performance during extreme events. This chapter investigates the behavior of
a new tension/compression device developed for bracing applications in buildings. The
device is designed to allow various forms of NiTi SMA, such as helical springs or
Belleville washers, to be used in compression. The device allows both overall extension
(tension) and contraction (compression) while subjecting the NiTi to a compression
deformation mode. It is possible, due to the versatility of the design, to adjust the force
and stroke of the device without changing the overall configuration. This new device
was subjected to a cyclic loading protocol that tests the NiTi element’s ability to recover
large deformations.
The effect of different NiTi configurations was evaluated in the
study. The results for the helical spring show good recentering and damping. However,
the Belleville washer results call for further investigation and development.
4.2.
Background
As mentioned in the literature review of CHAPTER 2, a variety of research initiatives
have looked at the viability of using SMAs as structural recentering and/or damping
elements in both bridges and buildings (Wilson and Wesolowsky, 2005). Dolce et al.
(2000) devised several types of recentering systems using SMA wires and bars as part
of the European Commission sponsored MANSIDE Project (1998). Experimental testing
of their devices showed predictable behavior, good energy dissipations, and excellent
40
recentering. However, the concepts and devices gleaned from Dolce’s research have
found limited application.
Additionally, other SMA-based systems have been
investigated without wide implementation, including a self-centering friction damped
brace by Zhu and Zhang (2008) and beam-column connections by Ocel et al. (2004),
Penar (2005), and Sepulveda (2008).
The inherent advantage of using an SMA-based system is that it can be
designed 1) to significantly reduce the residual deformations after an earthquake and 2)
to have the ductility and energy dissipation to prevent collapse. This research presents
the development and initial testing of a new device that facilitates the use of two new
forms of NiTi SMA: helical springs and Belleville washers. Whether the device is in
tension or compression, the SMA elements are compressed.
To the author’s
knowledge, there is no published research on the investigation of SMA helical springs or
Belleville washers for structural applications (besides that published as part of this work
(Speicher et al., 2009)).
4.3.
Device Description
The tension/compression (TC) device is a cylindrical shaped damper that can
accommodate a variety of SMA elements. The body and the shaft of the device were
made out of standard 304 stainless steel cylinders. Schematic drawings of the device
with a helical spring and a Belleville washer stack are shown in Figure 4-1. The device
is approximately 50 cm (19.7 in.) in length and 6.4 cm (2.5 in.) in diameter. The stroke
capacity of the damper is dependent on the active element that is inserted, with values in
the range of 2-5 cm (0.8-2.0 in.) for the arrangements presented in this study. The
damper was fitted with either helical springs or Belleville washers. Different strength and
stiffness properties can be easily obtained by using different combinations of active
41
elements. Additionally, this device setup is scalable to accommodate a wide range of
force and stroke capacities.
Figure 4-1: Internal view of tension/compression device.
4.4.
Active Element Description
Two different types of active elements were used in the testing of the device: NiTi helical
springs and NiTi Belleville washers. This section briefly describes each element.
4.4.1.
Helical Springs
Two springs were used in this study: a hollow spring and a solid spring. The springs
were made from NiTi 508 (50.8% atomic % Nickel).
The hollow NiTi spring has a
diameter of 3.8 cm (1.5 in.), an initial length of 14.2 cm (5.6 in.), and a deformation
capacity of 8.0 cm (3.1 in.) (undeformed vs. fully compressed). The hollow spring was
made from tubing with an outside and inside diameter of 12.5 mm (0.5 in.) and 9.5 mm
(0.37 in.), respectively. The solid NiTi spring has a diameter of 3.8 cm (1.5 in.), an initial
42
length of 13.0 cm (5.1 in.), and a deformation capacity of 4.6 cm (1.8 in.) and was made
from solid stock with a 12.5 mm (0.5 in.) diameter.
Both springs were made by heating small sequential sections of the stock with a
small torch just to the point of initial softening (very low red heat, approx. 650-700 °C).
The softened metal was then bent around a mandrel to produce a helix. The finished
coils were given a final heat treatment to achieve uniform properties and good
superelasticity.
Full details of this process are proprietary information of Nitinol
Technology Inc.
4.4.2.
Belleville (Spring) Washers
The NiTi Belleville washers were 5.5 cm (2.2 in.) wide, 0.64 cm (0.25 in.) tall, and 0.31
cm (0.12 in.) thick. The washers were cut with a waterjet from a hot-rolled sheet of
standard NiTi 508. Two phases of testing were conducted on the washers. In Phase I
(the first set), the conical shape was made using a 30° angled cone.
This yielded
washers with a cone angle of 23-25°. A set of 12 washers was used for all the testing in
this phase, including the individual and stacked washer tests. For Phase II (the second
set), the Phase I washers were reformed to have an increased cone angle of 27-30°.
This time a set of 8 washers were used for a single stacked test. Additionally, several
individual cyclic tests were conducted in Phase I and Phase II to investigate various
questions that surfaced during other tests.
4.5.
Experimental Setup
A 250 kN (55 kip) MTS Universal Testing Machine (shown in Figure 4-2a) was used for
the tests. The MTS machine was fitted with hydraulic vee-notched wedge grips which
could accommodate a rod diameter up to 1.9 cm (0.75 in.). Stainless steel coupler
elements were used to transfer the force from the 2.5 cm (1 in.) diameter rods of the
43
damper to 1.9 cm (0.75 in.) diameter rods gripped by the MTS machine. The MTS
machine was controlled by a Teststar controller running Testware software. The tests
were conducted in displacement control using the built-in LVDT attached to the bottom
grip.
A far field loading protocol, modeled after the protocol used in the SAC Steel
Project (SAC, 1997), was selected for the experiments. The loading protocol, shown in
Figure 4-2b, uses the testing machine’s stroke as the deformation parameter. For each
specimen arrangement, the maximum deformation was calculated and then 90% of this
value was set as the test-target maximum (Δmax). This was done to prevent overloading
of the device.
A quasi-static loading rate was set at 0.13 cm/sec (0.05 in./sec) to
eliminate dynamic effects. Though SMA’s behavior is not completely rate-independent,
loading rate effects were ignored for this study.
Additionally, all experiments were
carried out under ambient temperatures in the range of 26-28 °C. Self-heating was not
recorded because of the difficulty in monitoring the heat in the confined device and it
was not expected to greatly impact the tests due to the quasi-static protocol
implemented.
As mentioned before, the tension/compression device was fabricated to facilitate
the ability to implement different types of active elements. In this investigation, the
following six different tests were conducted:
ƒ
Test A: Hollow NiTi helical spring
ƒ
Test B: Solid NiTi helical spring
ƒ
Test C: 10 NiTi Belleville washers, single-stacked
ƒ
Test D: 12 NiTi Belleville washers, double-stacked
ƒ
Test E: 12 NiTi Belleville washers, triple-stacked
ƒ
Test F:
8 NiTi Belleville washers, triple-stacked, increased depth, spherical
spacer
44
Fraction of Maximum
Displacement
Additionally, element level tests were conducted on the individual washers.
1.0
0.5
0.0
-0.5
-1.0
0
200
400
600
800
Time (sec.)
Figure 4-2: Tension/compression device (a) test machine setup and (b) example loading
protocol.
4.6.
4.6.1.
Results and Discussion – Helical Spring Tests
Results – Hollow Helical Spring
Test A was performed using the hollow NiTi spring as the active element. The spring
was inserted into the device and the shaft nut was tightened to give the spring 4.1 cm
(1.6 in.) of precompression (shown in Figure 4-3). This was done to increase the initial
stiffness of the device. The length of the spring (in the precompressed state) was 10.1
cm (4.0 in.). The fully compressed length was approximately 5.8 cm (2.3 in.). This
resulted in a maximum device stroke of 4.2 cm (1.7 in.).
The test-target maximum deformation, Δmax, was set to 3.8 cm (1.5 in.) for this
test. Using the previously described protocol, the resulting force-deformation plot was
obtained as shown in Figure 4-4. The 1/3, 2/3, and full Δmax cycles are highlighted to
show the progressive behavior. The precompressed helical spring provided high initial
stiffness and recentering over the entire cyclic protocol.
45
Figure 4-3: Nitinol spring loaded on center shaft (Test A and B).
Deformation, Δ (in.)
-2
9
6
-1
0
1
2
2
Test A, Solid Helical Spring
Δmax = 4.57 cm
0
0
-3
Force (kips)
Force (kN)
1
3
-1
-6
-2
-9
-5.0
-2.5
0.0
2.5
5.0
Deformation, Δ (cm)
Force (kN)
1/3 Δ
9
6
3
max
2/3 Δ
Cycle
max
Cycle
ζ = 5.96%
1st Full Δ
ζ = 6.25%
max
3rd Full Δ
Cycle
max
Cycle
ζ = 6.58%
ζ = 6.17%
0
-3
-6
-9
-5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
Deformation, Δ (cm)
Figure 4-4: Force-deformation response of hollow Nitinol spring in device (Test A).
4.6.2.
Results – Solid Helical Spring
Test B was performed using the solid NiTi spring as the active element. Again the
spring was inserted into the device and the shaft nut was tightened to give the spring 1.2
cm (0.45 in.) of precompression.
The spring was only precompressed this amount
46
because of how the spring fit on the shaft.
The length of the spring (in the
precompressed state) was 11.8 cm (4.7 in.) and the fully compressed length was
estimated at 6.8 cm (2.7 in.). This resulted in a maximum device stroke of 5.1 cm (2 in.);
in which 90% of this value, 4.6 cm (1.8 in.), was used for the test-target maximum. The
force-deformation for Test B is shown in Figure 4-5. The qualitative behavior was similar
to that seen in Test A.
Deformation, Δ (in.)
-1.5
9
-1.0
-0.5
0.0
0.5
1.0
1.5
2
Test B, Hollow Helical Spring
Δmax = 3.81 cm
6
0
0
-3
Force (kips)
Force (kN)
1
3
-1
-6
-2
-9
-2.5
0.0
2.5
Deformation, Δ (cm)
Force (kN)
1/3 Δ
9
6
max
2/3 Δ
Cycle
max
Cycle
ζ = 8.76%
3
1st Full Δ
ζ = 7.63%
max
3rd Full Δ
Cycle
max
Cycle
ζ = 6.85%
ζ = 6.76%
0
-3
-6
-9
-4
-2
0
2
4
-4
-2
0
2
4
-4
-2
0
2
4
-4
-2
0
2
Deformation, Δ (cm)
Figure 4-5: Force-deformation response solid Nitinol spring in device (Test B).
47
4
4.6.3.
Discussion - Helical Spring Tests
The force-deformation relationships for both Tests A and B demonstrate good hysteretic
damping, limited strength degradation, and excellent repeatability.
In assessing the
performance of a damper, the equivalent viscous damping level and the consistency of
force levels are two important issues. The equivalent viscous damping is defined as:
ζ = ED/(4πEso)
where, ED is the energy dissipated in one cycle and Eso is the energy absorbed by an
equivalent linear elastic system loaded to the same maximum force and displacement
level as used in ED. In structural engineering, typical values of ζ are around 5-10%.
For this study, the “yield” force was defined as the force level in which the overall
device breaks from its initial stiffness; which is the “kinked” point in the bilinear loading
response. Also, the yield force is defined at the positive (tension) stroke of the device.
Ideally this should not matter, but in practice there were some small differences between
the positive and negative behavior.
The superelasticity combined with precompression of the spring resulted in a
slender flag-shaped hysteric loop that accounted for ζ ranging from 6-11%, with the
majority of the values between 6-7% for the hollow spring and 7-9% for the solid spring.
In Figure 4-6a, the trend of ζ as a function of deformation is presented. In comparison to
the solid spring, the hollow spring tended to have more stable levels of damping over the
entire cyclic range.
When interpreting the behavior of the force levels in Tests A and B, it should be
noted that the precompression given to the hollow spring was almost 4 times that given
to the solid spring. As a result, the hollow spring setup had a higher yield force then the
solid spring, which at first glance is counterintuitive. However, the stiffness of the sloped
loading plateau is clearly larger for the solid spring.
48
The yield forces for the hollow and solid springs are shown vs. the fraction of Δmax
in Figure 4-6b. Both springs have the same trend; the yield force decreases as the
loading cycles increase. The hollow spring yield force decreases faster than that of its
solid counterpart.
This can be contributed to the hollow spring having a larger
precompression. When the cyclic loading is applied, the hollow spring is presumably
pushed further into its superelastic range which results in an accumulation of residual
deformations. This accumulation presets stress in the material causing a reduction in
the yield force.
Finally, it noted that further investigation should be conducted to
12
2.5
10
2.0
8
6
4
solid spring
hollow spring
2
0
0.0
(a)
0.2
0.4
0.6
0.8
0.4
1.5
Fraction of Δmax
0.2
solid spring
hollow spring
0.5
0.0
0.0
1.0
0.3
1.0
(b)
0.1
Yield Force (kips)
0.5
Yield Force (kN)
Equivalent Viscous Damping, ζ (%)
investigate how much of the superelasticity of the NiTi is being exploited.
0.0
0.2
0.4
0.6
0.8
1.0
Fraction of Δmax
Figure 4-6: Helical spring tests (a) equivalent viscous damping and (b) yield forces over
a range of deformations.
4.7.
Results and Discussion – NiTi Belleville Washer Tests:
Phase I
For Phase I testing, the NiTi washers had a cone angle of approximately 23-25°. A
series of individual (monotonic) and stacked (cyclic) tests were carried out to assess the
behavior.
49
4.7.1.
Individual
Three washers were randomly selected for compression testing from the set of 12 used
in this phase of testing. These tests were performed using the MTS machine as shown
in Figure 4-7. Each individual Belleville washer was placed between two 1.3 cm (0.5 in.)
hardened disks and compressed until just short of flat. The resulting duck-head-shaped
force-deformation curves are shown in Figure 4-8.
The washers had good initial
stiffness and strength, but at a deformation of approximately 0.15 cm (0.06 in.) the force
carrying capacity peaks and there is a significant load drop-off until the imposed
deformation is released at 0.61 cm (0.24 in.).
The trends for all three individual washers were the same but there were varying
levels of strength, stiffness, and residual deformations.
The large initial stiffness
followed by a peaking and dropping-off of load carrying capacity can be explained when
looking at the geometry of the washer.
A handbook (Fromm and Kleiner, 2003)
produced by Schnorr Corporation thoroughly details the behavior of Belleville washers
made from Hookian elastic materials. Washers with similar geometry to those used in
these tests show a response characteristic similar to Figure 4-8, excluding the
superelastic recovery seen during the release of the deformation.
The effect of the superelasticity of the washer is not fully understood and more
investigation is needed. However, when the washers were loaded to the flat position,
some had the tendency to pass through a region of bifurcation and buckle (invert) into
another stable configuration. After recovering the shape with a wooden mallet, little-tono residual deformations were observed.
Generally in structural engineering, it is
desired to have materials that retain load carrying capacity when subjected to large
deformations, which is not the case here. A strategy to correct this behavior and prevent
inverting is proposed in the Phase II testing.
50
washer
Figure 4-7: Test setup for individual washer test.
Deformation, Δ (in)
0.0
0.1
0.2
0.0
0.1
0.2
0.0
0.1
0.2
Washer 1
15
Washer 2
Washer 3
4
3
10
2
5
1
0
Force (kips)
Force (kN)
20
0
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
Deformation, Δ (cm)
Figure 4-8: Response of individual NiTi Belleville washers under compression (Phase I).
4.7.2.
Single-Stacked
Test C was conducted on a washer stack with the most flexible configuration of 10
single-stacked washers as shown in Figure 4-9. Flat steel washers of 0.2 cm (0.08 in.)
thickness were inserted between each SMA washer in an attempt to prevent the SMA
washers from inverting as seen in preliminary tests.
51
As stated in the specimen
description section, the SMA washers used in this test were not virgin; they had been
used in preliminary tests.
The initial length of the washer configuration was 10.4 cm (4.1 in.) after the shaft
was hand-tightened. The Δmax was 5.1 cm (2.0 in.). The cyclic force-deformation curves
are shown in Figure 4-10. The washer stack gave semi-sporadic loading and unloading
plateau paths, but these paths were repeatable and consistent at smaller deformation
levels.
Residual deformations were observed as the device was subjected to larger
deformations. After the test was complete and the damper was disassembled, it was
observed that one of the washers had inverted. The flat washers did not completely
prevent the SMA washers from inverting. To recover its original shape, the washer was
hit with a wooden mallet against a hard surface. The washer promptly snapped back.
Figure 4-9: Washer configuration for Test C.
52
Deformation, Δ (in.)
20
Force (kN)
10
-1
0
1
2
Test C, Single Stacked Washer
Phase I
10 washers
Δmax = 5.08 cm
4
2
0
0
-10
-2
Force (kips)
-2
-4
-20
-5.0
-2.5
0.0
2.5
5.0
Deformation, Δ (cm)
1/3 Δ
Force (kN)
20
10
max
2/3 Δ
Cycle
max
Cycle
ζ = 8.90%
1st Full Δ
ζ = 11.77%
max
Cycle
ζ = 9.89%
3rd Full Δ
max
Cycle
ζ = 8.86%
0
-10
-20
-5.0 -2.5 0.0
2.5
5.0
-5.0 -2.5 0.0
2.5
5.0
-5.0 -2.5 0.0
2.5
5.0
-5.0 -2.5 0.0
2.5
5.0
Deformation, Δ (cm)
Figure 4-10: Force-deformation response of single-stacked washer configuration (Test
C).
4.7.3.
Double-Stacked
Test D was performed using a double-stacked 12-washer configuration (show in Figure
4-11). This configuration gave increased stiffness and strength in comparison to the
single-stacked test. Unlike the previous test, flat washers were not added since they
were determined ineffective in the previous test. Additionally, it was expected that the
double-washer arrangement would naturally prevent individual washers from inverting.
To fill the gap on the device center shaft, additional stainless steel cylinders were added
between the shaft nut and the hardened disk. The shaft nut was hand tightened and the
cylinder was slid into position.
53
The initial length and Δmax of the washer configuration were 7.9 cm (3.1 in.) and
3.3 cm (1.3 in.), respectively. The resulting force-deformation is shown in Figure 4-11.
A semi-sporadic response was observed, but this time fewer humps were noticed. After
the test was complete and the damper was disassembled, one washer was found to be
inverted. This washer was not the same one which inverted in the single-stacked test
(Test C).
Figure 4-11: Washer configuration for Test D.
54
Deformation, Δ (in.)
50
40
Force (kN)
30
20
-1
0
1
2
Test D, Double Stacked Washers
Phase I
12 washers
Δmax = 3.30 cm
10
5
Force (kips)
-2
10
0
0
-10
-20
-5
-30
-40
-10
-50
-5.0
-2.5
0.0
2.5
5.0
Deformation, Δ (cm)
Force (kN)
1/3 Δ
40
max
2/3 Δ
Cycle
max
Cycle
ζ = 11.15%
20
1st Full Δ
ζ = 9.77%
max
3rd Full Δ
Cycle
ζ =6.03%
max
Cycle
ζ = 5.12%
0
-20
-40
-5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
-2.5
0.0
2.5
5.0
Deformation, Δ (cm)
Figure 4-12: Force-deformation response of double-stacked washer configuration (Test
D).
4.7.4.
Triple-Stacked
The final test of Phase I, Test E, was done using a triple-stacked 12-washer
configuration (Figure 4-13), giving even more stiffness and strength in comparison to the
double-stacked test. Flat washers were again added in a second attempt to prevent the
inverting observed in the previous tests. Additional stainless steel cylinders were added
as fillers between the shaft nut and the hardened disk. Again the shaft nut was hand
tightened and the cylinder was slid into position.
The initial length and Δmax of the washer configuration were 6.8 cm (2.7 in.) and
2.0 cm (0.8 in.), respectively. The resulting force-deformation is shown in Figure 4-14.
55
This time a less sporadic load path was observed. The force-deformation curve had two
distinct humps with a minor intermediate hump. After the test was complete and the
damper was disassembled, no washers were found to be inverted.
Figure 4-13: Washer configuration for Test E.
Deformation, Δ (in.)
50
40
Force (kN)
30
20
-0.5
0.0
0.5
1.0
Test E, Triple Stacked Washers
Phase I
12 Washers
Δmax = 2.03 cm
10
5
10
0
0
-10
-20
-5
Force (kips)
-1.0
-30
-40
-10
-50
-2
-1
0
1
2
Deformation, Δ (cm)
Force (kN)
1/3 Δ
40
20
max
2/3 Δ
Cycle
max
Cycle
ζ = 5.78%
1st Full Δ
ζ = 10.39%
max
Cycle
ζ = 10.06%
3rd Full Δ
max
Cycle
ζ = 10.49%
0
-20
-40
-2
-1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
-2
-1
0
1
2
Deformation, Δ (cm)
Figure 4-14: Force-deformation response of triple-stacked washer configuration (Test
E).
56
4.7.5.
Discussion – Single, Double, and Triple-Stacked Washers
The behavior of the single-stacked configuration was governed by the tendency of
individual washers to lose their load carrying capacity as they were deformed beyond a
certain limit. This was the direct result of the duck-head-shaped behavior observed in
the individual washer tests. Since it can be assumed that each SMA Belleville washer
has different peak strengths, the response of the single-stacked washer configuration
was governed by the weakest link. As soon as the weakest washer was deformed to
approximately 0.15 cm (0.06 in.), this washer began to lose its strength and thus take on
the deformations of the other washers.
deformation humps.
This was reflected in the device’s force-
Once the displacement was increased enough to flatten the
weakest washer, the remaining washers began to acquire more deformation. This cycle
was repeated until the either the entire group of washers had flattened or the device
deformation was decreased.
Upon the release of the imposed deformation, the flattened Belleville washers
sprang back causing the force in the device to increase sporadically even while the
deformation was decreasing (see the unloading path in Figure 4-10, Figure 4-12, and
Figure 4-14). Residual deformations of each setup began to noticeably accumulate
during the 2/3 Δmax cycle. Upon the completion of the 3rd full Δmax cycle, the bulk of the
residual deformation could be attributed to a Belleville washer completely inverting (as
noted in the results section).
The double and triple-stacked configurations had progressively less sporadic
loading paths. Beyond the initial softness observed due to some of the washers settling
into their positions, the stiffness increased as more washers were nested together. This
initial stiffness, defined at a point half-way up the first hump, was 1.74, 2.45, and 3.93
kN/mm (9.94, 13.99, and 22.44 kip/in.) for the single, double, and triple-stacked
57
configurations, respectively. By adding more washers to each nest, fewer humps were
able to form because there were fewer nests to allow this to occur.
The equivalent viscous damping, ζ, of the stacked washer configurations is
shown in Figure 4-15 for each stacked washer test. The ζ ranged from approximately 413%. The Eso was calculated using the maximum deformation and the maximum force
of each respective cycle (not necessarily the same point). The damping values were
dependent on the location that each deformation cycle fell with respect to the humped
response.
The triple-stacked configuration showed increased damping at increased
deformation. It was expected that as more washers were nested together, additional
damping would result from the friction action between the nested surfaces. However,
the damping caused by each washer’s mechanical hysteresis seemed to be dominant in
Equivalent Viscous Damping (%)
comparison to this friction action.
14
12
10
8
6
4
Test C (single stacked)
Test D (double stacked)
Test E (triple stacked)
2
0
0.0
0.2
0.4
0.6
0.8
1.0
Fraction of Δmax
Figure 4-15: Comparison of equivalent viscous damping ratios for the stacked washer
tests (Phase I).
58
4.8.
Results and Discussion – NiTi Belleville Washer Tests:
Phase II
For Phase II testing, the shape of the original set of NiTi washers was reset to have a
27-30° cone angle and then re-heat treated to ensure superelasticity at room
temperature. A series of individual (monotonic and cyclic) and stacked (cyclic) tests
were then carried out to assess the new behavior.
4.8.1.
Individual
As in Phase I, individual washer tests were performed using the MTS machine. The
resulting duck-head-shaped force-deformation curves are show in Figure 4-16.
The
washers had good initial stiffness and strength, but at a deformation of approximately
0.15-0.20 cm (0.06-0.08 in.) the force carrying capacity peaked and there was a
significant drop-off in load. The drop-off in load was especially noticeable for Washer 2,
in which a sharper peak was obtained (attributed to an increased cone angle compared
to Washer 1). When the imposed deformation was released at 0.60-0.75 cm (0.24-0.30
in.), an unloading plateau was formed and the majority of the deformation was
spontaneously recovered. As for Washer 3, a smaller deformation level was imposed to
assess the effects of limiting the deformation.
In Figure 4-17, the cyclic behavior of two different washers was investigated
(Washer 4 and 5). First Washer 4 was cycled three times to almost flat (Figure 4-17a).
The response began to somewhat stabilize, but further cycles were not carried out to
determine the extent of this stabilization. Therefore, Washer 5 was cycled ten times to
50% of its flat deformation (Figure 4-17b). The response of Washer 5 clearly began to
stabilize as the cycling progressed. Residual deformations began to decrease from one
cycle to the next and the stress plateau began to flatten, thus eliminating the load drop-
59
off tendency (see the comparison in Figure 4-17c). This preliminary investigation shows
that NiTi Belleville washers can be trained to have improved force-deformation behavior
and opens the door to a wide range of potential applications.
Though further
applications are not studied, the potential for the superelastic Belleville washer use in
bolted connections could be one area of future research.
Deformation, Δ (in)
0.0
0.1
0.2
0.3
0.0
0.1
0.2
0.3
0.0
0.1
0.2
0.3
Washer 1
20
Washer 2
15
10
Washer 3
5
(reduced
deformation
demand)
4
3
2
5
1
0
Force (kips)
Force (kN)
25
0
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
1.0
Deformation, Δ (cm)
Figure 4-16: Response of individual NiTi Belleville washers under compression (Phase
II).
Deformation, Δ (in.)
0.00
25
0.04
0.12
0.00
0.04
0.08
Washer 4
20
Force (kN)
0.08
0.12
0.0
0.1
0.2
0.3
0.4
1st cycle
10th cycle
Washer 5
15
10
5
0
0.0
0.2
0.4
0.6
0.0
0.1
0.2
0.3
0.0
0.1
0.2
0.3
0.4
Deformation, Δ (cm)
(a)
(b)
(c)
Figure 4-17: Response of individual NiTi Belleville washers (Washer 4 and 5) under
cyclic compression. Plot (a) shows washer 1 cycled three times, (b) shows washer 2
cycled ten times, and (c) shows the first and tenth cycle of Washer 5.
60
4.8.2.
Single-Stacked
One of the issues with the testing in Phase I was the tendency of some of the washers to
invert. This resulted in sporadic behavior of a stacked assembly. Flat-washer spacers
were added in an attempt to prevent the washer from inverting, but this was not
successful. For the Phase II Test F, spherical washers (see Figure 4-18) were used as
spacers to prevent the washers from inverting and also limit the range of imposed
deformation. The spherical washers had a 3.0 cm (1.2 in.) inside diameter and a 5.7 cm
(2.25 in.) outside diameter.
The final test of Phase II (Test F) was done using a single-stacked 8-washer
configuration (Figure 4-19). Since thick spherical washers were used as spacers, the
deformation capacity of this configuration was only 4.1 cm (1.6 in.). The resulting forcedeformation behavior is shown in Figure 4-20. The recentering behavior of this stack
was good through the 1/3 Δmax cycle. However, beyond this the recentering became
poor because of accumulating residual deformations in each individual washer. The
energy dissipation also decreased as cycling continued, which was a direct result of the
residual accumulation. After the testing was completed, the assembly was examined
and there were no inverted washers.
To create an assembly with improved performance, it is suggested to train each
individual washer (as done in the individual test) and prevent the washers from buckling
by whatever means is deemed appropriate.
The training showed that behavior
degradation can be stabilized and the load drop-off effect can be reduced or eliminated.
61
Figure 4-18: Spherical washer used in Test F (McMaster-Carr, 2009).
Figure 4-19: Washer configuration for Test F.
Deformation, Δ (in.)
40
-0.5
0.0
0.5
1.0
1.5
Test F, Single Stacked Washers
Phase II
8 washers
Δmax = 3.66 cm
30
20
Force (kN)
-1.0
8
6
4
10
2
0
0
-10
-2
-20
-4
Force (kips)
-1.5
-6
-30
-8
-40
-4
-2
0
2
4
Deformation, Δ (cm)
1/3 Δ
Force (kN)
40
max
2/3 Δ
Cycle
max
Cycle
ζ = 8.30%
20
1st 3/3 Δ
ζ = 7.08%
max
3rd 3/3 Δ
Cycle
ζ = 4.26%
max
Cycle
ζ = 2.31%
0
-20
-40
-4
-2
0
2
4
-4
-2
0
2
4
-4
-2
0
2
4
-4
-2
0
2
4
Deformation, Δ (cm)
Figure 4-20: Force-deformation response of single-stacked washer configuration (Test
F).
62
4.9.
Conclusions
A SMA-based tension/compression device was investigated with two new forms of NiTi.
The results of this exploratory investigation showed promise, but clearly further work is
required. Particularly, the response of the NiTi helical springs was promising because of
the good superelasticity (as noted by the recentering), damping, and repeatability.
However, more research needs to be done to understand the stress levels in the spring
material and to determine if the springs can achieve full-scale load and stiffness levels.
Additional work needs to be done to better understand the effect of several design
parameters (coil diameter, pitch, and thickness) on the resulting strength values.
With regards to the NiTi Belleville washers, they behaved in a unique manner
that is traditionally undesirable in structural engineering (the load dropped off with
increased deformation).
However, the prospect of improving this behavior was
demonstrated through cyclic training and deformation demand reduction.
A key
attraction to using Belleville washers is the ability to stack them in numerous
arrangements to achieve a wide variety of force-deformation responses. However, work
needs to be done to improve the behavior of individual washers and verify the benefits of
training illustrated in this study. Furthermore, other applications should be explored,
such as implementing into a bolted beam-column connection.
63
CHAPTER 5
INVESTIGATION OF A RECENTERING BEAM-COLUMN
CONNECTION
5.1.
Introduction
In this chapter the conception, design, proof-of-concept testing, performance, and
behavior of a SMA-based recentering beam-column connection is presented. Since the
1994 Northridge earthquake, many different research initiatives have been undertaken to
create connections that have more robust performance under seismic loads. Numerous
vulnerabilities in fully restrained connections have resulted in the re-evaluation of their
partially restrained counterpart (i.e. bolted connections). This re-evaluation has shown
that properly detailed partially restrained connections have good seismic performance
(Murray, 1988; Ocel et al., 2004; Penar, 2005; Swanson and Leon, 2000). A SMAbased partially restrained connection is proposed in this research. The connection is
designed to have excellent ductility, yet maintain the ability to recenter after large drift
demands.
The experimental testing and results from five beam-column connection tests are
presented in the work herein. The connection was a modified version of the connection
previously tested by Penar (2005) at Georgia Tech.
Several enhancements to the
previous connection were made in order to ensure that all the inelastic deformations
were concentrated in the NiTi tendons. The performance of the connection is assessed
in terms of strength, stiffness, recentering, and damping. Additionally, the experimental
results are compared with analytical predictions from a simple model incorporating a
material object previously developed in OpenSEES by Fugazza (2003).
64
5.2.
Experimental Program
In this section a summary of the experimental procedures used to carry out the
recentering beam-column tests is presented. This includes details of the component
testing results, of the loading scheme, and of the instrumentation and data acquisition
plan.
A sketch of the connection is shown in Figure 5-1. The critical elements are the
following:
a) Shear tabs welded to the column flange and bolted to the beam web
b) L-shape anchor brackets
c) HSS transfer elements
d) SMA tendon elements
Further details of the connection are discussed in Section 5.3.
d)
c)
b)
B-B
a)
(a) front view
(b) side view, section B-B
Figure 5-1: An overview of the SMA beam-column connection.
5.2.1.
Component Testing
Various mechanical tests were performed to provide an understanding of the material
behavior of the elements that make up the connection. The mechanical test results for
the NiTi dogbone are shown in Figure 5-2a while the dogbone dimensions are shown in
65
Figure 5-2b.
After being cycled to 6% strain, the NiTi specimen displayed good
superelasticity with residual deformations of only 0.6%. The elastic modulus and the
yield stress (of the initial large cycles) was approximately 23.0 GPa (3340 ksi) and 325
MPa (47.0 ksi), respectively.
Mechanical test were also conducted on the steel and aluminum dogbones as
well as on two beam coupons. For these mechanical tests, the important quantities
(yield strength, elastic modulus, and the ultimate strain) were gleaned and the resulting
values are summarized in Table 5-1.
No coupons were tested from the column
specimen because of its sufficient overstrength. Beyond simple monotonic tests, several
cyclic tests were run in order to observe each materials cyclic behavior. For further
information on the mechanical tests, see APPENDIX B.
500
70
Stress (MPa)
50
300
40
30
200
Stress (ksi)
60
400
20
100
10
0
0.00
a)
0
0.01
0.02
0.03
0.04
0.05
Strain (EXT)
0.06
0.07
b)
Figure 5-2: The (a) stress-strain relationship of the NiTi dogbone and (b) the
corresponding dogbone dimensions (mm).
66
Table 5-1: Summary of the component mechanical tests.
Component Specimen
Beam-Column
Test
beam flange coupon
A-E
beam web coupon
A-E
steel tendon dogbone
A
steel tendon dogbone
B
NiTi tendon dogbone
D-E
AL tendon dogbone
E
5.2.2.
A,
cm2
(in2)
0.824
(0.128)
0.834
(0.130)
1.27
(0.196)
1.27
(0.196)
1.27
(0.196)
1.27
(0.196)
σy,
MPa
(ksi)
376
(54.5)
386
(56.0)
325
(47.1)
325
(47.0)
350
(50.8)
117
(17.0)
E,
GPa
(ksi)
197
(28600)
197
(28600)
197
(28600)
197
(28600)
32.5
(3340)
32.4
(4700)
εult
(%)
32
25
32
-
Loading Scheme
5.2.2.1. Loading Frame
The loading frame described in APPENDIX A was used as the platform for testing the
beam-column connection. The frame, with the SMA connection specimen, is shown in
Figure 5-3.
This frame was designed by fellow researcher Masahiro Kurata and
constructed by Kurata and the author. It was designed to be a flexible apparatus in
which numerous lateral-load-resisting systems could be tested. Further details of the
loading frame and a discussion of the frame-specimen interaction can be found in
APPENDIX A and APPENDIX B, respectively.
67
Figure 5-3: Loading frame schematic.
5.2.2.2. Loading Protocol
The connection was tested using the loading protocol from the SAC Steel Project as
shown in Figure 5-4 (SAC, 1997). The loading protocol consisted of 6 cycles at 0.375%,
0.50%, and 0.75% drift, followed by four cycles of 1% drift, and finished with two cycles
of 1.5%, 2%, 3%, and 4% drift.
performed.
For Test B-E an additional two cycles at 5% drift were
The SAC protocol was originally developed after the 1994 Northridge
Earthquake to investigate the behavior of fully-restrained welded moment connections,
and has since become a standard protocol for cyclic connection testing.
The drift angle was selected as the governing parameter for this protocol. The
load was applied in a quasi-static manner, at a rate of 51 mm (2.0 in.) per minute. This
protocol was implemented by manually inputting points into the ramp generator of the
MTS 407b controller, giving the operator step-by-step control of the loading.
68
6
5
4
Drift (%)
3
2
1
0
-1
-2
-3
-4
-5
-6
0
5
10
15
20
25
30
35
Cycle
Figure 5-4: The SAC loading protocol.
5.2.3.
Instrumentation and Data Acquisition Plan
In order to properly assess the performance of the beam-column connection, a variety of
sensors were utilized.
These sensors included load cells (LC), linear variable
displacement transducers (LVDT), string potentiometers (SP), extensometers (EXT),
and strain gauges (SG). A detailed layout of the instrumentation scheme is shown in
Figure 5-5 and Figure 5-6 . For a complete detailed schedule of the sensors employed,
see Table B-1 in APPENDIX B.
Data from the appropriate sensors was collected using a National Instruments
system connected to a Dell computer. The data was recorded every 0.9 seconds due to
limitations of the setup. Further details of the data acquisition system can also be found
in APPENDIX B.
69
50.8 [2.00]
bf/4
228.599 [9.00]
304.8 [12.00]
120Ω SG
(a) top view, section A-A
LVDT
A-A
bf/2
bf/4
Extensometer
228.6 [9.00]
B-B
bf/4
SG rosette
302.26 [11.90]
bf/2
(c) side view, section B-B
(b) front view
Figure 5-5: Instrumentation of specimen connection. Units in mm(in.).
47.466
actuator (with built-in
load cell and LVDT)
120Ω SG
144.78
167.64
137.795
18.415
16.51
pin load cell
string
potentiometer
Figure 5-6: Instrumentation of loading frame and specimen. Units in cm.
70
5.3.
Connection Details
The beam-column connection was designed to concentrate the inelastic deformation into
tendon “fuse” elements, while the rest of the connection remained elastic. It should be
noted that this was a proof-of-concept connection test; this connection was not intended
to be representative of a real connection that would be installed in a building. Issues
such as ease of installation and floor slab interference were ignored.
5.3.1.
Beams, Column, and Bracket Elements
Members left over from an investigation by Penar (2005) were used in this experimental
investigation. The beams and the column were W356x21 (W12x14) and W203x100
(W8x67) sections, respectively, and were made of A572 Grade 50 steel. The connection
was designed to fulfill the weak-beam strong-column requirements of the AISC seismic
provisions (AISC, 2005a). Additionally, the connection was designed to facilitate easy
modifications for future tests.
A picture of the connection is shown in Figure 5-7 and the details are given in
Figure 5-8.
This connection is designed to transfer moment primarily through the
coupled forces resulting from the HSS element bearing against the column face
(compression) and the tendons pulling against the stiffened bracket (tension).
The
anchor bracket and transfer element were made from a stiffened 152x102x9.23 mm
(6x4x3/8 in.) L-shape and a 102x76.2x6.35 mm (4x3x1/4 in.) HSS section. The L-shape
was stiffened with three 9.2 mm (3/8 in.) triangular plates, one in the middle and one on
each side.
The HSS was inserted to help transfer force from the L-shape bracket to the
column face and to increase the moment arm of the force couple. In previous work done
by Penar (2005) on a similar connection, the beam flange experienced local buckling
because of the large compression force transferred through the flange. The HSS added
71
stiffness to the beam flange, which effectively prevented the beam flange from buckling.
Additionally, after Test A was completed, the HSS was stiffened with a custom-fit 25.4
mm (1.0 in.) thick plate in order to prevent it from becoming inelastic.
This plate was
hammered into position at the center of the HSS member’s length.
Ultimately, the
addition of the HSS element resulted in a stiffer and stronger beam connection.
The L-shape bracket and HSS transfer element were connected to the flange of
the beam by A325 15.9 mm (5/8 in.) bolts and pretensioned per the turn-of-the-nut
method from the AISC 2005 Specification (AISC, 2005b). The bracket-beam connection
was designed as slip critical. The controlling moment (tension rupture at the bolt holes)
was found to be 73.9 kN-mm (654 kip-in). To ensure elastic performance in the beam,
the moment caused by the tendon-bearing couple was kept below this controlling
moment.
The connection details for the five tests (with the progressive changes in each
test noted) are shown in Figure 5-9. The bolts holding the HSS and L-shape elements
were left out for clarity. An additional set of brackets were attached to the inside of the
beam flanges to accommodate the additional tendons used in Test E. These brackets
were attached after Test A using the same bolts as the other brackets, as illustrated in
Figure 5-10.
72
Figure 5-7: Connection profile view.
(a) top view, section A-A
A-A
101.6x76.2x6.35
[4x3x14] HSS
12.7 [1/2] diameter
tendons (Steel or SMA)
152x102x9.23
[6x4x3 8 ] L-shape,
stiffened with 9.23 [3 8]
triangular plates
203.2 [8.00]
50.8 [2.00]
A325 bolts
B-B
165.1 [6.50]
101.6 [4.00]
shear tab
403.86 [15.90]
57.15 [2.25]
E70XX 9.53 [3 8]
fillet weld
101.6 [4.00]
47.625 [1.87]
3 bolts spaced
47.63 [1.875] apart
W356x21
[W12x14]
74.613 [2.94]
stiffeners, 9.23 [3 8]
triangular plates
W203x100
[W8x67]
(c) side view, section B-B
(b) front view
Figure 5-8: Connection details and dimensions. Units in mm (in).
73
steel
NiTi
martensitic
steel
NiTi
superelastic
NiTi
superelastic
HSS
stiffener
added
one
stiffener
(a) Test A
Figure 5-9:
testing.
AL
annealed
three
stiffeners
(b) Test B
(c) Test C
(d) Test D
(e) Test E
Connection details with highlighted differences over the progression of
additional
brackets
(a) front view
(b) side view, section B-B
Figure 5-10: Additional connection brackets for Test E.
5.3.2.
Shear Tab
A 203x127x6.35 mm (8x5x0.25 in.) plate was welded to both sides of the column face
using 9.5 mm (3/8 in.) beveled groove welds with E7018 electrodes to effectively transfer
the shear to the column. The shear tab had 17.5 mm (11/16 in.) holes slotted 25.4 mm
(1.0 in.) to accommodate the relative rotation expected between the beam and the
column. The beam was connected to the shear tab with three 16 mm (5/8 in.) bolts
tightened using a torque wrench to 135, 81, 81, 68 N-m (100, 60, 60, and 50 ft-lbs) for
74
Tests B, C, D, and E, respectively. For Test A, the bolts were hand tightened using a
250 mm (10 in.) long wrench, which provided a torque less than the lowest reading of 69
N-m (50 ft-lbs) on the torque wrench.
To assess the moment contribution of the shear tab connection and better predict
the experimental response of the entire setup, the connection was first tested without
tendons attached (shear-tab-only). This was done at various shear tab bolt torque levels
and the results are presented in Figure 5-11.
The shear tab friction provides a
significant contribution to the strength, stiffness, and energy dissipation in the positive
drift direction. However, once the beam was forced away from the column face and
there was nothing to pull it back (i.e. no superelastic tendons), the contribution of the
shear tab to the strength and stiffness was significantly decreased.
20
hand tight
68 N-m
81 N-m
108 N-m
136 N-m
Moment (kN-m)
10
150
100
5
50
0
0
-5
-50
-10
Moment (kip-in)
15
-100
-15
-150
-20
-0.04
-0.02
0.00
0.02
0.04
Drift
Figure 5-11: Tests ran on the connection with the shear tab bolts tightened to various
torque levels per a torque wrench. No tendons were installed.
75
5.3.3.
Tendon “Fuse” Elements
The tendon “fuse” elements were made from 19.1 mm (0.75 in.) diameter bar. Each bar
was machined, as shown in Figure 5-12, to concentrate the deformations in the reduced
section. The tendons were made from the following:
a) Unrated threaded steel rod, 19.05 mm (0.75 in) with 0.394 threads per mm
(10 threads per in), Test A
b) A36 steel, 19.05 mm (0.75 in) with 0.394 threads per mm (10 threads per in),
Test B
c) NiTi, martensitic (shape memory effect), 19.05 mm (0.75 in) with 0.63 threads
per mm (16 threads per in), Test C
d) NiTi, austenitic (superelastic), 19.05 mm (0.75 in) with 0.63 threads per mm
(16 threads per in), Test D and reused in Test E. Heat treatment: (1) 350 °C
for 0.5 hrs then air-cooled. (2) Machined per drawing. (3) 300 °C for 1.5 hrs
then immediately water-quenched.
e) 6061-T6 aluminum, annealed to achieve low strength, 19.05 mm (0.75 in) with
0.394 threads per mm (10 threads per in), Test E
Mechanical testing was performed on each type of material to determine the material
properties prior to implementing in the connection (as previously described in the
component testing section).
The tendon elements were each pretensioned after being inserted into the
connection. For the steel tendons in Test A and B, pretensioning was achieved by
cranking a torque wrench to 90 ft-lbs. This sufficiently snugged up the connection and
ensured there was good initial stiffness. For the NiTi tendons in Test C, D, and E, the
tendons were pretensioned to approximately 0.5% strain (as measured by high
76
elongation strain gauges). Further pretensioning was attempted but was not successful
due the tendency of the NiTi tendon to twist rather than allowing the nut to turn on the
threads.
Figure 5-12: Tendon details with threads 19.05-0.63 (3/4-16) UNF for the SMA tendon
and 19.05-0.394 (3/4-10) UNC for the steel and aluminum tendons. Units in mm (in.).
5.4.
Experimental Results
The results of the experimental tests are presented in this section. Additional figures
and information can be found in the supporting appendices.
The equations and
methodology used for data reduction can be found in APPENDIX C. Validation of the
results is detailed in APPENDIX D. For each test, the moment-rotation curves were
shifted in order to have the origin at the approximate center of the curves. This shifting
was done in an effort to further “zero” the connection data. The shifted amounts were in
the range of 1-2% of the data maximum. Complete data sets for all tests are given in
APPENDIX E. Only selected results are used for illustrative purposes in the following
discussions.
5.4.1.
Test A – Steel 1
In Test A, an unstiffened HSS transfer element and singly-stiffened L-shape anchor
brackets were used (refer to Figure 5-9). The tendon elements were made from 19.1
mm (0.75 in.) diameter threaded rod machined per Figure 5-12.
77
The shear tab bolts
were tightened by hand with a standard wrench (denoted “hand-tight” in Figure 5-11).
Test A was carried out in order to investigate the overall setup and to assess whether
any modifications needed to be made to the connection brackets before the NiTi tests
were performed. In addition, this test (along with Test B) provided benchmark data for
comparison purposes.
The left beam’s moment vs. concentrated rotation (hereafter moment-rotation)
relationship is presented in Figure 5-13. Similar response was seen in the right beam
and is shown in Figure E-4 of APPENDIX E. The connection remained elastic during the
0.375% drift cycles, but then began to show signs of yielding at the 0.5% drift level. Low
stiffness at small rotations and a hysteresis in the moment-rotation relationship were
observed.
Increasing the drift level resulted in a decrease in stiffness at small rotations and
an increase in hysteretic damping. These effects were due to yielding and friction in the
connection. Yielding occurred both in the tendon elements and in the connection HSS
and L-shape bracket members. The final residual strain in each steel tendon was 1.7,
1.7, 2.2, and 2.1% for the top-front (T1), top-back (T2), bottom-front (T3), and bottomback tendon (T4), respectively (Figure 5-14).
The stiffener in the L-shape bracket
experienced yielding and the HSS was noticeably deformed after the test was complete.
This was the result of the high level of compression transferred from the tendon
attachment point to the column flange face. Since the bracket yielding was not desired,
stronger brackets were fabricated for Tests B-E.
78
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
M
(+)
-60
-700
-0.04
-0.03
6 cycles at Δ = 0.00375
-0.02
-0.01
0.00
θconc.
0.01
0.02
6 cycles at Δ = 0.0050
0.03
0.04
0.05
6 cycles at Δ = 0.0075
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
4 cycles at Δ = 0.015
2 cycles at Δ = 0.02
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
Moment (kN-m)
80
Moment (kip-in)
Moment (kN-m)
80
6 cycles at Δ = 0.01
2 cycles at Δ = 0.03
2 cycles at Δ = 0.04
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-80
-0.04
-0.02
0.00
0.02
0.04
-0.04
-0.02
0.00
θconc.
0.02
θconc.
θconc.
-700
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-13: Moment vs. concentrated rotation for the left beam in Test A.
79
Moment (kip-in)
Moment (kN-m)
80
-525
Moment (kip-in)
-80
-0.05
Moment (kip-in)
Moment (kN-m)
80
Residual Strain
0.05
T1
T2
T3
T4
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
Drift (%)
Figure 5-14: Residual strain (EXT) in tendons at end of each drift level for Test B.
5.4.2.
Test B – Steel 2
After the conclusion of Test A, the beams were removed and the connection brackets
were modified in order to correct the observed deficiencies.
fabricated with the intent of ensuring elastic behavior.
New brackets were
The new HSS pieces were
stiffened with a custom fit 25.4 mm (1 in.) thick steel plate, which virtually eliminated any
potential yielding in the HSS section. New L-shape brackets were stiffened with three
triangular stiffeners in lieu of the single stiffener used in Test A. Additionally, the shear
tab bolts were tightened to 135 N-m (100 ft-lbs) with a torque wrench.
These modifications were done to prevent the anchor brackets from becoming
inelastic during the test, but are in no way suggestive of the most economical or efficient
connection design. Further comments on realistic connection design are made later in
this chapter in Section 5.5.6.
As with Test A, Test B was another “test-run” for the NiTi tests. A36 steel bars
were used as the tendon elements. Before presenting the results, it should be noted
that after the test was completed it was observed that the bolts connecting the right
beam to the pin-clevis-assembly end were only loosely tightened.
80
This oversight
resulted in unexpected performance from the right beam (and consequently the
connection), so the data should be interpreted in context of this error.
The connection remained elastic through the 0.75% drift cycles. During the
reverse stroke of the first 1.0% drift cycle, tendon T3 began to yield, resulting in
approximately 0.4% residual strain in the tendon, as shown in Figure 5-16. However,
while this took place, the connection’s global performance remained mostly elastic with
only a slight hysteresis in the moment-rotation curve. Once further cycles were imposed
at 1.0% drift, the tendon’s residual strain increased, reaching approximately 0.7% after
the final 1.0% cycle.
A small, but increasing, hysteretic loop was observed in the
moment-rotation curve indicating some influence of a small amount of tendon yielding
and the inherently present friction in the shear tab connection. The stiffness of the
connection remained constant at approximately 10 kN-m/rad (89 kip-in/rad).
During the forward stoke of the first cycle at 1.5% drift, tendon T4 began yielding,
resulting in approximately 0.8% residual tendon strain. Tendon T3 also experienced
further yielding during this step, resulting in approximately 1.3% residual strain.
Additionally, tendon T1 yielded both in the forward and reverse steps; resulting in
approximately 0.3% residual drift after the first cycle was completed. This resulted in a
large hysteretic loop being formed during the forward portion of the first cycle at 1.5%
drift and smaller hysteretic loops being formed during the rest of the 1.5% cycles.
Reduced stiffness was observed in the first cycle’s backward loading due to the
gap developed between the beam and the column face. This softening can be attributed
to the gap opening caused by the yielded tendons’ tendency to force the beams away
from the face of the column.
This gap effectively prevented moment from being
transferred by the tendon-bearing couple until the beam end brackets contacted the
column face at a sufficiently high drift level. Since the connection was designed with the
expectation that the tendons would pull the beams back into contact with the column
81
face (via superelastic tendons), this gap opening was an expected phenomena for the
steel tendon tests (Test A-B).
Upon the application of the first forward cycle at 2.0% drift, all of the tendons
yielded in nearly equal amounts. On the reverse cycle, more yielded was induced in
each bar. This first cycle of 2.0% drift added approximately 1.0% residual strain in each
tendon. The yielding further softened the connection by increasing the gap between the
beam end and the column face. The increase connection softness began to expose the
friction based hysteretic loop that was formed around the x-axis (caused by the bolted
shear tab).
Further cycling resulted in a similar pattern of yielding tendons and reduced
connection stiffness. During the 4.0% drift level, the connection had negligible stiffness
until the concentrated rotation reached approximately 2%. The hysteretic loops in the
moment-rotation plots for the left beam tended to be larger in the second quadrant
(negative moment, positive rotation) because the forward loading cycle induces the bulk
of the tendon yielding. After the 4% drift cycles were completed the test was stopped.
82
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
M
(+)
-0.01
0.00
θconc.
0.01
0.02
6 cycles at Δ = 0.005
0.03
0.04
-700
0.05
6 cycles at Δ = 0.0075
700
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
80
Moment (kN-m)
6 cycles at Δ = 0.00375
-0.02
60
-80
4 cycles at Δ = 0.010
-700
2 cycles at Δ = 0.015
2 cycles at Δ = 0.02
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-80
80
Moment (kN-m)
-0.03
-700
2 cycles at Δ = 0.03
2 cycles at Δ = 0.04
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.04
-0.02
0.00
0.02
Moment (kip-in)
Moment (kN-m)
80
-0.04
Moment (kip-in)
-80
-0.05
-525
0.04
-0.04
-0.02
0.00
θconc.
θconc.
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-15: Moment vs. concentrated rotation for the left beam in Test B.
83
Moment (kip-in)
-60
Moment (kip-in)
Moment (kN-m)
80
Residual Strain
0.05
T1
T2
T3
T4
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
Drift (%)
Figure 5-16: Residual strain (EXT) in tendons at end of each drift level for Test B.
5.4.3.
Test C – SMA 1
Test B demonstrated that the modifications from Test A produced a connection that
concentrated the inelastic deformations solely into the tendons. After the conclusion of
Test B, the steel tendons were removed and NiTi tendons were installed.
These
tendons were once again from previous connection testing done by Penar. The exact
processing and properties of the bars were unknown. It was unknown whether the bars
were superelastic due to the previous research’s inability to strain the tendons into the
phase transformation range. As the results of Test C confirmed, the NiTi tendons were
in the martensitic form (SME), rather than having superelastic behavior.
Nevertheless, the assumption was made before the test that the tendons were
superelastic. To encourage recentering and ensure good initial stiffness, each bar was
pretensioned to 0.5% strain as measured by the installed high elongation strain gauges.
Additionally, the shear tab bolts were tightened to 81 N-m (60 ft-lbs) per a torque
wrench.
The connection remained elastic until the first cycle of 0.5% drift load step in which
all tendons had residual strains up to approximately 0.1%. As seen in the previous two
84
tests, this caused some slight loss of stiffness in the moment-rotation response and a
slight hysteresis was formed in both the forward and reverse loading directions.
Significant loss of stiffness was not observed until the 0.75% load, in which the stiffness
went from 4.1 (36) to 3.6 kN-m/rad (32 kip-in/rad) for the last cycle at 0.5% to the first
0.75% cycle, respectively.
This stiffness degradation was due to the continued
unrecovered strains in the tendons.
It should be noted that the residual tendon strain was not due to yielding, as in
ordinary metals, but rather due to one of the following two phenomena:
1) the
superelastic NiTi’s crystal structure transforms from austenite to martensite and then,
due to lack of superelasticity, the strain is not automatically recovered or 2) the
martensitic NiTi’s crystal structure transforms from twinned martensite to detwinned
martensite and retains this residual strain until heated to a specified temperature. Since
the assumption was that the tendons were superelastic, heat was not applied to the
tendons until the testing protocol was completed.
Further loading continued to result in residual strain accumulation in the NiTi
tendons at varying degrees. The residual accumulation trend for each tendon is shown
in Figure 5-18. The final residual strains in the tendons were 0.038, 0.035, 0.044, and
0.035 for tendons T1, T2, T3, and T4, respectively. This accumulation of residual strain
shifted the beam away from the column face, resulting in initial softness in the
connection until the beam rotated sufficiently to bear against the column face (similar
trend seen in Test A and B).
Upon completion of the loading protocol, the left and right beams had shifted
away from the face of the column creating a gap of approximately 6.4 mm (0.25 in) and
5.9 mm (0.23 in). To investigate the NiTi shape memory properties, a heat gun was
used to recover the strain in the presumed detwinned martensite. After heating all the
tendons for approximately 30 seconds, both the left and right gaps closed significantly,
85
resulting in a 1.6 mm (0.125 in) gap on both sides. As stated previously, the connection
was designed for superelastic tendons therefore further testing was not carried out even
though the majority of the residual strain was recovered. During Tests B and C, the
residual elongation of the tendons produced softening in the connection rather than
added damping. If the connection was designed to force the tendons into both tension
and compression, added damping would have occurred.
86
700
60
525
40
350
20
175
0
0
-175
-20
-350
-40
M
(+)
-0.03
6 cycles at Δ = 0.00375
-0.02
-0.01
0.00
θconc.
0.01
0.02
0.03
0.04
-700
0.05
6 cycles at Δ = 0.0075
6 cycles at Δ = 0.005
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
4 cycles at Δ = 0.010
2 cycles at Δ = 0.02
2 cycles at Δ = 0.015
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
Moment (kN-m)
80
Moment (kip-in)
Moment (kN-m)
80
2 cycles at Δ = 0.03
2 cycles at Δ = 0.04
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.04
-0.02
0.00
0.02
0.04
-0.04
-0.02
θconc.
0.00
θconc.
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-17: Moment vs. concentrated rotation for the left beam in Test C.
87
Moment (kip-in)
Moment (kN-m)
80
-0.04
-525
Moment (kip-in)
-60
-80
-0.05
Moment (kip-in)
Moment (kN-m)
80
Residual Strain
0.05
T1
T2
T3
T4
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
Drift (%)
Figure 5-18: Residual strain (EXT) in tendons at end of each drift level for Test C.
5.4.4.
Test D – SMA 2
Since the NiTi tendons of Test C did not exhibit superelastic behavior, new bars were
machined and heat treated as per the protocol recommended by McCormick (2006).
The NiTi bars were first heat treated to 350 °C for 30 min. and air cooled, then machined
to the appropriate tendon size (see Figure 5-12), and finally heat treated again to 300 °C
for 1.5 hrs. and immediately water quenched. The NiTi dogbone specimen shown in
Figure 5-2 also used this protocol. The new tendons were installed and prestrained to
approximately 0.5% (as measured by the mounted strain gauges).
The connection remained elastic through the 0.5% drift level. After the forward
stroke of the first 0.75% drift cycle, a small amount of residual deformation was recorded
in tendon T2 (top-back) while the other tendons exhibited full recentering. Additionally,
small hysteretic loops were observed in the beam-column moment-rotation during this
drift step.
Initial stiffness remained steady through the 0.75% drift level for the left beam.
However, the initial stiffness for the right beam displayed some softness even during the
small 0.375 and 0.5% drift levels.
This phenomenon became especially noticeable
88
during the 0.75% drift cycles, in which the NiTi tendons were reaching strains of up to
0.28%. As shown in Figure 5-20, the residual strains in the tendons remained negligible.
During the 1.0% and 1.5% drift cycles, the left beam had good recentering,
moderate hysteretic loops, and little-to-no softening in its moment-rotation response. In
contrast, the right beam continued lag in performance compared to the left beam,
perhaps due to the loading sequence (push to the right, then to the left). The right
beam’s initial moment-rotation softness and residual rotation continued to slowly grow.
Upon loading into the 2.0% drift level, the connection began to display a more
recognizable flag-shaped hysteretic loop characteristic of superelastic NiTi. The strains
induced in the tendons were between 1.25% and 1.50%, which indicated that the initial
part of the phase transformation had been reached.
Once the 3.0% drift level was imposed, the tendons were strained up to 3.25%,
which was well into the phase transformation range. The flag-shaped hysteresis of the
moment-rotation behavior became more pronounced and recentering was still fully
achieved in the left beam. Residual rotations (and thus initial softness) continued to
increase slowly in the right beam’s response. Furthermore, there was slight stiffness
and strength degradation in the connection, most assuredly due to the degradation of
NiTi’s mechanical behavior as seen in mechanical tests.
During the 4.0% drift level, the tendons were strained up to approximately 5.0%,
which was approaching the zone where all the austenite has transformed to martensite.
From this stage and beyond, it was expected that there would be increased residual
rotation accumulation based on the tendency of deformations to be accommodated by
plastic strains (dislocation movements) in lieu of phase transformation at high strain
levels. As expected, the residual accumulation contributed to the flag-shaped hysteresis
continuing to enlarge. At this point, some slight initial softness was finally observed in
the left beam moment-rotation while the right beam moment-rotation continued to have
89
increased initial softness. Additionally, continued strength degradation was observed as
a result of the NiTi tendons mechanical characteristics.
The final 5.0% drift cycles induced on the connection were performed to push the
tendons further along their stress plateaus.
Both beams moment-rotation response
showed increased initial softness. For the left beam, a very small stiffness was recorded
for approximately +/- 0.00125 radians (2.8% of the total). Upon returning to the zero
position, the tendons exerted a recentering force until 0.0025 radians (5.6% of the total).
For the right beam, a very low stiffness was observed for approximately +/- 0.005
radians of rotation (10% of the total). Upon returning to the zero position, the tendons
kept the recentering force until 0.009 radians (20 % of the total). After the testing was
completed, there was no gap between the left beam and the column face. In contrast,
there was a 3.0 mm (0.125 in.) gap between the right beam and the column face, which
was expected due to the loss of initial stiffness observed during the test.
90
700
60
525
40
350
20
175
0
0
-175
-20
-350
-40
M
(+)
-0.03
6 cycles at Δ = 0.00375
-0.02
-0.01
0.00
θconc.
0.01
0.02
6 cycles at Δ = 0.005
0.03
0.04
-700
0.05
6 cycles at Δ = 0.0075
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
4 cycles at Δ = 0.010
2 cycles at Δ = 0.015
2 cycles at Δ = 0.02
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
Moment (kN-m)
80
Moment (kip-in)
Moment (kN-m)
80
2 cycles at Δ = 0.04
2 cycles at Δ = 0.03
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.04
-0.02
0.00
0.02
0.04
-0.04
-0.02
θconc.
0.00
θconc.
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-19: Moment vs. concentrated rotation for the left beam in Test D.
91
Moment (kip-in)
Moment (kN-m)
80
-0.04
-525
Moment (kip-in)
-60
-80
-0.05
Moment (kip-in)
Moment (kN-m)
80
Residual Strain
0.05
T1
T2
T3
T4
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
Drift (%)
Figure 5-20: Residual strain (EXT) in tendons at end of each drift level for Test D.
5.4.5.
Test E – SMA 2 + AL (PARA)
With the positive results from Test D, the effect of adding an additional element in
parallel with the NiTi tendons was pursued. The intent was to provide additional energy
dissipation without losing the recentering capability.
This was done by adding low
strength aluminum (AL) tendons to interior connection anchor brackets. These AL bars
were encased with a 19.1 mm (0.75 in.) interior diameter steel tube in order to limit
buckling.
The connection remained elastic through the 0.50% drift cycles, as with Test D.
After the first cycle at 0.75% drift, both the NiTi tendons and the AL tendons displayed
slight residual strains according. Small hysteretic loops were observed in the momentrotation curves for both beams. The initial stiffness remained stable with full recentering
occurring after each cycle.
During the 1.0% drift level, the AL tendons reached a strain of up to 0.42%, well
above the yield strain of 0.36%. Upon returning to the zero position, the AL tendons
were forced into compression due the NiTi tendons’ superelastic restoring force. Due to
the AL tendons small moment of inertia, the bars easily buckled until they were inhibited
92
by both the steel tube encasing and the column flange holes.
This led to double
curvature buckling at both ends of the tendons and unknown buckling inside the steel
tube. Even with this phenomenon taking place, the connection continued to display
good stiffness and recentering which indicated that the NiTi tendons were retaining good
superelasticity.
During the first and second 1.5% drift cycles, the connection began to lose
stiffness at small drift levels. This softening effect can be attributed to the increased
yielding and buckling of the AL tendons and the residual strain accumulation in the NiTi
tendons. At the end of the second 1.5% drift cycle, the residual strains in the NiTi
tendons were 0.02, 0.05, 0.03, and 0.05% for the T1, T2, T3, and T4 tendons,
respectively. These small values indicate the connection still had a large amount of
recentering capability.
Further loading cycles resulted in a continued increase in the hysteretic loop area
and continued softening in both beam moment-rotation relationships. The residual strain
in the tendons had its first noticeable increase during the 3.0% drift level. During the 4
and 5.0% drift cycles, the residual strains continued to increase in tendon T3, but
decreased in the other three tendons.
During the 5.0% drift cycles, both beams had reduced stiffness near the origin
(as seen in Figure 5-21).
For the left beam, a small stiffness was observed for
approximately +/- 0.0035 radians (7.8% of the total). Upon returning to the zero position,
the tendons exerted a recentering force until 0.006 radians (13% of the total).
For the
right beam, a small stiffness was observed for approximately +/- 0.005 radians (10% of
the total). Upon returning to the zero position, the tendons kept the recentering force
until 0.0075 radians (17% of the total). After the testing was completed, no gap was
present between the left beam and the column face. In contrast, there was a 3.0 mm
93
(0.125 in.) gap between the right beam and the column face, which was exactly what
was seen in Test D.
94
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
M
(+)
-80
-0.05
-0.03
6 cycles at Δ = 0.00375
-0.02
-0.01
0.00
θconc.
0.01
0.02
6 cycles at Δ = 0.005
0.03
0.04
-700
0.05
6 cycles at Δ = 0.0075
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
2 cycles at Δ = 0.02
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
Moment (kN-m)
80
Moment (kip-in)
Moment (kN-m)
80
2 cycles at Δ = 0.015
4 cycles at Δ = 0.010
2 cycles at Δ = 0.04
2 cycles at Δ = 0.03
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.04
-0.02
0.00
0.02
0.04
-0.04
-0.02
θconc.
0.00
θconc.
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-21: Moment vs. concentrated rotation for the left beam in Test E.
95
Moment (kip-in)
Moment (kN-m)
80
-0.04
-525
Moment (kip-in)
-60
Moment (kip-in)
Moment (kN-m)
80
Residual Strain
0.05
T1
T2
T3
T4
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
Drift (%)
Figure 5-22: Residual strain (EXT) in tendons at end of each drift level for Test E.
5.5.
5.5.1.
Discussion of Results
General Behavior
While the previous section presented the performance of the five beam-column tests,
this section takes an in-depth look into these results and tries to explain the underlying
behavior. Comparisons between the tests are made in order to demonstrate the ability
of the superelastic NiTi to provide the restoring force for the recentering system. While
the ultimate goal is to produce and validate a model that corresponds well with the
experimental results, many different trends are explored along the way. These trends
include changes in stiffness, strength, energy dissipation, and recentering.
5.5.1.1. Average Response
In order to simplify the discussion, the average of the left and right beam’s momentrotation was taken. This average was obtained by the following equations:
M AVG =
96
(M R − M L )
2
(5.1)
θ AVG =
(θR + θ L )
2
(5.2)
The average moment was obtained by switching the sign of the left beam in order to
obtain a sign convention in which the average moment is positive when the frame is
moved to the right of center. This averaged moment-rotation relationship and the sign
convention are shown in the upper left of Figure 5-23. Since the left and right beams
were not independent of each other due to the shared tendon configuration, the average
moment-rotation is a reasonable representation of the overall connection behavior. In
addition, the overall connection response can be easily found by doubling the average
moment values.
97
700
60
525
40
350
20
175
0
-20
-175
-40
-350
-60
-525
-0.03
6 cycles at Δ = 0.00375
-0.02
-0.01
0.00
θconc.
0.01
0.02
6 cycles at Δ = 0.005
0.03
0.04
-700
0.05
6 cycles at Δ = 0.0075
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
4 cycles at Δ = 0.010
2 cycles at Δ = 0.015
2 cycles at Δ = 0.02
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
Moment (kN-m)
80
Moment (kip-in)
Moment (kN-m)
80
2 cycles at Δ = 0.04
2 cycles at Δ = 0.03
2 cycles at Δ = 0.05
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.04 -0.02
0.00
0.02
0.04
-0.04 -0.02
θconc.
0.00
θconc.
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-23: The averaged connection moment vs. concentrated rotation for Test D.
98
Moment (kip-in)
Moment (kN-m)
-0.04
Moment (kip-in)
-80
-0.05
80
0
Moment (kip-in)
Moment (kN-m)
80
5.5.1.2. Response Path
Before the response parameters are examined, it is helpful to look at an individual
moment-rotation curve for the NiTi tendon tests. Figure 5-24 shows the moment-rotation
curve for the first 5% drift cycle for the superelastic SMA test (Test D). This test was
selected because it exhibited all of the different transition points. The transition points (a
through g) are plotted to help delineate the different phenomena that were occurring as
the connection was cycled.
During small rotations levels of the loading portion, the connection was prone to
stiffness degradation due to the accumulating residual strains in the tendons, as denoted
from points a to a’ in Figure 5-24. From point a’ to b, the combined tension in the
tendons and the friction in the shear tab resulted in an approximate linear momentrotation stiffness. Once point b was reached, the NiTi began to transition into its phase
transformation region. At point c, the SMA had presumably reached the stress in which
the austinite began to transform into detwinned martensite, which allowed the increased
accommodation of strain with smaller changes in stress. At point d, the austinite had
almost fully transformed to martensite, and there was some indication of the stiffer
martensitic behavior being displayed.
For the unloading portion, the tendons remained in the detwinned martensite
phase until the transition started to happen at point e and was completed at point f. At
point f, the detwinned martensite began to fall back into the austinite phase, because it
was more stable at the lower stress levels.
From point f to g’, the NiTi tendons
attempted to pull back the connection because of the reverse phase transformation.
Because of the resistance caused by the shear tab friction and the trend of residual
accumulation in the NiTi, point g’ fell somewhere to the right of point g. This distance is
defined as the residual rotation in the connection. Further cycling resulted in this path
being followed all over again, with the previous cycle affecting the current cycle.
99
It should be noted that if both points a-a’ and g-g’ are at the same coordinates,
then full recentering would be obtained. Additionally, when the frame was loaded and
unloaded in the opposite direction (frame moves to the left for the loading), the resulting
behavior was similar.
1st cycle at Δ = 0.050
80
700
525
40
20
a
0
b
a'
350
c
e
f
0
g g'
-20
175
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
60
d
Test D
-700
-80
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-24: Example moment-rotation response for Test D.
5.5.2.
Yield Moment and Effective Stiffness
The cyclic curves for the first cycle at 2.0% and 5.0% drift are shown in Figure 5-25.
Straight lines were overlaid in order to approximate the effective stiffness, Keff, and
“yielding” moment, My, of the connection (where “yielding” is really phase transformation
for the SMA). The line for determining the stiffness was drawn asymptotically to the
forward and reverse loading curves and runs approximately through the origin as
depicted in Figure 5-25. In order to determine the “yielding” plateau, another line was
drawn. For the smaller drift cycle (2.0% and below), the “yield” plateau was difficult to
determine. Using Figure 5-23 as a gauge, it was determined that a “yielding” plateau
100
was not reached for drift levels at and below 1.5%. This observation is supported by the
strain levels observed in the tendons (Figure E-55 through Figure E-58).
For each cycle, the Ke and My were determined using the described
methodology. The change in My over the range of drift is shown in Figure 5-26 for Tests
B, D, and E. The My for Test C is not reported because of an indistinguishable yielding
point (however, it is clear that the connection yielded by looking at the residual
accumulation in both the tendons and overall connection). For tests B, D, and E, My was
not fully reached for drift levels below 1.5%. Conversely, for drift levels at and above
1.5%, the My for Test B increased steadily while that of Test D and E remained fairly
constant. The increase in My for Test B is justified by the strain hardening that occurred
in the A36 tendons. The relatively constant trend of My vs. drift level for Tests D and E is
attributed to the NiTi and AL tendons’ stable hysteretic behavior.
The change in Ke is shown in Figure 5-27 for Tests B-E. All connections lost
stiffness at larger drift levels due to the accumulation of residuals in the setup. For Test
B, Ke dropped from 2.0e4 kN-m/rad (1.77e5 kip-in/rad) to 2.8e3 kN-m/rad (2.48e4 kipin/rad) over the drift range. This dramatic decrease was due to the yielding of the steel
tendons, resulting in the Ke being governed by the initial softness of the connection
rather than the tendon material stiffness. Test C had a similar trend to that of Test B, but
with lower values due to the smaller elastic modulus of NiTi compared to that of steel.
For Test D, the stiffness during the 5.0% drift level was more than half of the stiffness
during the initial drift levels due to the superelastic behavior of the NiTi tendons. This
behavior was the result of reduced residual deformations.
Finally, for Test E, the initial
stiffness of the connection was greater than that of Test D due to the additional AL
tendons.
The AL tendons yielded during the 0.0375% and 0.5% drift levels which
resulted in reduced connection stiffness. For drift levels greater the 0.5%, the trend of
the Ke for Test E was comparable to that seen in Test D. During the repeated cycling of
101
the connection, the AL tendons were forced into compression buckling by the
superelastic NiTi tendons. This buckling limited the effectiveness of the AL tendons at
low drift levels which explains the similarity between Test D and E’s Ke trends. However,
once the AL tendons became fully engaged the resulting parallel action of the AL and
NiTi tendons produced a slightly stronger connection, which can be seen when
comparing Figure 5-19 to Figure 5-21.
1st cycle at Δ = 0.020
1st cycle at Δ = 0.050
80
Test D
40
My
20
Ke
525
350
My
175
Ke
0
0
-20
-175
-40
-350
approximation
experimental data
-60
-80
-0.04
-0.02
0.00
θconc.
0.02
0.04
(a)
approximation
experimental data
-0.04
-0.02
0.00
θconc.
0.02
-525
-700
0.04
(b)
Figure 5-25: Straight line approximation of the M-θ response to get My and Ke.
102
Moment (kip-in)
Moment (kN-m)
60
700
Test D
600
60
My not
reached
450
40
300
20
150
0
Yield Moment, My (kip-in)
Yield Moment, My (kN-m)
80
Test B
Test D
Test E
0
0
1
2
3
4
5
Drift (%)
2.5e+4
2e+5
2.0e+4
2e+5
1.5e+4
1e+5
1.0e+4
5e+4
5.0e+3
0.0
0
0
1
2
3
4
Effective Stiffness, Ke (kip-in/rad)
Effective Stiffness, Ke (kN-m/rad)
Figure 5-26: My over a range of drift levels for Tests B, D, and E.
Test B
Test C
Test D
Test E
5
Drift (%)
Figure 5-27: Effective stiffness, Ke, over a range of drift levels for Tests B-E.
5.5.3.
Residual Rotation
The change in stiffness in the connection was mainly due to the accumulation of
residuals in the respective steel, AL, or NiTi tendons and each tendon’s inability to
completely overcome the forces resisting recentering.
The connection residual was
defined as the point in which the slope changes on the unloading curve as shown in
103
Figure 5-28. This point was manually approximated for each cycle and the trend is
shown in Figure 5-29. For Test B, the residual rotation, θres, began accumulating during
the 1.5% drift level and linearly increased to 0.025 rad at 4% drift (recall Test B was not
cycled to 5%). For Test C, θres began to accumulate at an earlier 0.75% drift and then
increased linearly to 0.028 rad at 5.0% drift. This earlier accumulation was the result of
the smaller NiTi elastic modulus which enabled the connection to strain the tendons
more at smaller drift levels.
The superelastic NiTi connection tests resulted in a clear reduction in residuals
(as expected). For Test D, θres accumulation was not observed until the 1.0% drift level,
and then increased in a semi-linear fashion to 0.006 rad at 5.0% drift. For Test E, θres
accumulation was not observed until the 1.5% drift level and then increased in a semilinear fashion to 0.007 rad at 5.0% drift. The larger residual accumulation observed later
in Test E compared to Test D was most likely due to the training that the NiTi tendons
had already been through since the same physical tendons were used for both Test D
and Test E.
1st cycle at 5% drift
80
525
40
350
20
175
0
0
-20
-175
θres
-40
-350
Moment (kip-in)
Moment (kN-m)
60
700
Test D ( superelastic NiTi )
-525
-60
-700
-80
-0.04
-0.02
0.00
0.02
0.04
θconc.
Figure 5-28: Definition of residual rotation, θres.
104
Residual Rotation, θres (rad)
0.030
0.025
0.020
Test B
Test C
Test D
Test E
0.015
0.010
0.005
0.000
0
1
2
3
4
5
Drift (%)
Figure 5-29: Residual Rotation, θr, over a range of drift levels for Tests B-E.
5.5.4.
Energy Dissipation
During a seismic event, the earth imparts a certain amount of energy into a structure that
must be either dissipated through inelastic action and damping or stored and released
elastically. Energy dissipation provided by a connection generally has beneficial effects
on the performance of the structure. As investigated in CHAPTER 3 of this thesis, it has
been found that the right combination of energy dissipation and recentering creates a
system that has reduced maximum deformations and limited residual strains. However,
recentering has also been found to generally create increased acceleration demands in
comparison to an equivalent elastoplastic system (Wang and Filiatrault, 2008).
Therefore, the properties of a recentering system need to be properly balanced in order
to produce a good performing system.
The energy dissipation for the first cycle at each drift level is shown in Figure
5-30. The cumulative energy dissipation for the first cycle at each drift level is shown in
Figure 5-31: Cumlative hysteretic energy dissipated for the 1st cycle of each drift step
vs. drift level for Test B-E.Figure 5-31. At first glance, it is surprising that the energy
105
dissipation in Test B was greater than or equal to that of the other tests at drift levels up
to the 4%. However, recall the effects of the shear tab bolt tightening shown in Figure
5-11. These different torques explain the larger than expected energy dissipation for
Test B and C.
In structural engineering it is customary for damping to be quantified by
calculating the equivalent viscous damping ,ζ, as shown in Figure 5-32 (first cycle) and
Figure 5-33 (second cycle). The ζ varied from 2-14%, with the first cycle generally
greater than that of the second cycle. Test A and B had the most notable drop in ζ from
cycle 1 to 2, with values dropping 75% at some drift levels. Test D (superelastic SMA)
and Test E maintained ζ of 5-13% over the entire range, with ζ values increasing as drift
levels increased.
Energy dissipation can be generally associated with improving structural
response by decreasing drifts and accelerations. However, several studies have come
to different conclusions on the need for energy dissipation in recentering systems. As
pointed out in the literature review (CHAPTER 2), the research performed on PT
recentering systems and corresponding SDOF systems indicate that recentering
systems can produce response on par with systems focused on dissipating energy. The
SDOF study done as part of this research (CHAPTER 3), demonstrated that there can
be improvement in response by increasing the hysteretic area of a recentering system.
However, the results of this SDOF suggest that recentering is the driving factor in the
response; therefore energy dissipation is only an added secondary benefit.
Furthermore, a fairly extensive analysis of partially-restrained moment frames performed
by Taftali (2007) demonstrated that neither recentering nor energy dissipation produces
the optimal response over a range of hazard levels. Rather, Taftali concluded that it
may be beneficial to incorporate both recentering and energy dissipation elements into
106
the same system to optimize the performance while understanding that increased
3.0
25
1st cycle at each drift level
2.5
20
2.0
15
1.5
10
1.0
5
0.5
0.0
0
0
1
2
3
4
5
Energy Dissipated per Cycle (kip-in)
Energy Dissipated per Cycle (kN-m)
recentering results in reduced system residual deformations.
Test B
Test C
Test D
Test E
6
Drift (%)
12
100
1st cycle at each drift level
10
80
8
60
6
40
4
20
2
0
0
0
1
2
3
4
5
6
Cumlative Energy Dissipated (kip-in)
Cumlative Energy Dissipated (kN-m)
Figure 5-30: Hysteretic energy dissipated for the first cycle of each drift step vs. drift
level for Test B-E.
Test B
Test C
Test D
Test E
Drift (%)
Figure 5-31: Cumlative hysteretic energy dissipated for the 1st cycle of each drift step
vs. drift level for Test B-E.
107
Equivalent Viscous Damping, ζ (%)
20
1st cycle at each drift level
15
Test A
Test B
Test C
Test D
Test E
10
5
0
0
1
2
3
4
5
Drift (%)
Equivalent Viscous Damping, ζ (%)
Figure 5-32: Equivalent viscous damping of the first cycle at each drift level for each
test.
20
2nd cycle at each drift level
15
Test A
Test B
Test C
Test D
Test E
10
5
0
0
1
2
3
4
5
Drift (%)
Figure 5-33: Equivalent viscous damping of the second cycle at each drift level for each
test.
5.5.5.
Connection Modeling
5.5.5.1. Predicted Behavior Comparison
The response of the beam-column connection was governed by three parameters: (1)
the mechanical properties of the tendons, (2) the location and behavior of the pivoting
108
surface, (3) and the friction resistance of the shear tab. Assuming that the pivoting
surface behavior is known and the bracket elements do not slip and remain effectively
rigid, the contribution from the tendons and the shear tab are of most interest. In order
to understand the response of the shear tab, some cyclic tests were carried out without
tendons in place (as shown previously in Figure 5-11). These shear-tab-only tests were
used to calibrate the shear tab elements in the connection model. Correspondingly, the
mechanical tests on each material type (steel, NiTi, and AL) were used to calibrate the
behavior of each tendon in the connection model.
The overall response of the beam-column connection was predicted quite well by
a relatively simple model developed in OpenSEES. The model, shown in Figure 5-34,
incorporated the various actions of the connection by using an appropriate combination
of elements. The full loading frame was modeled because of its kinematic contribution
to the connection response. The tendons were modeled as truss members with either
Steel02 or SMA material properties. The shear tab was modeled by connecting two
nodes and an elastic no-tension (ENT) element. This ENT element was calibrated to
give the corresponding stiffness and yield moment as observed in the shear-tab-only
tests (Figure 5-11).
The predicted response is plotted along with the experimental response for Test
D in Figure 5-35. The model captured the basic trends (reduced yield moment and
residual accumulation) as seen in the experiment. The hysteretic damping was less in
the model then in the experimental results. Two of main differences between the model
and the experiment are noted in Figure 5-36. The model predicts a sharper transition
zone near the loading plateau and also fails to predict the hardening experienced in the
experiment for larger drift levels (which tended to decrease the concentrated rotation for
equivalent drift levels).
109
Figure 5-34:
connection.
Modeling details for the prediction analysis of the beam-column
80
700
Moment (kN-m)
60
Predicted
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Experimental
-700
-80
-0.04
(a)
-0.02
0.00
0.02
0.04
θconc. (rad)
-0.04
(b)
-0.02
0.00
0.02
0.04
θconc. (rad)
Figure 5-35: (a) Averaged experimental moment-rotation response for Test D vs. (b) the
predicted moment-rotation response using OpenSEES
110
80
700
Experimental
Predicted
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
60
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure 5-36:
highlighted.
Experimental vs predicted reponse for Test D with some differences
5.5.5.2. Simplified Connection Model
In order to create a model that can be more efficiently implemented into analysis of a
building, a simplified model is needed. A simplified model was easily created by using a
zero-length
element
(zeroLengthSection)
available
in
OpenSEES.
First,
a
uniaxialMaterial object was defined in order to describe the force-deformation (or in this
case the moment-rotation) response of the section. The uniaxialMaterial chosen was a
SMA material model developed and implemented into OpenSEES by Fugazza (2003).
This is the same material model used in all the analysis of SMAs in this research. With
the moment-rotation described, a Uniaxial section object was created with the
uniaxialMaterial assigned to the moment resistance, Mz.
Next, a zeroLengthSection
element was created to join the beam end node to the column node (these nodes were
given the same coordinates), in which the Uniaxial section object was used. Finally, a
111
multipoint constraint object (equalDOF) was created to constrain the translational
degrees of freedom, simulating the shear tab. Although there are other ways one can
create a simplified model in OpenSEES, other research suggests this is the most
computationally efficient (Taftali, 2007). The simplified connection is shown in Figure
5-37.
The simplified connection model was calibrated with the experimental data and
the response is shown Figure 5-38a-b. The simplified model is much more efficient than
the model used for the prediction (3 nodes vs. 19 nodes per connection). However, the
cost of the increased efficiency is the models inability to accumulate residuals show
degradation in strength. To correct this deficiency in the simplified model, there is a
need for a more advanced uniaxialMaterial object to be developed in OpenSEES that
incorporates residual accumulation and strength reduction. With the current OpenSEES
toolkit, it is recommended that the simplified model be used, but a thorough parametric
assessment would need to be undertaken to back this judgment.
Investigating further, a simple way to create a model with residual accumulation
is to add a hysteretic material in parallel with the SMA. This was done by using the
uniaxialMaterial Steel02 in OpenSEES and then creating a parallel material with the
uniaxialMaterial Parallel command.
The results of this change are shown in Figure
5-38c-d. For this example, the Steel02 and SMA materials were given 20% and 80% of
the stiffness and strength of the original simple model (Figure 5-38c-d), respectively. A
comparison between the experimental results and this model is shown in Table 5-2.
In terms of maximum moment and maximum concentrated rotation, the model does a
good job of capturing the response, especially for drift levels above 1.0%. Below 1.0%
the model’s inability to capture the smooth/rounded transition zone tends to result in an
over-prediction of the moment and an under-prediction of the rotation. This over- and
under-prediction also affected the model’s equivalent viscous damping. For small drift
112
levels (1.0% and below), the model had minimal ζ, while the experiment had values of 58%. The author feels that the effect would be minimal because the model captures other
behaviors successfully and the lower damping in the model is conservative in terms of
performance results (maximum drift and acceleration).
Nonetheless, additional
analytical studies should be carried out to determine the effect of this difference on
frame performance.
As for the residual accumulation, the model under-predicts the residual rotation in
the connection for small and large rotation but accurately predicts the residual rotation at
the intermediate 3.0% drift level. This is an improvement from the simple model, where,
by definition, no residuals are accumulated. Moreover, other researchers have found
that small levels of residual have minor effects on the overall response of a structure
(Andrawes and DesRoches, 2008). Nonetheless, because of the ease of implementing
the residual accumulations and the fact that a more refined model could be calibrated,
the model with the residual accumulation is recommended (or a model of
similar/improved behavior).
Figure 5-37: Simplified connection model.
113
80
700
Moment (kN-m)
Simplified
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Experimental
60
-700
-80
-0.04
-0.02
0.00
0.02
0.04
θconc. (rad)
(a)
-0.04
-0.02
0.00
0.02
0.04
θconc. (rad)
(b)
80
Moment (kN-m)
Zoomed View
Simple model with residual
60
θres
40
20
0
-20
-40
-60
-80
-0.04
(c)
-0.02
0.00
0.02
0.04
θconc. (rad)
-0.010
(d)
-0.005
0.000
0.005
0.010
θconc. (rad)
Figure 5-38: Moment-rotation response of (a) experiment (averaged left and right beam
from Test D), (b) simplified model, (c) simplified model with residual accumulation, and
(d) zoomed view of the simplified model with residual accumulation.
114
Table 5-2: Comparison of the experimental results (Test D) versus the model with
residual accumulation in terms of the maximum concentrated rotation, maximum
moment, residual rotation, and equivalent viscous damping.
Experimental = Exp, Model with Residual Accumulation = Mod
Exp
Mod
Exp
Mod
Max Moment,
kN-mm
(kip-in)
Exp
Mod
Residual Rotation θres,
rad
Exp
Mod
Equiv. Viscous
Damping ζ , %
Drift,
%
Max Conc. Rotation,
rad
0.375
0.0023
0.0026
13930 (123)
15460 (137)
-
-
5.4
0
0.5
0.0027
0.0032
18060 (160)
18950 (168)
-
-
6.8
0.02
0.75
0.0048
0.0051
23890 (211)
29510 (261)
-
-
8.0
0.3
1.0
0.0067
0.0070
28310 (251)
35230 (312)
0.0010
0.0003
8.5
3.6
1.5
0.0109
0.0114
37380 (331)
38360 (340)
0.0015
0.0008
8.8
9.4
2.0
0.0154
0.0161
44580 (395)
41150 (364)
0.0020
0.0013
9.5
11.9
3.0
0.0256
0.0268
51620 (457)
49400 (437)
0.0026
0.0023
12.1
13.4
4.0
0.0357
0.0373
57620 (510)
57340 (508)
0.0040
0.0032
12.9
13.7
5.0
0.0455
0.0472
66320 (587)
64980 (575)
0.0070
0.0040
12.2
13.7
5.5.6.
From Research to Practice: Potential Applications
As mentioned previously, the design details of this connection were not intended to
represent a connection that would be appropriate for application in the construction
practice. Rather, these connection tests were performed in order to demonstrate that
one can predict the behavior of some of the “spring” elements in the connection (in this
case the NiTi tendons).
The other “rigid” element (anchor brackets, etc.) can be
modified as needed with the goal of creating a connection that could be practically
implemented into real-world construction.
One potential path in which NiTi tendons could be implemented into a connection
is by integrating them into a Kaiser bolted bracket (KBB) connection (Adan and Gibb,
2008). The Kaiser bolted bracket was originally created after the 1994 Northridge and
1995 Kobe earthquakes as a way to rehabilitate damaged fully-restrained connections.
The creators also saw potential in the economic and performance benefits for the
115
implementation of these brackets in new construction. Currently, the KBB is prequalified
and is an extremely viable option for various construction projects.
The KBB connection shifts the beam’s inelastic rotation away from the column
face, thus creating a very ductile system. However, the extensive damage to the beams
during a large earthquake would inevitable require demolition or extensive repair of the
structure. To elevate this performance to a higher level, it is proposed that NiTi tendons
be integrated into the system. Rather than the beam yielding, the NiTi could provide a
“fuse” in order to absorb the deformations and limit force transfer. This type of system
would provide another layer of protection to a structure and have potential to greatly
enhance the performance.
Additional solutions, such as the welded T-stubs being
developed by Swanson and Leon (2000), could also be investigated.
5.5.7.
Analytical Study
Though a formal analytical study was not conducted in this research, Taftali (2007)
presented an extensive study on the probabilistic seismic demand of SMA connections
in steel frames. Superelastic SMA connections were shown to be most beneficial in
reducing or eliminating residual deformations.
Taftali demonstrated that neither
recentering nor energy dissipation produced the optimal response over a complete
range of hazard levels. Rather, Taftali concluded that it may be beneficial to incorporate
both recentering and energy dissipation elements into the same system to optimize the
performance while understanding that increased recentering results in reduced system
residual deformations.
116
5.6.
Summary
Five tests were conducted on a beam-column connection in order to assess the viability
of creating a recentering connection using superelastic NiTi tendons. Test A and B were
preliminary tests ran to ensure that all of the inelastic action would be concentrated into
the tendon “fuse” elements. Modifications were made to the anchor brackets after Test
A and the adequacy of these modifications were verified in Test B. Test C was the first
attempt at obtaining recentering connection behavior; however, the NiTi tendons proved
to be martensitic, resulting in strain recovery only after the application of heat.
Recentering response was obtained in Test D after new superelastic NiTi tendons were
created and installed.
This recentering action could be predicted accurately by a
detailed finite element model in OpenSEES. However, in order to create a model that
could be implemented efficiently into a full structural analysis, a simplified model was
created and the adequacy of this model was verified. Finally, in Test E, aluminum
tendons were installed in parallel with the NiTi tendons used in Test D. Once again the
connection had good recentering behavior and demonstrated that NiTi tendons can exert
significant force during their shape recovery. The connection in Test E had increased
strength, stiffness, and energy dissipation.
However, the lack of effective buckling
restraint on the aluminum bars decreased the complete benefits of this parallel system.
The results of these five tests demonstrated that a NiTi SMA-based connection
can be developed to have excellent ductility, energy dissipation, and recentering. The
following conclusions and significant observations are:
ƒ
NiTi tendons possess significant superelastic properties which were able
fully recenter a connection at drift levels below 1.0% and adequately
recenter a connection at drift levels above 1.0%.
Additionally, the
connection was able to recover 85% of its drift at the 5.0% drift level.
117
ƒ
The NiTi connection had equivalent viscous damping that varied from
approximately 6 to 13% as drift levels increased from 0.375 to 5.0%. The
energy dissipation in the connection was a direct result of NiTi’s hysteretic
mechanical behavior and friction in the shear tab connection.
ƒ
The equivalent viscous damping in the superelastic NiTi (Test D) connection
was greater than that of the parallel (Test E) connection. This surprising
result is explained by the following observations: 1) the same physical
tendons were used in both tests, resulting in reduced material hysteresis for
Test E (as was observed in the mechanical test conducted herein and other
training studies); and 2) the AL tendons buckled in compression resulting in
a minimal increase in hysteretic area at larger drift levels.
ƒ
For the test connection layout, a 0.5% prestrain was applied to all NiTi
tendons. Prestraining of the NiTi tendons was effective in increasing the
recentering capability, and the overall behavior of the connection.
ƒ
A simple model in OpenSEES provided a good fit to the experimental data.
However, this model tended to overestimate the strength and stiffness at
small drift levels due to its inability to capture the behavior at the transition
zones. A simple model with residual accumulation accurately predicted the
equivalent viscous damping and forward stress plateau of the connection.
Both simple models enable the NiTi connection to be efficiently
implemented into further analytical studies.
The next step for such a connection is to create a prototype that is designed with
realistic, efficient, and cost effective construction details.
Such a connection could
involve integrating NiTi tendons into other promising connection types currently being
118
developed, such as the Kaiser Bolted Bracket connection (Adan and Gibb, 2008) or the
welded T-stub (Kasai and Xu, 2002a; Kasai and Xu, 2002b) connection.
119
CHAPTER 6
INVESTIGATION OF A RECENTERING ARTICULATED
QUADRILATERAL BRACING SYSTEM
6.1.
Introduction
This chapter presents the conception, design, and proof-of-concept testing of a SMAbased recentering articulated quadrilateral bracing system.
Braced frames have
received renewed interest since the 1994 Northridge and 1995 Kobe earthquakes
because of the unexpected damage found in a large amount of welded moment frames.
This poor performance under moderate earthquakes has resulted in a reevaluation of
steel moment resisting frames. Researchers have thus begun to revisit other lateral load
resisting systems, giving the engineering community new options to obtain earthquake
resilience.
Braced frames are one of the main viable alternatives to moment resisting
systems.
To obtain good ductility, and therefore enable higher strength reduction
factors, traditional bracing systems have to be designed with special attention to the
connections. However, even with special measures, traditional braces are characterized
by a loss of load carrying capacity due to compression buckling and degrading behavior
after repeated cycling. To improve this behavior, newer systems, such as the buckling
restrained brace (BRB), have become an excellent option when a high level of
performance is needed. The BRB performance is characterized by an elastoplastic-type
response with good energy dissipation, controlled strength, and large ductility.
As an alternative to an elastoplastic system, several researchers have
investigated the benefits of recentering systems. Analytical and experimental studies
120
have shown that recentering systems are a viable alternative to both traditional and
advanced systems, especially when residual deformations need to be limited.
In this chapter a SMA-based recentering system is proposed, developed, and
tested.
The system is based on a unique articulated quadrilateral geometry and
implements SMA wire bundles that can either act alone or be placed in parallel with cshaped conventional steel energy dissipators. The details of the AQ are first outlined
and then the experimental results from three braced frame tests are presented and
summarized. The behavior is then assessed in terms of strength, stiffness, recentering
ability, and energy dissipation.
Lastly, an analytical case study is conducted to
investigate the potential benefits of such a system.
121
6.2.
Background
Quadrilateral arrangements of the type proposed in this research have been investigated
before.
Pall and Marsh (1982) investigated the use of a special arrangement of
members to create a friction damped bracing system as shown in Figure 6-1a. Renzi et
al. (2004) referred to this arrangement as an articulated quadrilateral (hereafter AQ).
One key advantage of an AQ arrangement is that both tension and compression can
occur in the inside elements, while all other elements experience only tension. The link
members of the AQ force the contraction of one diagonal when the opposite diagonal is
being extended. Since yielding elements require both tension and compression to cycle
about the origin, this configuration provides a convenient way to create hysteretic
damping without the need for buckling restraint in a global brace member. Additionally,
due to the kinematics of the AQ, if the adjacent bracing members are sufficiently stiff,
these bracing members will be forced to stay in tension.
Other researchers have investigated similar types of geometry with friction or
yielding as the energy dissipation mechanism (Ciampi et al., 1995; Tyler, 1983; 1985a;
1985b). More recently, Renzi et al. (2007; 2004) used an AQ setup with c-shaped
energy dissipators, as shown in Figure 6-1b. The concept is similar to that devised by
Pall and Marsh, but friction dissipation is replaced with flexural yielding dissipation.
When the c-shape is loaded, a constant moment (at small displacements) is developed
along its body, resulting in a theoretically uniform plastic moment along the c-shaped
length. The results from Renzi’s experimental tests showed the c-shaped dissipator
produced good dissipating behavior.
122
Figure 6-1: (a) Pall friction AQ (Aiken et al., 1993) and (b-c) c-shape dissipator in AQ
(Renzi et al., 2007).
6.3.
6.3.1.
Test Setup
General AQ
The general setup of the AQ is shown in Figure 6-2 with both the SMA and c-shape
dissipators. The dimensions of the AQ were governed by the dimensions of the loading
frame (length-to-width ratio) and the length of the available SMA bundles. The SMA
bundles were 711 mm (28 in.) long. Figure 6-3 shows the resulting dimensions that
were selected for the AQ. The AQ links were made from 12.7 mm (0.5 in.) thick, 50.8
mm (2.0 in.) wide A36 flat bar. The joints were pinned with A490 22.2 mm (0.875 in.)
bolts. The anchor blocks, made from A572 grade 50 steel, served to transfer the load
from the cable assembly to the SMA wire bundles via two 12.7 mm (0.5 in.) grade 8
coarse-threaded rods connected to a 19.1 mm (0.75 in.) square bar combined with a
19.1 mm (0.75 in.) stainless steel half-round (not shown). The c-shape was attached to
the anchor block on the outside of the AQ links via the joint bolts.
123
Figure 6-2: General articulated quadrilateral (AQ) setup with c-shapes and SMA wire
bundles.
Figure 6-3: Dimension of AQ without c-shapes and SMA. Units in mm (in.).
124
6.3.2.
Cable Assembly
The following components were used to create the cable assemblies that formed the
remaining balance of the brace:
ƒ
A 25.4 mm (1.0 in.) 18-7 bright wire cable with thimbles and swag sleeves
installed at each end, giving the cables 95% of its rated 222 kN (50 kips)
breaking strength.
ƒ
A 25.4 mm (1.0 in.) 457 mm (18 in.) take-up turnbuckle with jaw-jaw ends and a
breaking strength of 222 kN (50 kips).
ƒ
A 22.2 mm (0.875 in.) Crosby shackle with breaking strength of 454 kN (104
kips)
ƒ
A tensile load cell created from 25.4 mm (1.0 in.) grade 8 coarse-threaded rod.
ƒ
A padeye anchor attached to the testing frame with four 7/8 in. A325 bolts. The
padeye anchors were fabricated from 31.8 mm (1.25 in.) thick A572 grade 50
steel. The dimensions are shown in Figure 6-5.
The entire bracing system is shown in Figure 6-4 with the cable assembly labeled.
Cable Assembly
Figure 6-4: AQ brace system in loading frame.
125
Figure 6-5: Padeye dimensions for AQ tests. Units in mm (in.).
6.3.3.
Test A: SMA-only
Test A was conducted using SMA wire bundles as shown in Figure 6-6. The details of
the wire bundles are described in the component test section (Section 6.5.1). The SMA
bundles were prestrained approximately 2.5 mm (0.1 in.) in order to give the device
some initial stiffness. Further prestraining was not possible due to the AQ links buckling
in compression. After the SMAs were prestrained, the AQ was inserted into the test
frame and the cable assemblies were tightened in a sequential manner to give each
cable approximately 6.7 kN (1.5 kips) of tension.
Lastly, the nuts on the SMA
attachments were further tightened 1/3 turn to increase the pretension in the SMA wires.
The test was performed at 26 °C.
126
Figure 6-6: AQ setup for the SMA-only test, Test A.
6.3.4.
Test B: C-shape-only
Test B was performed with two c-shapes installed in the AQ. The c-shapes were put in
the same direction and braced to one another in order to increase their out-of-plane
buckling resistance. The dimensions of the c-shapes are shown in Figure 6-7. They
were fabricated from 203 mm (8.0 in.) wide, 12.7 mm (0.5 in.) thick A36 flat bar. A
plasma cutter was used to cut the shape and then the edges were finished with a grinder
and a mill file. The AQ specimen is shown in Figure 6-8. The cables were again pretensioned to 6.7 kN (1.5 kips). The test was performed at 27 °C.
15.24 [6.000]
Ø2.22 [Ø.875]
8.89 [3.500]
3.17 [1.250]
83.82 [33.000]
4.13 [1.625]
4.45 [1.750]
Figure 6-7: C-shape dimensions for Test B, t = 12.7 mm (0.5 in.). Units in mm (in.).
127
Figure 6-8: AQ setup for the c-shape-only test, Test B.
6.3.5.
Test C: Parallel System (SMA + c-shape)
Test C was performed with SMA bundles installed in parallel with two c-shape
dissipators.
The same size c-shapes were used as those in Test B, with one
modification; the holes were slotted 19.1 mm (0.75 in.). This was done to alleviate some
of the kinematic stiffening seen in the c-shape (see APPENDIX G for further discussion).
The c-shapes were again put in the same direction, but were only tied together at two
points rather than six. The c-shape dimensions are shown in Figure 6-9. The specimen
is shown in Figure 6-10. The cables were pretention to 6.7 kN (1.5 kips) and the test
was performed at 24 °C.
128
15.24 [6.000]
Ø2.22 [Ø.875]
3.17 [1.250]
4.13 [1.625]
83.82 [33.000]
8.89 [3.500]
4.45 [1.750]
Figure 6-9: C-shape dimensions for Test C, t = 12.7 mm (0.5 in.). Units in mm [in.].
Figure 6-10: AQ setup for the c-shape-only test, Test C.
6.4.
Testing Scheme
This section describes the testing scheme used for the experimental portion of this
study.
The same loading frame described in CHAPTER 5 was used for this
experimental investigation.
Further details of this loading frame can be found in
APPENDIX A.
129
6.4.1.
Instrumentation
The instrumentation for the experimental testing plan is shown in Figure 6-11. The cable
loads were monitored by custom-made cable load cells. A 25.4 mm (1.0 in.) highstrength threaded rod was milled to create a section that was 18 mm (0.7 in.) square and
50 mm (2.0 in.) long. FLA-3-11 TML 120-ohm strain gauges were attached to each flatmilled surface in alternating longitudinal and transverse directions. These four gauges
were then wired together to form a Wheatstone Bridge. The resulting output voltage was
linearly related to the applied load. The load cells were calibrated to 145 kN (32.5 kips)
and the sensitivity values for a 10 V excitation are shown in Table 6-1.
To obtain the AQ diagonal deformations, stringpots were mounted to 6.4 mm
(0.25 in.) bolts that were screwed into threaded holes at the ends of the joint bolts.
These stringpots were guided by a sliding aluminum tube assembly (Figure 6-12).
Another stringpot was used to obtain the lateral displacement of the testing frame.
Additionally, the actuator load cell and LVDT were monitored in order to obtain
redundant measurements of base shear and lateral drift of the bracing system. To verify
that the padeyes were not slipping at the end of the cable assemblies, LVDTs were
mounted between the padeyes and the loading frame beams.
Finally, for the tests
incorporating the c-shape dissipators, four strain gauges were installed at quarter-points
along the length (noted in Figure 6-13).
130
Figure 6-11: Instrumentation scheme for AQ testing.
Table 6-1: Tensile load cell calibration values with 10V excitation.
Load Cell
Sensitivity (kN/mV)
LC1
4.650
LC2
4.499
LC3
4.716
LC4
4.560
LVDT
guide
stringpot
Load Cell
(a)
(b)
Figure 6-12: Instrumation details for (a) the AQ and (b) the cable assembly.
131
Figure 6-13: Close-up view of instrumentation scheme for AQ testing.
6.4.2.
Loading Protocol
The loading protocol used for these tests was the same as that used for the beamcolumn connection test in CHAPTER 5, except for a few deviations that are noted in the
test results section. The interstory drift was selected as the controlling parameter, based
on a 437 cm (172 in.) story height. The testing protocol was implemented using a MTS
407b controller.
132
6.5.
Pretests
6.5.1.
Component Test: Wire Bundle
The SMA wire bundle was first tested in a 250 kN (55 kip) MTS Universal Testing frame.
The force-deformation behavior is shown in Figure 6-14. The SMA bundle had a crosssection of 320 0.71 mm (0.028 in.) diameter superelastic NiTi wires. To create this
cross-section, a NiTi wire was wound 160 times around 9.6 mm (0.375 in.) thimbles and
then fixed with a 9.6 mm (0.375 in.) double-saddle cable clip. The cross-sectional area
of the SMA bundle was 130 mm2 (0.20 in2). The effective length, defined as the distance
from clamp-to-clamp, was 559 mm (22 in.). The length from bearing-to-bearing was 711
mm (28 in.).
The bundle had great ductility and limited residual deformations.
The
transformation stress was approx. 550 MPa (80 ksi), compared to 325 (47.0 ksi) found in
the bar (see Section 5.2.1). This stress increase was most likely due to cold working.
Additionally, the hysteretic area is larger for the wire bundle than that displayed in the
bar, which is also a result of cold working and has been noted in previous work
(DesRoches et al., 2004).
133
120
Fy = 70 kN (15.7 kips)
25
εy = 2%
(based on 56 cm effective length)
100
20
15
60
10
40
Force (kips)
Force (kN)
80
5
20
0
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Strain (%)
Figure 6-14: Cyclic force-strain relationship of 129 mm2 (0.2 in2) SMA wire bundle.
6.5.2.
Shakedown Test
A “shakedown” test was carried out in order to get rid of some of the cable assemblies’
expected inelastic deformations. This test consisted of installing two extra SMA wire
bundles and systematically cycling the frame, tightening the turnbuckles, and then
cycling the frame until the cable load cells reach 133 kN (30 kips). The majority of the
inelastic deformation came from the cable thimbles collapsing and the accompanying
thimble bearing service flatting out.
This shakedown effectively locked-in the
deformations into the cable-assembly elements.
134
6.6.
Experimental Results
6.6.1.
Test A
In Test A, SMA wire bundles were the only elements installed in the AQ. The actuator
displacement time history is shown in Figure 6-15. The resulting base shear vs. story
drift is shown in Figure 6-16, assuming the story height to be 437 cm (172 in.).
The
brace remained elastic through the 1.0 % drift cycles, with full recentering at the end of
each cycle.
During the 1.5% cycle, the SMA wire bundles reached their transformation
stress, as is evident by the load plateau in Figure 6-16. Figure 6-17 plots the cable force
(averaged from the two load cells on each diagonal) vs. the AQ deformation. This plot is
essentially the force-deformation plot of the SMA element. Additionally, the cable force
vs. drift is plotted in Figure 6-18.
During the 2% drift cycle, the SMA was pushed further along its loading plateau
but not completely into its martensitic phase.
The brace showed little strength
degradation and little stiffness degradation. To finish the test, the frame was cycled six
times to 3% drift.
The brace began to have some strength degradation and some
residual accumulation (and therefore effective stiffness degradation).
response stabilized after several cycles.
135
However, the
100
4
50
2
0
0
-50
-2
-100
-4
Displacement (in.)
Displacement (mm)
150
-150
1000
2000
3000
4000
5000
6000
7000
Time (step)
Figure 6-15: Actuator displacement time history for Test A.
125
25
100
20
(-)
75
Base Shear (kN)
50
10
25
5
0
0
-25
-5
-10
-50
-15
-75
-20
-100
(+)
-125
-3
-2
-1
0
1
2
Drift (%)
Figure 6-16: Base shear vs. story drift for Test A.
136
3
-25
Base Shear (kips)
15
Deformation, s (forward-slash measurement) (in.)
-3
-2
-1
0
1
2
3
120
25
100
80
15
60
10
40
Cable Force (kips)
Cable Force (kN)
20
5
20
s
(-)
s
(+)
0
-80
-60
-40
-20
0
20
40
60
0
80
Deformation, s (forward-slash measurement) (mm)
Figure 6-17: Cable force vs. AQ deformation for Test A.
120
Cable 1 (forward-slash)
Cable 2 (back-slash)
25
100
15
60
10
40
5
20
(-)
(+)
0
0
-3
-2
-1
0
1
2
Drift (%)
Figure 6-18: Cable force vs. drift for Test A.
137
3
Cable Force (kips)
Cable Force (kN)
20
80
6.6.2.
Test B
In Test B, two c-shape dissipators were installed in the AQ. The actuator displacement
time history is shown in Figure 6-19. The resulting base shear vs. story drift is shown in
Figure 6-20. The brace remained essentially elastic through the 0.5% drift cycles, with
only small hysteretic loops forming.
During the 0.75% and 1.0% cycles, the hysteresis grew, indicating the c-shapes
were being deformed beyond their elastic limit. Figure 6-22 shows the cable force vs.
AQ deformation, respectively. This plot is essentially the force-deformation plot of the cshape element. Additionally, the cable force vs. drift is plotted in Figure 6-22.
During the 1.5% drift cycles (and beyond), the ties that connected the two cshapes together began bearing against the AQ links. This resulted in a jump in stiffness
upon further loading and eventual yielding of the AQ links. This issue was addressed
and corrected in Test C. The deformed shape and associated interference is show in
Figure 6-23.
At larger drift levels, the brace stiffened when cycled to the left (negative drift).
This was the result of the tension/compression asymmetry of the c-shape. This issue is
explored more in the discussion of results.
Nonetheless, the brace strength and
stiffness were stable and c-shape was able to deliver good hysteretic damping. The test
was stopped after the first 3% cycle due to significant flexural yielding of one of the AQ
links caused by bearing of the c-shape ties.
138
4
100
50
2
x, time step vs y, mm
0
0
-50
-2
-100
-4
Displacement (in.)
Displacement (mm)
150
-150
2000
3000
4000
5000
6000
7000
Time (step)
Figure 6-19: Actuator displacement time history for Test B.
60
c-shape compression
(+) drift
Base Shear (kN)
40
20
20
10
0
0
-20
-10
-40
-20
s
(-)
s
(+)
-60
-3
-2
-1
0
1
2
Drift (%)
Figure 6-20: Base shear vs. story drift for Test B.
139
3
Base Shear (kips)
c-shape tension
(-) drift
Deformation, s (forward-slash measurement) (in.)
-2
-1
0
1
2
c-shape tension
(-) drift
50
3
c-shape compression
(+) drift
s
(-)
s
(+)
12
10
Cable Force (kN)
40
8
30
6
20
4
10
test
stopped
0
Cable Force (kips)
-3
60
2
0
-100
-50
0
50
100
Deformation, s (forward-slash measurement) (mm)
Figure 6-21: Cable force vs. AQ deformation for Test B.
120
c-shape tension
(-) drift
c-shape compression
(+) drift
Cable 1 (forward-slash)
Cable 2 (back-slash)
100
25
(-)
(+)
15
60
10
40
20
5
0
0
-3
-2
-1
0
1
2
Drift (%)
Figure 6-22: Cable force vs. drift for Test B.
140
3
Base Shear (kips)
Base Shear (kN)
20
80
Interference
Figure 6-23: C-shape interference at 1.5% drift.
6.6.3.
Test C
In Test C, two c-shape dissipators were combined in parallel with SMA wire bundles.
The resulting base shear vs. story drift is shown in Figure 6-24 and the resulting base
shear vs. story drift is shown in Figure 6-25. The brace remained mostly elastic through
the 1.5% drift cycles, with good recentering at the end of each cycle.
During the 2.0% cycle, the SMA elements reached their transformation stress, as
is evident by the load plateau in Figure 6-25 and Figure 6-26. Figure 6-26 plots the
cable force (average from the two load cells on each diagonal) vs. the AQ deformation.
This plot is essentially the force-deformation plot of the SMA element paralleled with the
c-shape element. Additionally, Figure 6-27 shows the cable force vs. the drift. During
the 2.5% drift cycle (added for this test), the SMA was pushed further along its loading
plateau. The brace showed little strength and stiffness degradation.
To finish the test, the frame was cycled two times to 3% drift. As expected, the
brace began to have some strength degradation and some residual accumulation (and
therefore stiffness degradation).
141
4000
6000
8000
Time (step)
Figure 6-24: Actuator displacement time history for Test C.
125
25
100
20
(-)
75
50
10
25
5
0
0
-25
-5
-10
-50
-15
-75
-20
-100
(+)
-125
-3
-2
-1
0
1
2
Drift (%)
Figure 6-25: Base shear vs. story drift for Test C.
142
3
-25
Base Shear (kips)
15
Displacement (in.)
5
4
3
2
1
0
-1
-2
-3
-4
-5
2000
Base Shear (kN)
Displacement (mm)
150
125
100
75
50
25
0
-25
-50
-75
-100
-125
-150
Deformation, s (forward-slash measurement) (in.)
-3
-2
-1
0
1
2
3
140
30
100
20
80
60
10
40
20
s
(-)
Cable Force (kips)
Cable Force (kN)
120
s
(+)
0
0
-80
-60
-40
-20
0
20
40
60
80
Deformation, s (forward-slash measurement) (mm)
Figure 6-26: Cable force vs. AQ deformation for Test C.
Cable 1 (forward-slash)
Cable 2 (back-slash)
140
30
120
100
20
80
15
60
10
40
5
20
(-)
(+)
0
0
-3
-2
-1
0
1
2
Drift (%)
Figure 6-27: Cable force vs. drift for Test C.
143
3
Cable Force (kips)
Cable Force (kN)
25
6.7.
Discussion of Results
6.7.1.
General Behavior
While the previous section presented the performance of three braced frame tests, this
section takes an in-depth look into these results and tries to explain the underlying
behavior.
The goal is to evaluate the performance of this new bracing system and
assess this performance with analytical simulations. Several response parameters are
investigated including changes in stiffness, strength, energy dissipation, and recentering.
Before these performance parameters are examined, the effect of the relative
stiffnesses of the elements combined to make the bracing system need to be discussed.
When SMA and elastic elements are combined in series, a resulting quantitative force
deformation relationship will form as shown in Figure 6-28. The length of the loading
plateau relative to the yield deformation (plateau ductility factor, η) will decrease as a
consequence. To maximize η, the brace elements combined in series with the SMA
element should be sufficiently stiff. For a perfectly rigid connecting member, a η greater
than 4 can be obtained (dependent on the SMA, approximately 2.5 for this experiment).
Figure 6-29, Figure 6-30, and Figure 6-31 show the contributing elements for Tests A, B,
and C, respectively.
Further studies need to be conducted to determine the full
implications of this effect (further discussion in APPENDIX H ).
144
SMA
Elastic
=
SMA + Elastic (series)
β
dF
F / Fy
+
β
1
ksma
u / uy
ke
dF/ke
k
u / uy
u / uy
Figure 6-28: The resulting force-deformation characteristics of an SMA element
combined in series with an elastic element.
145
Element Deformation (forward-slash measurement) (in.)
0
120
1
2
3
4
SMA
Cable Assembly
Series
25
100
80
15
60
10
40
Cable Force (kips)
Cable Force (kN)
20
5
20
(+)
0
-20
0
20
40
60
80
100
0
120
SMA
120
Series
(SMA + Cable Assembly)
Cable Assembly
25
100
20
80
15
60
40
10
20
5
0
0
-20 0
20 40 60 80 100
-20 0
20 40 60 80 100
-20 0
20 40 60 80 100 120
Element Deformation (forward-slash measurement) (mm)
Figure 6-29: Contributions of the different brace elements in series for Test A.
146
Cable Force (kips)
Cable Force (kN)
Element Deformation (forward-slash measurement) (mm)
Element Deformation (forward-slash measurement) (in.)
-3
60
-2
-1
0
1
2
c-shape tension
(-) drift
3
4
c-shape compression
(+) drift
12
50
10
(-)
Cable Force (kN)
40
8
30
6
20
4
10
Cable Force (kips)
(+)
2
test
stopped
0
-100
-75
-50
-25
0
25
50
75
0
100
Element Deformation (forward-slash measurement) (mm)
Cable Assembly
12
50
10
40
8
30
6
20
4
10
2
0
0
-100
-50
0
50
100 -100
-50
0
50
100 -100
-50
0
50
Cable Force (kips)
60
Cable Force (kN)
Series
(SMA + Cable Assembly)
SMA
100
Element Deformation (forward-slash measurement) (mm)
Figure 6-30: Contributions of the different brace elements in series for Test B.
147
Element Deformation (forward-slash measurement) (in.)
0
1
2
3
4
140
30
100
20
80
60
10
40
Cable Force (kips)
Cable Force (kN)
120
20
(+)
0
0
-20
0
20
40
60
80
100
120
Element Deformation (forward-slash measurement) (mm)
Series
(SMA + Cable Assembly)
Cable Assembly
140
120
100
80
60
40
20
0
30
25
20
15
10
5
0
-20 0
20 40 60 80 100
-20 0
20 40 60 80 100
-20 0
20 40 60 80 100 120
Element Deformation (forward-slash measurement) (mm)
Figure 6-31: Contributions of the different brace elements in series for Test C.
148
Cable Force (kips)
Cable Force (kN)
SMA
6.7.1.1. Response Path
Before the response parameters are examined, it is helpful to look at an individual cycle
of base shear vs. drift for Tests A and C. Figure 6-32 shows the base shear vs. drift
response of the first 3% drift cycle for the SMA test (Test A) and the parallel test (Test
C).
The transition points (a through g) are plotted to help delineate the different
phenomena that were occurring as the braces were cycled.
For both tests, the brace was prone to have some loss in stiffness at small drift
levels due to accumulating residual strains in the SMA wires (plus the compression
resistance of the c-shape for Test C). This portion is denoted by a to a’. For Test A
these two points were generally closer (and sometimes undistinguishable) than in Test
C, because of the added c-shape resistance.
Moving along the response path, the brace remained linearly elastic from point a’
to b. At point b, the SMA wires began transitioning into its plateau range (and the cshape began to yield for Test C).
From points c to d the SMA (and the c-shape)
traversed across their loading plateaus and exhibited some slight stiffening as the
response approached point d. At this point, the SMA wires had transformed almost
entirely into martensite.
For the unloading portion, the SMA wires began transforming from martensite
back into austinite at point e. The unloading plateau was fully reached at point f, in
which the SMA began recentering the frame. For Test C, point f’ was approximated as
the point in which the c-shape was fully yielding in tension. Points g’ and g were the final
two points on the path. These two points, similar to a and a’, represent the level of
recentering the system experienced. When g and g’ occupy the same coordinates, full
recentering is achieved.
Test A generally had much better recentering, as was
expected.
149
1st cycle at 3% drift
20
Test C
Test A
d
b
50
a
0
15
c
10
a'
f
e
5
0
g g'
-5
-50
-10
-100
-150
-4
(a)
(a)
-3
-2
-1
0
1
2
3
b
Base Shear (kip)
Base Shear (kN)
100
20
d
a
15
c
f
a'
10
e
5
f'
g g'
0
-5
-10
-15
-15
-20
-20
4 -4
Drift (%)
-3
(b)
-2
-1
0
1
2
3
Base Shear (kip)
1st cycle at 3% drift
150
4
Drift (%)
Figure 6-32: General response path of braced frame (a) Test A and (b) Test C.
6.7.1.2. C-shape Behavior: Kinematic Effects
Before moving on to the remainder of the discussion, it is helpful to look at the
kinematics of the c-shape elements at large deformations. In Figure 6-33, the response
of the c-shape test (Test B) is plotted on the top and the corresponding kinematic
relationship between the hole-separation, s, and arm rotation angle, φ, is plotted at the
bottom. Notes were made in Figure 6-33a to highlight the response of the c-shape in
tension. Assuming the hole-separation, s, comes entirely from bending of the c-shape
body (and the arms are rigid), the relationship between s and the arm rotation, φ, can be
found as plotted in Figure 6-33b. For the holes to have further separation, the c-shape
must have any combination of the following:
elongation of its holes, or bending of its arms.
axial elongation of its body, bearing
This kinematic hardening played a
significant role in the behavior of the c-shape in tension. To try to reduce this effect, the
c-shapes in Test C were given slotted holes, providing a “fuse” for the deformations.
Further discussion on this topic can be found in APPENDIX G.
150
c-shape tension
(-) drift
c-shape compression
(+) drift
c-shape lateral brace tie
bearing against AQ leg
AQ leg yielding in-plane
Base Shear (kN)
40
test paused in order to
shift the lateral brace tie
to try an prevent contact
with AQ leg
20
10
0
0
-20
-10
-40
c-shape stiffening due to
kinematic hole seperation limit
(illustrated in the plot below)
aluminum instrumentation guide
was snagged and broken at this
point
-60
-3
-2
-1
(a)
0
1
2
3
1
2
3
Drift (%)
-3
2.0
-2
-1
0
c-shape tension
(-) drift
c-shape compression
(+) drift
1.5
an increase in hole seperation, s,
is not possible without axial elongation
1.0
Angle, φ (rad)
20
0.5
s
(-)
0.0
s
(+)
-0.5
a
2φ
(−)
s/2
m
-1.0
⎡⎛
m ⎞ ⎛ φ ⎞ m⎤
s = 2 ⎢⎜⎜ a + ⎟⎟sin⎜ ⎟ − ⎥
φ ⎠ ⎝2⎠ 2 ⎦
⎣⎝
-1.5
-100
(b)
-50
0
50
100
Hole Seperation, s (mm)
Figure 6-33: Discussion of c-shape disspator response for Test B.
151
-20
Base Shear (kips)
60
6.7.2.
Effective Stiffness and Yield Moment
The cyclic curves for the first cycle at 1.5% and 3.0% drift for Test A are shown in Figure
6-34 . Straight lines were overlaid in order to approximate the effective stiffness, Ke, and
“yielding” base shear, Vby, of the braced frame (where “yielding” for the SMA is really a
phase transformation) . The line for determining the stiffness was drawn asymptotically
to the forward and reverse loading curves and runs approximately through the origin. In
order to determine the “yielding” plateau, another line was drawn. The SMA did not hit
its transformation stress for drift levels less than 1.0% in Test A and 1.5% in Test C.
The resulting trends for stiffness and strength are plotted in Figure 6-35 and
Figure 6-36, respectively. The stiffness generally decreased with increasing drift level,
though the decrease was only 15-20% at 3% drift. The strength also had a moderate
decrease for both tests.
Test C decreased at a faster rate due to more residual
accumulation, which will be discussed in the next section. As expected, Test C had
larger stiffness and strength than that of Test A due to the addition of the c-shape
dissipators.
1st cycle at 1.5% drift
1st cycle at 3.0% drift
100
Test A
20
Test A
Vby
10
Ke
Ke
0
0
-10
-50
approximation
experimental data
-100
-4
(a)
-2
0
2
approximation
experimental data
4 -4
Drift (%)
(b)
-3
-2
-1
0
1
2
3
Base Shear (kip)
Base Shear (kN)
Vby
50
-20
4
Drift (%)
Figure 6-34: Straight line approximations of the base shear vs. drift response to obtain
My and Ke.
152
9
1.4
8
1.2
7
6
1.0
5
0.8
4
0.6
3
0.4
Test A
Test C
0.2
2
1
0.0
Effective Stiffness, Kef (kip/in)
Effective Stiffness, Keff (kN/mm)
1.6
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Drift (%)
Figure 6-35: Effective stiffness, Ke, over a range of drift levels for Tests A and C.
Vby not
reached
0.08
600
450
0.06
300
0.04
0.02
150
Test A
Test C
0.00
Yield Base Shear, Vby (kip)
Yield Base Shear, Vby (kN)
0.10
0
0
1
2
3
Drift (%)
Figure 6-36: Yield base shear, Vby, over a range of drift levels for Tests A and C.
6.7.3.
Residual Drift
The change in stiffness of the braced frame was mainly due to the accumulation of
residual strains in the SMA wires. For these tests, the residual drift was set to the point
in which the response path crossed the zero base shear line. The residual drifts, Δres,
were manually picked from the response curves and the trend is shown in Figure 6-37.
153
Test A performed the best, having only 0.12% residual drift after being subjected to 3.0%
drift. Test C had approximately four times the residual drift than Test A, which was
mainly due to the c-shape dissipator preventing recentering.
To achieve better
recentering in the parallel system (Test C), the SMAs should be given increased
pretension.
Residual Drift, Δres (%)
0.5
Test A
Test C
0.4
0.3
0.2
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Drift (%)
Figure 6-37: Residual drift, Δres, over a range of drift levels in Tests A and B.
6.7.4.
Energy Dissipation
The energy dissipation of the brace is assessed by calculating the equivalent viscous
damping, ζ, for the first and second cycles of Tests A and C. The trend in ζ is shown in
Figure 6-38. The ζ varied from 3-9%, with the first cycle’s ζ generally greater than that
of the second cycle. At 0.375% and 0.5% drift, the ζ was greatly influenced by the
friction in the system. This had less of effect at the 1.0% drift level, therefore the ζ
dropped. However, at 1.5% drift and greater, the ζ rapidly increased. For 1.5-3% drift,
the ζ was approximately 6-8% for Test A due to the hysteresis that formed in the SMA
wires. For Test C, the ζ did not increase as quickly because a higher drift level was
154
needed to cause the SMAs to transform. This was due to the increased stiffness in the
AQ elements which resulted in the cable assemblies taking up more of the deformations.
For 2-3% drift, the ζ was approximately 7-9% for Test C.
Though recentering is the main focus of this bracing system, the added damping
has been shown to have a positive impact on a recentering system’s dynamic
performance (see CHAPTER 3). The purpose of adding the c-shape damping in parallel
with the SMA wire bundle was to enhance the brace’s damping while maintaining good
recentering. The ζ plots are slightly deceiving, in this regard, because the two systems
that are compared had different “yield” drifts and “yield” strengths.
This effectively
shifted the response of the Test C’s ζ to the right by approximately 0.5% drift. With this
in mind, the damping of Test C was enhanced by the addition of the c-shape, as would
be expected. Nonetheless, the balance between recentering and energy dissipation
Equivalent Viscous Damping, ζ (%)
needs further development to ensure optimized system behavior.
10
1st cycle at each drift level
2nd cycle at each drift level
8
6
4
2
Test A
Test C
Test A
Test C
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Drift (%)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Drift (%)
Figure 6-38: Equivalent viscous damping in the first and second cycle for Tests A and
C.
155
6.8.
6.8.1.
Analytical Study
Description and Setup
In order to assess the effectiveness of the SMA-based bracing system, the response of
a seven-story building outlined in the 2005 NEHRP Design Examples (FEMA 451,
section 5.2, alternative B) is investigated (FEMA, 2006). The seven-story building was
modeled in OpenSEES. Four different brace behaviors were investigated to assess the
SMA-based system’s performance.
Some liberty was taken in giving the braced
members several different types of force-deformation responses without further
refinement of the design parameters (i.e. R, Cd, and Ω0 factors).
6.8.1.1. Brace Models
First, the brace members were modeled as traditional moderately stocky braces (special
concentrically brace frame (SCBF) as designed in the Design Examples) which are
allowed to buckle in compression. This brace model is referred to as the Brace A model.
To capture the buckling response, an initial out-of-straightness is given at the midpoint of
the brace and rotational springs are applied at the end of the brace. Each brace was
calibrated to buckle in compression at the nominal capacity, Pn, and have a postbuckling
strength of 0.3Pn at 20 times the buckling deformation. This procedure was adopted
from the recommendations made by Yang et al. (2008) in their study of chevron zipper
frames. The qualitative response of the SCBF, Brace A, is shown in Figure 6-39a.
Next, the traditional braces were replaced with an SMA-based bracing system
(Brace B) with the same strength and stiffness. The SMA brace behavior was modeled
after the response of Test A in the experimental results of this chapter (SMA-only brace).
However, in order to maximize the plateau ductility parameter, the steel cables were
assumed very stiff relative to the SMA (see the discussion in APPENDIX H for further
information). The constitutive model used for the SMA material was a modified one156
dimensional model implemented into OpenSEES by Fugazza (2003) and first proposed
by Auricchio and Sacco (1997). The resulting qualitative brace response for the SMA,
Brace B, is shown in Figure 6-39b.
Additionally, the braces were modeled as
tension/compression elements with half the strength and stiffness of each brace in the
experimental system.
This effectively gave the same story stiffness (since the
experimental system was tension-only) and created an easy way to model the parallel
brace investigated next
Third, the braces were assigned the force-deformation characteristics seen in the
parallel (PARA) bracing system (c-shape plus SMA) of experimental Test C. Again, the
brace model (Brace C) assumed that the cable assemblies were rigid, thus
concentrating all the brace deformation into the SMA and c-shaped elements.
The
parallel SMA and c-shaped elements were modeled using the Parallel material
command in OpenSEES. The parallel element was made up of 80% SMA and 20%
elastoplastic behavior, set as reasonable values from the experimental results. This
resulted in the qualitative response for Brace C as shown in Figure 6-39c.
Finally, the braces were assigned an idealized buckling restrained brace (BRB)
force-deformation relationship (Brace D). The BRBs were modeled with the Steel01
material in OpenSEES, which does not consider stiffness and strength degradation.
Isotropic hardening was set to zero and the strain hardening was set to 0.02. The
resulting qualitative response for Brace D is shown in Figure 6-39d.
SCBF, Brace A
SMA, Brace B
1.43
1
F / Fy
1
(a)
PARA, Brace C
BRB, Brace D
1
1
4.4
0.77
u / uy
(b)
u / uy
(c)
u / uy
(d)
Figure 6-39: Brace models used in analysis.
157
u / uy
6.8.1.2. Building Model
The plan view of the seven-story building is shown in Figure 6-40. The frame was
designed as a special concentrically braced frame (SCBF) to be built in the Los Angeles,
California area (Seismic Design Category D, Seismic Use Group I, R = 6, Ω0 = 3, Cd =
5). Complete details of the building can be found in the FEMA 451 publication (FEMA,
2006).
To simplify the analysis, only one direction of loading was considered (N-S) and
only one braced-frame section was modeled. Since the building was designed with four
braces in the N-S direction, one-fourth of the mass was assigned to this frame and was
lumped at each floor height (half at each intersecting beam-column node). The lateral
resistance of the non-braced frames was ignored and torsion was not considered. The
columns were fixed at the base and the beam-column connections were modeled as
pinned, thus ignoring the stiffness that would result from the gusset plate at the end of
the brace.
158
Figure 6-40: Details of the seven-story braced frame analyzed (FEMA, 2006).
6.8.1.3. Ground Motions
The braced-frame was subjected a suite of ground motion, LA21-40, with a 2%
probability of exceedance in 50 years (Somerville et al., 1997). The ground motions
were taken as-is from Somerville’s study (i.e. no additional scaling).
159
6.8.2.
Results and Discussion
6.8.2.1. Behavior Due to Individual Ground Motions
To highlight some of the issues that were encountered during the analysis, the behavior
of the braced frames subjected to two different earthquakes is first explored. The two
ground motions investigated are LA30 (1974 Tabas earthquake with a magnitude of 7.4
and PGA of 972.58 cm/sec2 (382.9 in/sec2)) and LA25 (1994 Northridge earthquake with
a magnitude of 6.7 and a PGA of 851.62 cm/sec2 (335.3 in/sec2)). To get a sense of the
frequency content, the response spectrum for these two earthquakes is shown in Figure
6-41. For the analyses, the fundamental period was approximately 0.85 sec and the
second mode’s period was approximately 0.29 sec.
For LA30, the base shear vs. first floor drift is shown in Figure 6-42a-d for the
four different braced frames. Additionally, the first floor drift time histories are shown in
Figure 6-42e. The maximum first story drifts for Braces A-D were 1.50, 1.35, 1.30, and
1.05%, respectively. The residual first story drifts for Braces A and D were 0.05 and
0.45%, respectively. Braces B and C had no residual drifts. Both systems with SMA
(Braces B and C) had an approximately 10-15% reduction in maximum drift compared to
the SCBF (Brace A), but approximately equal maximum drift compared to the BRB
(Brace D).
For LA25, different relative performance was observed amongst the systems.
The four system’s base shear vs. first floor drift are shown in Figure 6-43a-d and first
floor drift time histories are shown in Figure 6-43e. The maximum first story drifts for
Braces A-D were 3.2, 1.6, 1.6, and 2.3%, respectively. The residual first story drifts for
Braces A and D were 1.3 and 0.7%, respectively.
residual drifts.
Again, Braces B and C had no
Both systems with SMA had approximately 50% reduction in drift
compared to the SCBF and a 30 % reduction compared to the BRB. Furthermore, the
160
SCBF and the BRB both suffered from large levels of residual drift, as opposed to the
SMA-based systems which displayed their recentering capabilities.
The high drift
demand can be related to the reduction in effective stiffness caused by the extensive
yielding in the SCBF and the BRB. This effectively shifted the fundamental period of the
structure and, as can be seen the LA25 response spectrum (see Figure 6-41), resulted
in higher deformation demand.
It should be noted that the results from the LA25 ground must be reviewed with
caution. The force levels in both SMA systems reached high up into the post-plateau
stiffness region.
From mechanical tests, it is clear that SMAs begin to lose
superelasticity in this region. Additionally, the high forces in these elements could be
problematic due to overloading of other elements that are intended to stay elastic.
Clearly further analysis should be carried out to determine appropriate design
1000
LA25
LA30
800
30
Ti= 0.85
600
20
400
10
200
Tj
0
0
0
1
2
3
Deformation Response (in.)
Deformation Response (mm)
procedures to limit these issues.
4
Period, T (sec.)
Figure 6-41: Deformation response spectrum for LA25 and LA30 with the SCBF and
BRB period shift noted.
161
2
0
0
-10
-2
(a)
(b)
PARA, Brace C
BRB, Brace D
-4
3
Base Shear (10 kN)
20
4
10
2
0
0
-10
-2
(c)
(d)
-4
-20
-3
-2
-1
0
1
2
3
-3
First Story Drift (%)
-2
-1
0
1
2
3
10
Base Shear (10 kips)
4
SMA, Brace B
3
SCBF, Brace A
Base Shear (10 kips)
3
Base Shear (10 kN)
20
3
First Story Drift (%)
2
First Story Drift (%)
1
0
SCBF, Brace A
SMA, Brace B
PARA. Brace C
BRB, Brace D
-1
(e)
-2
0
10
20
30
40
50
Time (sec.)
Figure 6-42: (a-d) Base Shear vs. first story drift and (e) first story drift time history for
SCBF,SMA, PARA, and BRB subjected to the LA30 ground motion.
162
2
0
0
-10
-2
(a)
(b)
PARA, Brace C
BRB, Brace D
-4
3
Base Shear (10 kN)
20
4
10
2
0
0
-10
-2
(c)
(d)
-4
-20
-3
-2
-1
0
1
2
3
-3
First Story Drift (%)
-2
-1
0
1
2
3
10
Base Shear (10 kips)
4
SMA, Brace B
3
SCBF, Brace A
Base Shear (10 kips)
3
Base Shear (10 kN)
20
3
First Story Drift (%)
4
First Story Drift (%)
2
0
SCBF, Brace A
SMA, Brace B
PARA. Brace C
BRB, Brace D
-2
(e)
-4
0
5
10
15
20
Time (sec.)
Figure 6-43: (a-d) Base Shear vs. first story drift and (e) first story drift time history for
SCBF, SMA, PARA, , and BRB subjected to the LA25 ground motion.
163
6.8.2.2. Behavior Due to Suite of Ground Motions
Now the response is investigated over the entire suite of ground motions.
Though
several performance parameters exist, the performance of this braced frame was
assessed by looking at the maximum displacements, interstory drifts, and residual drifts.
For the suite of earthquakes with a 2% probability of exceedance in 50 years, the
results for SCBF (Brace A), SMA (Brace B), PARA (Brace C), and BRB (Brace D) are
shown in Figure 6-44a-d, respectively. From these plots, the following observations can
be made:
ƒ
The SCBF had large drifts forming in the first, second, and third stories. Drifts
exceeded 3% in the second story for several ground motions, which would very
likely result in collapse. However, collapse is not accounted for in the model.
ƒ
The SMA and PARA frames were both effective in decreasing the drifts demands
in the first three stories. However, as mentioned in the analysis of the individual
ground motions, care must be exercised in designing an SMA-based system to
ensure the load plateau is not being greatly exceeded, otherwise forces being
transferred to adjacent members could violate the capacity design method being
used here.
ƒ
The SMA and PARA frames had smaller maximum interstory drifts compared to
the SCBF and the BRB. This was due to the SMA and PARA frames’ ability to
distribute the drift demand move uniformly along the height of the structure and
thus reducing undesirable soft-story behavior.
ƒ
In comparing the SMA and the PARA frames, the PARA system had a slight
performance advantage in terms of maximum drifts. However, the results are not
conclusive. Further investigation needs to be conducted to more fully understand
the impact of a PARA system on the response of a complete structural system.
164
ƒ
The residual drifts were highest in the SCBF, where the bottom three stories had
an average residual drift of 0.6%. The BRB frame was also prone to acquiring
residual drift, though on average the residual drift was half that seen in the
SCBF.
From these observations, SMA-based braces were effective in decreasing interstory drift
for the suite of large earthquakes. The SMA braces did a good job of distributing the
drift demands over the height of the building and thus reducing soft stories. They also
have a clear advantage due to recentering.
165
8
7
7
7
6
6
6
4
5
4
5
4
3
3
2
2
2
0
200
400
1
600
0
D r i ft ( m m )
2
1
4
In t e r s t o r y d r i ft ( % )
9
8
8
7
7
7
6
6
6
4
5
4
5
4
3
3
2
2
2
0
200
400
1
600
0
D r i ft ( m m )
2
1
4
In t e r s t o r y d r i ft ( % )
9
0
8
7
6
6
6
Story Level
7
Story level
8
7
5
4
5
4
3
3
3
2
2
2
1
1
(c)
0
200
400
600
0
Drift (mm)
2
1
4
Interstory drift (%)
8
7
7
7
6
6
6
5
4
5
4
3
3
2
2
2
(d)
0
200
400
D r i ft ( m m )
600
1
0
2
In t e r s t o r y d r i ft ( % )
4
8
3
1
2
9
BRB
Brace D
Story Level
Story level
9
8
4
0
Residual Interstory Drift (%)
9
5
4
9
PARA
Brace C
8
4
2
R e s i d u a l In t e r s t o r y D r i ft ( % )
9
5
4
8
3
1
2
9
SMA
Brace B
Story Level
5
0
R e s i d u a l In t e r s t o r y D r i ft ( % )
9
(b)
Story level
8
3
1
Story level
9
SCBF
Brace A
Story Level
5
(a)
Story level
Story level
9
8
Story level
Story level
9
4
1
0
2
4
R e s i d u a l In t e r s t o r y D r i ft ( % )
Figure 6-44: Drift, interstory dift, and residual drift for the first story of the (a) SCBF, (b)
SMA, (c) PARA, and (d) BRB. Braces A-D (mean = black line, data point = red circles).
166
6.9.
Summary
In this chapter, an articulated quadrilateral bracing system was proposed as a unique
way to implement SMAs. The behavior of the AQ created a platform for SMAs to be
combined in parallel with energy dissipating elements. If properly calibrated, it was
envisioned that this bracing system would have good recentering with optimized energy
dissipation.
The following main conclusions are made from this experimental
investigation:
ƒ
SMA wire bundles were able to recover large levels of strain (from 9-12% in this
study).
ƒ
The relative stiffness of the elements combined to make the bracing assembly
have an effect on the length of the loading plateau relative to the yield
deformation (plateau ductility parameter). To maximize this parameter, the brace
elements combined in series with the SMA element should be sufficiently stiff.
In this experimental test, the brace had a ductility factor of approximately 2.5.
ƒ
C-shape dissipators are unique damping elements that display stable hysteretic
behavior and can be fabricated to a variety of strength, stiffness, and deformation
capacities.
ƒ
The SMA-only bracing system was the best choice when residual drifts needed
to be minimized. The SMA-only system had drifts less than 0.12% after being
pushed to 3% drift.
ƒ
The bracing system that incorporated both SMA and c-shape dissipators (PARA)
had a larger level of damping.
Recentering was sacrificed to obtain this
additional damping. After being cycled to 3% drift, the frame had 0.47% residual
drift.
167
Both SMA-only and the PARA systems had little loss in strength and stiffness
ƒ
after repeated cycling, demonstrating that such a system is well suited for
earthquake loading.
In the analytical study, the SMA and PARA frames had the best performance in
ƒ
terms of interstory and residual drifts. These systems both tended to distribute
the drifts move evenly over the height of the structure, thus reducing the
likelihood of the formation of a soft-story.
This study was exploratory in nature, focusing on the effects of recentering vs. energy
dissipation. It is recommended that further work be done to develop such a device and
more fully determine the performance advantages. Some areas of potential future work
are as follows:
ƒ
Create an AQ that allows for higher levels of SMA-pretension.
This will
increase the recentering ability of the system.
ƒ
Investigate different methods to supplement the SMA damping. One option that
could have good potential is a friction mechanism used by Pall Dynamics.
ƒ
Further investigate the benefits of increased damping in a SMA-based system
(i.e. PARA system).
ƒ
Develop system behavior factors.
168
CHAPTER 7
SUMMARY, CONCLUSIONS, AND RECOMMENDED FUTURE
RESEARCH
7.1.
Summary and Conclusions
Shape memory alloys have the unique ability to spontaneously recover up to 8% strain
upon the removal of load.
NiTi SMAs, known for their superb superelasticity and
corrosion resistance, have only been used in a handful of applications in the civil
engineering industry since their discovery over four decades ago.
The potential to
provide both recentering and supplemental damping is the hallmark of SMA’s behavior
for applications in civil engineering. In this research, it was hypothesized that enhanced
structural performance can be obtained by appropriately balancing recentering and
damping, thus limiting maximum displacements while maintaining reduced residual
displacements.
To demonstrate this fundamental idea, a single-degree-of-freedom
(SDOF) study was first investigated. The SDOF study showed that a recentering system
performs best when the flag-shaped hysteresis is maximized (i.e. the energy dissipation
is maximized while the recentering is retained).
With this observation in mind, three different SMA-based systems were
developed and tested: a tension/compression device, an interior beam-column
connection, and an articulated quadrilateral (AQ) bracing system. Each system was
subjected to a cyclic loading protocol to simulate deformation demands expected during
an earthquake. Because these investigations were exploratory in nature, each system
needs further development and refinement in order to be implemented into practice.
169
Nonetheless, this work was done in hopes of providing justification and motivation for
this further development.
For the SMA tension/compression device, several creative forms of SMAs were
implemented. NiTi helical springs inserted into a stainless steel device were subjected
to compression loading. The results showed that the device has excellent recentering
behavior (no residual deformations) due to the superelasticity and the precompression of
the helical spring. The device’s equivalent viscous damping was approximately 6% over
the entire deformation range. Though the initial results were promising, work needs to
be done to determine if the springs can achieve full-scale load and stiffness levels (the
levels reached in this study were low for typical structural applications). Additionally,
work needs to be done to better understand the effect of several design parameters (coil
diameter, pitch, and thickness) on the resulting strength and stiffness values.
With regards to the SMA Belleville washers, they can be stacked in numerous
different parallel and series arrangements, creating different force and deformations
capacities. For the washer stacks investigated in this study, the equivalent viscous
damping ranged from 4-12%. The force-deformation curve was not predictable due to
the weakest washer losing load carrying capacity thus taking on high levels of
deformation until it was completely flat. The maximum force levels ranged from 20 kN
(4.5 kips) for the single-stacked arrangement to 35 kN (7.9 kips) for the triple-stacked
arrangement. Improved behavior of an individual washer was shown through cyclic
training and deformation demand reduction; when an individual washer was cycled to
approximately 60% of its flat deformation, the load drop-off was eliminated and residual
deformations were greatly reduced.
After the tension/compression device investigation was completed, an innovation
interior SMA beam-column connection was tested.
This investigation was done to
evaluate the efficacy of using SMA tendons as recentering and damping elements in a
170
partially-restrained connection. The design consisted of four SMA tendons attached to
the end of the beams via anchor brackets. When drift was imposed, the beams were
forced to pivot off the face of the column flange which resulted in the SMA tendons
stretching. The results demonstrated that a SMA-based connection can be developed to
have good ductility, energy dissipation, and recentering. The following conclusions and
significant observations are made from the experimental testing:
ƒ
SMA tendons possessed significant superelastic properties which fully
recentered the connection at drift levels below 1.0% and adequately recentered
the connection at drift levels above 1%. The connection was able to recover
85% of its deformation after being cycled to 5% drift.
ƒ
The SMA connection had equivalent viscous damping that varied from
approximately 6 to 13% as drift levels increased from 0.375 to 5%. The energy
dissipation in the connection was a direct result of NiTi’s hysteretic mechanical
behavior and friction in the shear tab connection.
ƒ
The equivalent viscous damping in the SMA-only (Test D) connection was
greater than that of the SMA + aluminum (Test E) parallel connection. This
surprising result can be explained by the following observations: 1) the same
physical tendons were used in both tests, resulting in reduced material hysteresis
for Test E; and 2) the AL tendons buckled in compression resulting in a minimal
increase in hysteretic area at larger drift levels.
ƒ
For the test connection layout, a 0.5% prestrain was applied to all SMA tendons.
Prestraining of the SMA tendons was effective in increasing the recentering
capability, and the overall behavior of the connection.
ƒ
A simple model in OpenSEES provided a good fit to the experimental data and
could account for some level of residual deformation.
171
However, this model
tended to overestimate the strength and stiffness at small drift levels due to its
inability to capture the behavior at the transition zone.
Finally, a SMA-based bracing system was developed and tested. The system
consisted of a special articulated quadrilateral (AQ) arrangement that accommodated
710 mm (28 in.) long SMA wire bundles. The AQ created a convenient platform for the
SMA wire bundles to be combined in parallel with energy dissipating elements.
If
properly calibrated, it was envisioned that this bracing system would have good
recentering with optimized energy dissipation. The following main conclusions are made
from this experimental investigation:
ƒ
SMA wire bundles were able to recover large levels of strain (approximately 912% in this study).
ƒ
C-shape dissipators are a unique damping element that display stable hysteretic
behavior and can be fabricated to a variety of strength, stiffness, and deformation
capacities.
ƒ
Both SMA-only and the SMA plus c-shape (PARA) systems had little loss in
strength and stiffness after repeated cycling, demonstrating that such a system is
well suited for earthquake loading.
ƒ
The relative stiffnesses of the SMA elements and those put in series with the
SMA elements (steel cables in this case) are important. The adjacent elements
should be made stiffer than that of the SMA in order to get full advantage of the
SMA loading plateau.
ƒ
An analytical study showed that the SMA system and the PARA system had the
best performance in terms of interstory and residual drifts. These SMA systems
tended to distribute the drifts move evenly over the height of the structure, thus
172
reducing the likelihood of the formation of soft-stories. Additionally, the SMA
systems had a clear advantage in terms of residual drifts.
7.2.
Recommended Future Research
This study was exploratory in nature, focusing on the effects of recentering vs. energy
dissipation and the development of innovative systems that provided both.
It is
recommended that further work be done to develop each system investigated in this
work. Some areas of potential future work are as follows:
ƒ
Assess and improve the behavior of individual SMA Belleville washers and verify
the benefits of training illustrated in CHAPTER 4. Integrate these washers into
partially-restrained connections.
The unique response of the SMA Belleville
washer could enhance the behavior of the connection and give it some degree of
recentering.
ƒ
Create a SMA-based beam-column connection that is designed with realistic,
efficient, and cost effective construction details. Such a connection could involve
integrating SMA tendons into other promising connection types currently being
developed, such as the Kaiser Bolted Bracket connection (Adan and Gibb, 2008)
or the welded T-stub connection (Kasai and Xu, 2002a; Kasai and Xu, 2002b).
Additionally, new ways to impose higher levels of pretension on the SMA tendons
should be investigated, since these tendons tended to twist rather than allow
further pretensioning. This work should be done in collaboration with practicing
engineers who have a firm grasp on the design and construction process.
ƒ
Investigate different methods to supplement the SMA hysteretic damping in the
AQ arrangement.
One option that could have good potential is a friction
mechanism used by Pall Dynamics Limited.
173
ƒ
Investigate different spatial arrangements of SMA connections and braces to see
how best a high level of performance can be achieved. Also investigate the uses
of SMA-based systems as part of a dual system.
ƒ
Develop a design procedure for SMA-based systems (both moment-resisting and
braced frames). SMA-based systems behave differently than other traditional
and advance systems, therefore system design factors need to be determined
(i.e. R, Ω0, and Cd).
ƒ
Further investigation is needed to advance the performance of large bar diameter
SMAs. Guidelines should be developed for controlling the properties of SMAs
with regard to the properties that are important to civil/structural engineers.
ƒ
A study needs to be performed that assesses the root causes for the lack of
implementation of SMAs in civil engineering. Though SMAs have shown great
promise over the last several decades, limited applications have reached
practice. The gap between research and practice needs to be closed.
174
APPENDIX A
LOADING FRAME DETAILS
This appendix gives detailed description of the lateral loading frame used throughout the
experimental portion of this research. For the frame beams, two 801.4 cm (315.5 in.)
long W914x224 (W36x150) members were used. These members were left over from
other experimental work and had a variety of stiffeners already in place, as indicated by
Figure A-1. Additional angled stiffeners were welded at the left end of the top member to
transfer the actuator force without buckling the top beam web. The bottom beam was
leveled by shimming and post-tensioned to the strong floor. For the frame columns, two
327.7 cm (129.0 in.) W356x216 (W14x145) members were used. These columns had
2.54 cm (1.0 in.) thick plates welded to each end which enabled them to be easily
attached to pin-clevis assemblies.
For the pin-clevis assemblies, two types were installed in the frame. At the top,
existing assemblies were used with Strainsert SPA-160 load sensing clevis pins. These
pins have a capacity of 717 kN (160 kip) and a sensitivity of 2 mV/V at full scale. For the
bottom assemblies, larger capacity assemblies were fabricated using 1479 kN (330 kip)
Strainsert SPA-330 pins with a sensitivity of 2 mV/V at full scale.
These bottom
assemblies integrated low friction ball bearings in order to minimize the overall frame
friction resistance.
For the load application, a 1000 kN (220 kip) +/- 25.4 cm (10 in.) hydraulic
actuator was used.
The actuator, controlled by a digital MTS 407b PIDF servo
controller, was installed between two stiffened W-sections. The reaction frame was
175
designed to handle two actuators in parallel for a total capacity of 2000 kN (440 kips).
For this research, only one actuator was used.
For the tests presented in CHAPTER 5, interior members were added to the
frame to accommodate a half-scale beam-column connection specimen. Appropriate
members and shim plates were installed to raise the center of the specimen connection
with that of the loading frame in order to reduce kinematic issues (see discussion in
APPENDIX B, Section B.2).
Loading pin-clevis assemblies were designed and
fabricated to transfer the load from the frame to the specimen (Figure A-2).
The
specimen beams have a slotted pin in order to enable the beams to move laterally
during the testing.
The pins at the ends of the specimen column and beams are
representative of the location of inflection points in a full framing system.
Figure A-1: Loading frame test bed.
176
Figure A-2: Column pins with shim plates installed.
177
APPENDIX B
BEAM-COLUMN CONNECTION: EXPERIMENTAL PROGRAM
This appendix gives detailed information on the mechanical tests of the various
connection components and additional information on the testing scheme employed to
test the connection.
B.1
COMPONENT TESTING
This section describes the setup and component tests of the beam coupons, steel
tendons, NiTi tendons, and aluminum tendons.
B.1.1
Component Test Setup
Mechanical tests were carried out using an 810 MTS Universal Testing Machine as
shown in Figure B-1. The MTS machine has a capacity of 250 kN (55 kip) measured by
a built-in load cell and a +/-127 mm (5 in.) stroke measured by a built-in LVDT. The
machine was fitted with hydraulic vee-notched wedge grips which could accommodate a
bar diameter up to 19.05 mm (0.75 in.).
The tests were run in displacement control
using the stroke as the controlling parameter. The machine was controlled by Teststar
running Testware software. During some of the tests a 25.4 mm (1.0 in.) gauge MTS
extensometer and a 120-ohm strain gauge were used for additional measurements.
178
Figure B-1: The 810 MTS Universal Testing Machine.
B.1.2 Beam Coupons
For the connection to behave properly, the A572 Grade 50 beams were designed to
remain elastic throughout the connection tests. To confirm the mechanical properties of
the beam, two coupons were taken from an extra beam section, one along the edge of
the flange and the other at the center of the web. The coupons were subjected to a
monotonic loading protocol at a rate of 0.127 mm (0.005 in.) per min. until 0.4% strain
and then 1.27 mm (0.05 in.) per min. until failure. The results are shown in Figure B-2
(a-d). The coupons yielded at 376 MPa (54.5 ksi) and 386 MPa (56.0 ksi), which both
exceeded the required strengths for A572 grade 50 materials.
179
600
40
200
Leff = 62.4 mm
0
1000
2000
3000
4000
0
0.0
60
40
200
Leff = 62.4 mm
0
0
1000
(a)
2000
0.2
0.3
Strain
(SG & LVDT)
80
500
300
100
0
0.1
600
80
E = 197 GPa
σy = 386 MPa
400
20
(b)
600
500
0
5000
Strain, με
(SG)
(a)
40
200
100
3000
4000
20
Stress (MPa)
0
20
300
60
400
300
40
200
20
100
0
5000
0
0.0
Strain, με
(SG)
(b)
Stress (ksi)
100
60
400
Stress (ksi)
300
Stress (MPa)
60
Stress (ksi)
400
80
500
Stress (ksi)
500
600
80
E = 197 GPa
σy = 376 MPa
0
0.1
0.2
0.3
Strain
(SG & LVDT)
Figure B-2: Stress-strain relationship of the beam coupons.
B.1.3
Steel Bars
For beam-column Tests A and B, steel bars were used as the tendon elements.
Monotonic and cyclic tests were conducted on dogbone specimens of these steel bars.
The tests were run in displacement control at 2.5 mm (0.1 in.) per min.
The bar
dimensions for the tests are shown in Figure B-4. Each bar was machined as per the
ASTM E8-03 standard for tensile testing of round bars (ASTM, 2003). Steel bars were
used in the connection instead of SMA bars in order to provide a less expensive first-run
test on the connection and to provide a benchmark performance comparison of a
recentering connection using superelastic SMAs.
180
Two different types of steel bars were used. In Test A, plain steel threaded rod
of unknown ASTM grade was purchased and machined. The stress-strain curves are
shown in Figure B-5 for a) a monotonic test used to calculate the elastic modulus and
the yield stress, b) the same monotonic test used to show gross strain based on the
LVDT reading, and c) a cyclic test. The elastic modulus, yield stress, and ultimate stress
were found to be 197 GPa (28,600 ksi), 325 MPa (47.1 ksi), and 490 MPa (71.1 ksi),
respectively. During the monotonic loading, the bar fractured at approximately 32%
strain. During the cyclic loading, the bar had a stable hysteretic response with the yield
plateau beginning and ending at approximately 375 MPa (54.4 ksi) and 450 MPa (65.3
ksi), respectively.
In Test B, standard A36 steel was used. The bars were already machined from
previous work (Penar, 2005) on the beam-column connection. Only one mechanical
test, a cyclic loading protocol, was run on this bar and is shown in Figure B-6 . The
elastic modulus and yield stress were found to be 197 GPa (28,500 ksi) and 350 MPa
(50.8 ksi), respectively. The bar was not stretched until failure, therefore neither the
ultimate strength nor the ultimate strain was known.
7
Strain (%)
6
5
4
3
2
1
0
0
2
4
6
8
10
12
Steps
Figure B-3: Cyclic loading protocol for the mechanical testing.
181
Figure B-4: Dogbone mechanical test specimen dimensions ( units in mm).
600
600
300
40
30
200
φ = 12.7 mm
Leff = 56.1 mm
0
(a)
20
500
70
400
60
50
300
40
30
200
20
100
10
0
1000 2000 3000 4000 5000
10
0
0.00
Strain, με
(Strain Gauge)
0.05
0.10
0.15
0.20
0.25
Strain
(LVDT)
(b)
600
80
60
400
40
200
20
0
0
-20
-200
-40
-400
Stress (ksi)
0
Stress (MPa)
50
Stress (ksi)
60
400
100
80
70
Stress (MPa)
Stress (MPa)
500
80
-60
-600
0.00
(c)
-80
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Strain
(LVDT)
Figure B-5: Stress-strain of the steel threaded bar for Test A.
182
0.30
0
0.35
Stress (ksi)
E = 197 GPa
σy = 325 MPa
600
50
40
30
200
20
100
φ = 12.7 mm
Leff = 73.7 mm
0
0
(a)
1000
2000
Stress (MPa)
300
80
60
400
20
0
0
-20
-200
10
-400
0
-600
3000
40
200
-40
-60
-80
0.00
Strain
(Strain Gauge)
Stress (ksi)
E = 197 GPa
σy = 350 MPa
Stress (ksi)
Stress (MPa)
400
0.01
(b)
0.02
0.03
0.04
0.05
0.06
0.07
Strain
(LVDT)
Figure B-6: Stress-strain of A36 steel bar for Test B (data from Penar, 2005).
B.1.4 NiTi Bars
The loading protocol followed for the SMA mechanical testing was the same as that for
the steel testing as shown in Figure B-3. Again, this protocol was implemented using
displacement control, with the strain calculated as the crosshead displacement divided
by the effective length of the specimen (69.9 mm (2.75in.) in this case). It should be
noted that this gross strain is smaller than that which is obtained from the more
concentrated strain recorded from the extensometer.
The NiTi bars had an elastic
modulus and yield strength of approximately 23 GPa (3300 ksi) and 325 MPa (47.0 ksi),
respectively. These values were both less then seen in previous research testing of
similar bar specimens (McCormick 2006).
183
500
70
Stress (MPa)
50
300
40
30
200
Stress (ksi)
60
400
20
100
10
0
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Strain (EXT)
Figure B-7: Stress-strain of the NiTi dogbone.
B.1.5 Aluminum Bars
In order to create a connection with a parallel resisting system as proposed in the SDOF
study of CHAPTER 3, low strength aluminum (AL) bars were used. A low strength
material was needed in order to prevent the connection beam from being overloaded.
Readily available 6061-T6511 AL was purchased and tested; it displayed a yield
strength of approximately 414 MPa (60 ksi). Since lower strength material was desired,
the AL was annealed.
First the tendons were machined and threaded.
Next, the
tendons were heated to 425 °C for 4 hrs., then cooled 30 °C/hr. until the temperature fell
below 260 °C, and then finally air-cooled (annealing procedure adopted from the
Handbook of Aluminum) (Alcan, 1970).
The loading protocol followed for the AL mechanical testing was the same as that
for the steel and SMA testing as shown in Figure B-3. The effective length of the test
specimen was 71.9 mm (2.83 in.). The resulting stress-strain relationship is show in
Figure B-8. The elastic modulus and yield stress were 32.4 GPa (4700 ksi) and 117
MPa (17 ksi), respectively.
The low strength was a direct result of the annealing
process.
184
150
20
10
50
0
0
-50
-10
Stress (ksi)
Stress (MPa)
100
-100
-150
-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
(a)
Strain
(Extensometer)
-20
-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
(b)
Strain
(LVDT)
Figure B-8: Stress-strain for the annealed aluminum bar.
B.2
LOADING FRAME AND SPECIMEN INTERACTION
When the loading frame deflects laterally, the frame’s top beam translates downward
(vertical) due to the arc traced by the top of the frame’s column. The amount of vertical
translation is a function of the height of the frame column. The larger the height of the
column, the less this vertical translation is per unit horizontal movement. Since the
installed specimen column does not have the same height as that of the frame column,
tension is induced in the specimen column by lateral movement of the loading frame. In
order to reduce this unwanted kinematic effect, steel plates were used as shims to
provide some precompression to the specimen column. The column was installed with
the frame displaced 120 mm (4.7 in.) to the right. When the frame was moved back to
center, the kinematics described above resulted in precompression of the column.
During the testing the specimen column must first give up the precompression before it
can go into tension, thus reducing the magnitude of the tension that is ultimately
induced.
Another kinematic issue identified is the tendency for specimen’s lateral
dimension to grow as the frame is cycled. This is caused by the beams pivoting off the
185
face of the column. During traditional testing of an interior beam-column connection, the
beams are not restrained from elongation in the axial direction. Therefore, in order to
relieve the unwanted axial load that this would cause, the end beams were fitted with
slotted pins that allow beam ends to slide in the horizontal direction. Additionally, the
specimen was installed at mid-height of the frame because the beam ends will travel
approximately half that of the top of the specimen columns.
B.3
INSTRUMENTATION
A detailed schedule of the instrumentation is given in Table B-1. Figure B-9 and Figure
B-10 show a detailed layout of where the instrumentation was placed.
Table B-1: Instrumentation Schedule for the Beam-Column Tests.
#
Type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
LVDT
LC
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SG
SP
SP
SP
SP
EXT
EXT
EXT
Details
Location
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
FLA-5-11-5L
PA-10-35090455
PA-10-35090456
PA-20-35090457
PA-20-35090460
3545-0200-020-ST
3545-0200-025-ST
3545-0200-020-ST
Actuator
Actuator
CF-left-up-mid
CF-left-up-side
CF-right-up-mid
CF-right-up-side
CF-left-down-mid
CF-left-down-side
CF-right-down-mid
CF-right-down-side
BF-left-up-mid
BF-left-up-side
BF-left-down-mid
BF-left-down-side
BF-right-up-mid
BF-right-up-side
BF-right-down-mid
BF-right-down-side
B-left
B-right
C-bottom
C-top
T-top-front
T-top-back
T-bottom-front
186
SCXI
Block
1303
1303
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1317
1303
1303
1303
1303
1314
1314
1314
SCXI
Card
1100
1100
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1520B
1100
1100
1100
1100
1520
1520
1520
Comments
10 in.
220 kips
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
120 ohm
10 in.
10 in.
20 in.
20 in.
Epsilon
Epsilon
Satec
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
EXT
LVDT
LVDT
LVDT
LVDT
Pin LC
Pin LC
Pin LC
Pin LC
SG
SG
SG
SG
SG
SG
SP
SG
SG
545-0100-025-ST
DCTH500-42979
DCTH500-42976
DCTH500-42978
DCTH500-42966
SPA-160
SPA-160
SPA-330
SPA-330
FRA-5-11-5L
FRA-5-11-5L
FRA-5-11-5L
FRA-5-11-5L
FRA-5-11-5L
FRA-5-11-5L
PA-20-35090459
FLA-5-11-5L
FLA-5-11-5L
T-bottom-back
top-left
top-right
bottom-left
bottom-right
top-left
top-right
bottom-left
bottom-right
PZ-upper-left 1
PZ-upper-left 2
PZ-upper-left 3
PZ-middle 1
PZ-middle 2
PZ-middle 3
Frame-top
B-left-top-mid
B-right-top-mid
1314
1303
1303
1303
1303
1303
1303
1303
1303
1317
1317
1317
1317
1317
1317
1303
1317
1317
1520
1100
1100
1100
1100
1100
1100
1100
1100
1520B
1520B
1520B
1520B
1520B
1520B
1100
1520B
1520B
44
SG
YEFLA-5-11-5LT
T-top-front
1314
1520
45
SG
YEFLA-5-11-5LT
T-top-back
1314
1520
46
SG
YEFLA-5-11-5LT
T-bottom-front
1314
1520
47
SG
YEFLA-5-11-5LT
T-bottom-back
1314
1520
Epsilon
+/- 0.5"
+/- 0.5"
+/- 0.5"
+/- 0.5"
Strainsert
Strainsert
Strainsert
Strainsert
rosette, 120 ohm
rosette, 120 ohm
rosette, 120 ohm
rosette, 120 ohm
rosette, 120 ohm
rosette, 120 ohm
20"
120 ohm
120 ohm
high elongation,
120 ohm
high elongation,
120 ohm
high elongation,
120 ohm
high elongation,
120 ohm
SG = strain gauge, LC = load cell, LVDT = linear variable displacement transducer, EXT = extensometer,
SP = string potentiometer, C(F) = column (flange), B(F) = beam (flange), PZ = panel zone
187
50.8 [2.00]
bf/4
228.599 [9.00]
304.8 [12.00]
120Ω SG
(a) top view, section A-A
LVDT
A-A
bf/2
bf/4
Extensometer
228.6 [9.00]
B-B
bf/4
SG rosette
302.26 [11.90]
bf/2
(c) side view, section B-B
(b) front view
Figure B-9: Instrumentation of specimen connection (units in cm).
188
47.466
actuator (with built-in
load cell and LVDT)
120Ω SG
144.78
167.64
137.795
18.415
16.51
pin load cell
string
potentiometer
Figure B-10: Instrumentation of frame and specimen (units in cm).
B.4
DATA ACQUISITION
Data from the appropriate sensors was collected using a National Instruments SCXI1001 chassis fitted with the following module cards and terminal blocks:
•
Slot 1: (a) SCXI-1520 8-channel Wheatstone bridge module card (b) SCXI-1314
universal strain terminal block
•
Slot 2: (a) SCXI-1521 350 Ω 24-channel quarter bridge module card (b) SCXI1317 terminal block
•
Slot 3: (a) SCXI-1521B 120 Ω 24-channel quarter bridge module card (b) SCXI1317 terminal block
•
Slot 4: (a) SCXI-1100 module card (b) SCXI-1303 32-channel thermocouple
terminal block
This chassis was connected to a Dell computer running National Instruments Labview
version 8.0. A virtual instrument was designed within Labview to excite sensors and
189
collect the corresponding data. Data was sampled at 100 readings per second. In order
to smooth out some of the existing noise, 50 readings were collected (per ½ second),
averaged, and then recorded as the value for the corresponding channel.
This
effectively gives recording rate of 2 average readings per second. However, due to the
DAQ’s speed limitations, the actual recording rate was reduced to approximately every
0.9 seconds.
190
APPENDIX C
BEAM-COLUMN CONNECTION: DATA REDUCTION
C.1
DEFINITIONS
General
ε
Strain
d
Distance
δ
Displacement
δLV1
LVDT displacement at top of left beam
δLV2
LVDT displacement at top of right beam
δLV3
LVDT displacement at bottom of left beam
δLV4
LVDT displacement at bottom of right beam
E
Elastic modulus
I
Section moment of inertia
M
Moment
θ
Rotation
σ
Stress
Sign Convention
The sign convention followed for the moment and rotations are illustrated in Figure C-1.
Figure C-1: Sign convention for the M-θ plots.
191
C.2
MOMENT
The moments in the specimen beams and the specimen column were calculated based
on the strain gauge readings mounted at a distance d from the respective connection
bracket. It is assumed herein, and experimentally verified for all tests that the beams
and the column remained elastic; therefore Hooke’s Law applies:
σ = Eε
(C.1)
In order to get the stress at the outside flange surface, the middle and quarter strain
gauges are averaged as follows:
(σ tm + σ tq )
σt =
σb =
2
(σ bm + σ bq )
σa =
σM =
2
(σt
+ σb )
2
(C.2)
(C.3)
(C.4)
(σ b − σt )
(C.5)
2
where σt, σb, σa, and σm are the top flange stress, bottom flange stress, axial stress
component, and bending stress component, respectively.
The moment can be calculated by the flexure formula:
M = ∫ yσ ⋅ dA ⇒ M =
A
σM I
(d 2 )
(C.6)
where d is the depth of the beam.
C.3
ROTATIONS
C.3.1 Concentrated rotations
The concentrated rotation calculated from the LVDT readings for the right (concR) and
left (concL) beam are:
192
θ concR =
θ concL =
(δ LV 2 − δ LV 4 )
d′
(δ LV 1 − δ LV 3 )
d′
(C.7)
(C.8)
where d’ is the distance between the LVDTs and δLV1, δLV2, δLV3, and δLV4 are the
readings from the top-left, top-right, bottom-left, and bottom-right LVDTs, respectively.
C.3.2 Total Rotation
The total rotation is defined as:
θ total =
δ col
Lc
(C.9)
where δcol is the displacement at the top of the column (at centerline of the pin)
C.4
PRINCIPLE STRAINS
The three gauge rosettes provided means to calculate the principle strains in the panel
zone. The three readings in each gauge are denoted by εA, εB, and εC as depicted in
Figure C-2. Knowing the strain gauges are 45° apart, the strain in each gauge can be
written in terms of the principle strains, ε1 and ε2, as follows:
ε1 + ε 2 ε1 − ε 2
+
cos(2φ)
2
2
(C.10)
εB =
ε1 + ε 2 ε1 − ε 2
+
cos(2φ + 45°)
2
2
(C.11)
εC =
ε1 + ε 2 ε 1 − ε 2
+
cos(2φ + 90°)
2
2
(C.12)
εA =
With three equations and three unknowns (ε1, ε2, and φ), the principle strains are solved
for giving:
ε1,2 =
ε A + εC
1
+
2
2
193
(ε A − ε B )2 + (ε B − εC )2
(C.13)
Figure C-2: Strain gauge rosette orientation for principle strain calculations.
C.5
DRIFT CONTRIBUTION CALCULATIONS
In the following calculations, small angles are assumed which affords the following
approximations:
sin(θ) ≅ θ
cos(θ) ≅ 1
1 − cos(θ ) ≅
θ2
2
(C.14)
C.5.1 Drift contribution due to beam and column elastic flexure
General Formulation
Starting with the established relationship between curvature, φ, and moment, M,
dθ
M
=φ=
dx
EI
(C.15)
M
dx
EI
(C.16)
Solving for the rotation, θ
θ=∫
The moment is linearly changing along the length, therefore
M = mx
(C.17)
Where m is the slope of M and x is the distance along the member as illustrate in Figure
C-3. Solving for θ yields
θ=
mx 2
+c
2EI
(C.18)
Accounting for the boundary conditions to solve for the constant c (i.e. θ = 0 at x = L)
gives
194
mL2
2EI
c=−
(C.19)
Now, solving for the deflection δ in terms of x
δ=
(
)
m
2
2
∫ x − L ⋅ dx
2EI
(C.20)
m ⎛ x3
2⎞
⎜
⎟
−
xL
⎟
2EI ⎜⎝ 3
⎠
(C.21)
δ=
Beam Calculations
The various variables are defined in Figure C-3. Solve for θa0
θa0 =
δ a0
Lb'
(C.22)
where
Lb' = Lb +
dc
2
m b Lb
3EI b
δ a0 = −
(C.23)
3
(C.24)
Column Calculations
The various variables are defined in Figure C-3. Solve for θa1
δ a1
Lc '
(C.25)
Lc − d c '
2
(C.26)
θ a1 =
where
Lc ' =
δ a1 = −
mc Lc '
3EI c
3
(C.27)
Also,
δ a3 = θa0 d b'
195
(C.28)
Overall frame
The overall drift contribution due to flexure can be calculated by first finding δa2 then
summing the appropriate δ’s.
δ a 2 = (θ a 0 + θ a1 ) ⋅ Lc '
(C.29)
Finally, the drift contribution due to elastic bending of the beam and column is:
δ a = 2δ a 2 + δ a 3
(C.30)
Figure C-3: Schematic defining parameters in order to calculate the drift from beam and
column flexure.
196
C.5.2 Drift Contribution Based on Column Joint Shear
The drift contribution due to panel zone shear is:
(Lc
δb =
⎛L
⎞
− d b ' )⎜⎜ c − 1⎟⎟
⎝ d b'
⎠V
c
Gt p d c
(C.31)
Where Vc is the shear force in the column calculated from the strain gauges in the
column by the following formula
Mc Lc '
d b'
(C.32)
E
2(1 + ν )
(C.33)
Vc =
G=
where ν = 0.3, Mc is the moment in the column at the outside face of the connection, Lc’
is the length of the column as show in Figure C-3.
C.5.3 Drift contribution Based on Beam Concentrated (Inelastic) Rotation
The following equations first relate the concentrated rotation, θconc., to the column
rotation, θc1. Once this relation is known, the equation for the drift contribution, δ, based
on θconc. is found. Figure C-4 and Figure C-5 define the parameters used to make these
calculations.
Right Beam
When the imposed drift is to the right, the right beam is governed by the following
equations which ultimately relate the θconcR to the θc1R (where the “R” denotes the right
beam).
θ concR =
(δ LV 2 − δ LV 4 )
d′
(C.34)
Where δLV2 and δLV2 are defined in Section A.3.1. The variable d’ is the depth of the
beam plus the mounting brackets.
197
From geometry, the following equations can be written
δ cR 0 = δ cR1 + δ cR 2
(C.35)
δ cR1 =
Lc
θ cR1
2
(C.36)
δ cR 2 =
dc
θcR1
2
(C.37)
δ cR1 =
Lc
δ cR 2
dc
(C.38)
Therefore
Substituting (C.37) into (C.35) gives
⎛L
⎞
δ cR 0 = ⎜⎜ c + 1⎟⎟δ cR 2
⎝ dc
⎠
(C.39)
Getting θcR2 in terms of θcR1 yields
θ cR 2 =
δ cR 0 (Lc + d c ) ⋅ θ cR1
=
Lb
2Lb
⎡ (L + d c ) ⎤
θ concR = θ cR1 + θ cR 2 = ⎢ c
+ 1⎥ θ cR1
⎣ 2Lb
⎦
(C.40)
(C.41)
Therefore
θ cR1 =
1
⎡ (Lc + d c ) ⎤
+ 1⎥
⎢
⎣ 2Lb
⎦
θ concR
(C.42)
Equation (C.42) is the rotation of the specimen column with respect to the ground in
terms of the right beam’s concentrated rotation.
Finally, the drift contribution is
δ cR = Lc θ cR1
198
(C.43)
Left Beam
In contrast to the right beam, the left beam is governed by different equations when the
imposed drift is to the right (due to the kinematics of the setup). The following equations
give the relation between θconcL to the θcL1, where the “L” denotes the left beam.
θ concL =
(δ LV 1 − δ LV 3 )
d′
(C.44)
Where δLV1 and δLV3 are defined in section A.2.1
δ cL 0 = δ cL1 + δ cL 2
(C.45)
Where
δ cL2 = (1 − cos(θcL1 ))
Lc
2
(C.46)
δ cL2 = (1 − cos(θcL1 ))
Lc
2
(C.47)
Substituting in (A.7c)
δ cL2 =
Lc
2
θ cL1
4
(C.48)
Concurrently
δ cL 2 = Lb (θ cL1 − θ concL ) +
dc
θ cL1
2
(C.49)
Setting (A.20) equal to (A.21), and solving the quadratic equation for θcL1 gives
θ cL1 =
(Lb + d c 2) ± (Lb + d c 2)2 − Lc Lb θ concL
Lc 2
(C.50)
When θconcL= 0 then θcL1 = 0. Only the negative root satisfies this condition, therefore
θ cL1 =
(Lb + d c 2) − (Lb + d c 2)2 − Lc Lb θ concL
Lc 2
(C.51)
Finally, the drift contribution is
δ cL = Lc θ cL1
199
(C.52)
Both Beams
In theory the δcR and the δcL should be equal. Therefore, the average is taken as the drift
contribution, δc, due to concentrated inelastic beam rotation.
δc =
δ cR + δ cL
2
(C.53)
Note that when the imposed drift is to the left, the equations are switched for the right
and left beams. This is programmed into the script when the data reduction is carried
out.
200
Figure C-4: Schematic defining parameters in order to calculate the drift per the left
beam instrumentation.
201
Figure C-5: Schematic defining parameters in order to calculate the drift per the right
beam instrumentation.
202
APPENDIX D
BEAM-COLUMN CONNECTION: VALIDATION
This appendix walks through selected experimental data obtained from each test, with
the intent to lend validity to the results. The calculations made in the data reduction of
each beam-column test assumed the beams and column remained elastic.
To confirm this assumption, the strain time histories as recorded from the SGs
attached at a distance d from the L-shape bracket termination (see Figure B-9) are
shown in Figure D-1.
Additionally, a dashed line is plotted by extrapolating this SG
reading to get the strain at the face of the column.
This extrapolated value is
conservative because the majority of the forces have already been transferred into the
bracket elements before the column face is reached. Nevertheless, this extrapolated
value is assumed to be the largest strain present in the member. From the coupon tests,
the yield strain, εy, is calculated to be approximately 2000 microstrain. The SG readings
(both real and extrapolated) are well below the εy, confirming the assumption of the
beams remaining elastic.
The panel zone elasticity also needs to be verified. Plots of principal strains
calculated from the strain gage rosettes are shown in Figure D-2. The strain levels in
the panel zone never exceed 1000 microstrain, which is well below the yielding value.
To further validate the results, the drift contributions are calculated as described
in APPENDIX C.
The contributions are schematically illustrated in Figure D-3 and
include the elastic action of the beam and column, δa; the shear deformation action in the
panel zone, δb; and the inelastic action of the beam at the column face, δc.
203
No
contribution from the column inelastic action was calculated because the column
remains fully elastic at the joint interface.
On the left side of Figure D-4, the sum of these three contributions, δ = δa+δb+δc,
and the drift as measured by the mounted sensors (SP), δsensor, are plotted vs. time for
each test. On the right side of Figure D-4, the difference between these drift values, δδsensor, is plotted and the maximum absolute value of this difference is noted for each
test. Since these values should be equal, the difference is a measure of error in the
experimental calculations. This error ranged in between 5-10%, which was determined
to be satisfactory.
204
Microstrain
2000
Test A
at SG location (d away from bracket)
extrapolated to column face
1000
0
-1000
-2000
0
2000
4000
6000
8000
10000
12000
Microstrain
2000
Test B
1000
0
-1000
-2000
0
1000
2000
3000
4000
5000
Microstrain
2000
6000
Test C
1000
0
-1000
-2000
0
2000
4000
8000
Data point
2000
Microstrain
6000
Test D
1000
0
-1000
-2000
0
2000
4000
Data point
2000
Microstrain
6000
Test E
1000
0
-1000
-2000
0
2000
4000
6000
8000
Data point
Figure D-1: Strain time history of top-mid SG on left beam for each test.
205
Microstrain
2000
Test A
ε1
1000
ε2
0
-1000
-2000
0
2000
4000
6000
8000
10000
12000
Microstrain
2000
Test B
1000
0
-1000
-2000
0
1000
2000
3000
4000
5000
Microstrain
2000
6000
Test C
1000
0
-1000
-2000
0
2000
4000
8000
Data point
2000
Microstrain
6000
Test D
1000
0
-1000
-2000
0
2000
4000
Data point
2000
Microstrain
6000
Test E
1000
0
-1000
-2000
0
2000
4000
6000
8000
Data point
Figure D-2: Principle strain time history at center of the panel zone for each test.
206
Figure D-3: Description of the drift contributions.
207
sum of drift contributions, δ
drift per SP reading, δsensor
100
δ−δsensor
Test A
50
0
-50
δ − δ sensor
MAX
δ − δ sensor
MAX
δ − δ sensor
MAX
δ − δ sensor
MAX
δ − δ sensor
MAX
= 4.3mm
-100
100
Test B
50
0
-50
= 8.8mm
-100
Drift (mm)
100
Test C
50
0
-50
= 5.6mm
-100
100
Test D
50
0
-50
= 5.9mm
-100
100
Test E
50
0
-50
= 8.3mm
-100
Time
Figure D-4: Drift time histories as calculated by the (1) sum of the drift contributions, (2)
the SP sensor, and (3) the difference these two values.
208
APPENDIX E
BEAM-COLUMN CONNECTION: DATA
E.1
TEST A
100
4
75
3
50
2
25
1
0
0
-25
-1
-50
-2
-75
-3
-100
-4
-125
0
2000
4000
6000
Time (step)
Figure E-1: Actuator displacement time history for Test A.
209
Displacement (in)
Displacement (mm)
125
Actuator Displacement (in)
-4
-2
0
2
4
100
20
80
15
60
Actuator Force (kN)
20
5
0
0
-20
-5
-40
Actuator Force (kips)
10
40
-10
-60
-15
-80
-20
-100
-100
-50
0
50
100
Actuator Displacement (mm)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-3: M-θ at the column face of the left beam for Test A.
210
Moment (kip-in)
Moment (kN-m)
Figure E-2: Actuator force-displacement for Test A.
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
Figure E-4: M-θ at the column face of the right beam for Test A.
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-5: M-θ at outside L-shape for column per top strain gauges for Test A.
211
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-6: M-θ at outside L-shape for column per bottom strain gauges for Test A.
Top of column Displacement (in)
-4
-2
0
2
4
4
100
2
50
1
0
0
-1
-50
-2
Actuator Displacement (in)
Actuator Displacment (mm)
3
-3
-100
-4
-100
-50
0
50
100
Top of Column Displacement (mm)
Figure E-7: Displacements at the top of the column vs. at the actuator for Test A.
212
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
top-front
top-back
bottom-front
bottom-back
0.6
10
0.4
5
0.2
0
0.0
Gap Opening (in)
Gap Opening (mm)
15
-5
-125
-100
-75
-50
-25
0
25
50
75
100
125
Top of Column Displacement (mm)
Figure E-8: Gap openings (LVDT) vs. top of column displacement for Test A.
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
left beam
right beam
0.6
10
0.4
5
0.2
0
0.0
Gap Opening (in)
Gap Opening (mm)
15
-5
-125
-100
-75
-50
-25
0
25
50
75
100
125
Top of Column Displacement (mm)
Figure E-9: Average gap opening (LVDT) vs. top of column displacement for Test A.
213
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-10: Strain in the top-front tendon vs. Mbeam,avg for Test A.
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-11: Strain of the top-back tendon vs. Mbeam,avg for Test A.
214
Moment (kip-in)
400
40
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-12: Strain of the bottom-front tendon vs. Mbeam,avg for Test A.
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-13: Strain in the bottom-back tendon vs. Mbeam,avg for Test A.
215
Moment (kip-in)
400
40
350
50
30
200
150
20
100
10
50
0
a) top front
350
Stress (MPa)
0
b) top back
300
50
Strain
250
40
30
200
150
20
100
10
50
0
c) bottom front
0.00
0.02
0.04
0.06
d) bottom back
0.00
0.02
Stress (ksi)
40
250
0.04
Stress (ksi)
Stress (MPa)
300
0
0.06
Strain
Strain
Figure E-14: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
A.
216
Displacement (in)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
a) left beam
-80
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
b) right beam
-80
-4
-3
-2
-1
0
1
2
3
4
Displacement (mm)
Figure E-15: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test A.
217
E.2
TEST B
100
4
75
3
50
2
25
1
0
0
-25
-1
-50
-2
-75
-3
-100
-4
-125
0
1000
2000
3000
4000
5000
Time (step)
Figure E-16: Actuator displacement time history for Test B.
218
Displacement (in)
Displacement (mm)
125
Actuator Displacement (in)
-4
-2
0
2
4
100
20
80
15
60
Actuator Force (kN)
20
5
0
0
-20
-5
-40
Actuator Force (kips)
10
40
-10
-60
-15
-80
-20
-100
-100
-50
0
50
100
Actuator Displacement (mm)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-18: M-θ at the column face of the left beam for Test B.
219
Moment (kip-in)
Moment (kN-m)
Figure E-17: Actuator force-displacement for Test B.
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
Figure E-19: M-θ at the column face of the right beam for Test B.
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-20: M-θ at outside of the HSS for column per top strain gauges for Test B.
220
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-21: M-θ at outside of the HSS for column per bottom strain gauges for Test B.
Top of column Displacement (in)
-4
-2
0
2
4
4
100
2
50
1
0
0
-1
-50
-2
Actuator Displacement (in)
Actuator Displacment (mm)
3
-3
-100
-4
-100
-50
0
50
100
Top of Column Displacement (mm)
Figure E-22: Displacements at the top of the column vs. at the actuator for Test B.
221
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
Gap Opening (mm)
top-front
top-back
bottom-front
bottom-back
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (kip-in)
20
125
Top of Column Displacement (mm)
Figure E-23: Gap openings (LVDT) vs. top of column displacement for Test B.
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Moment (kip-in)
Gap Opening (mm)
left beam
right beam
125
Top of Column Displacement (mm)
Figure E-24: Average gap opening (LVDT) vs. top of column displacement for Test B.
222
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-25: Strain in the top-front tendon vs. Mbeam,avg for Test B.
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-26: Strain in the top-back tendon vs. Mbeam,avg for Test B.
223
Moment (kip-in)
400
40
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-27: Strain in the bottom-front tendon vs. Mbeam,avg for Test B.
80
600
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-28: Strain in the bottom-back tendon vs. Mbeam,avg for Test B.
224
Moment (kip-in)
400
40
400
40
300
30
200
20
100
10
0
a) top front
500
Stress (MPa)
0
b) top back
400
50
Strain
40
300
30
200
20
100
10
0
c) bottom front
0.00
0.02
0.04
0.06
d) bottom back
0.00
0.02
Stress (ksi)
50
0.04
Stress (ksi)
Stress (MPa)
500
0
0.06
Strain
Strain
Figure E-29: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
B.
225
Displacement (in)
-0.1
0.0
0.1
0.2
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
a) left beam
-80
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
b) right beam
-80
-4
-2
0
2
4
6
Displacement (mm)
Figure E-30: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test B.
226
E.3
TEST C
100
4
75
3
50
2
25
1
0
0
-25
-1
-50
-2
-75
-3
-100
-4
-125
0
2000
4000
6000
Time (step)
Figure E-31: Actuator displacement time history for Test C.
227
8000
Displacement (in)
Displacement (mm)
125
Actuator Displacement (in)
-4
-2
0
2
4
100
20
80
15
60
Actuator Force (kN)
20
5
0
0
-20
-5
-40
Actuator Force (kips)
10
40
-10
-60
-15
-80
-20
-100
-100
-50
0
50
100
Actuator Displacement (mm)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-33: M-θ at the column face of the left beam for Test C.
228
Moment (kip-in)
Moment (kN-m)
Figure E-32: Actuator force-displacement for Test C.
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
Figure E-34: M-θ at the column face of the right beam for Test C.
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-35: M-θ at outside of the HSS for column per top strain gauges for Test C.
229
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-36: M-θ at outside of the HSS for column per bottom strain gauges for Test C.
Top of column Displacement (in)
-4
-2
0
2
4
4
100
2
50
1
0
0
-1
-50
-2
Actuator Displacement (in)
Actuator Displacment (mm)
3
-3
-100
-4
-100
-50
0
50
100
Top of Column Displacement (mm)
Figure E-37: Displacements at the top of the column vs. at the actuator for Test C.
230
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
Gap Opening (mm)
top-front
top-back
bottom-front
bottom-back
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (in)
20
125
Top of Column Displacement (mm)
Figure E-38: Gap openings (LVDT) vs. top of column displacement for Test C
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (in)
Gap Opening (mm)
left beam
right beam
125
Top of Column Displacement (mm)
Figure E-39: Average gap opening (LVDT) vs. top of column displacement for Test C
231
80
600
Strain Gauge
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-40: Strain in the top-front tendon vs. Mbeam,avg for Test C
80
600
Strain Gauge
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-41: Strain in the top-back tendon vs. Mbeam,avg for Test C
232
Moment (kip-in)
400
40
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-42: Strain in the bottom-front tendon vs. Mbeam,avg for Test C
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-43: Strain in the bottom-back tendon vs. Mbeam,avg for Test C
233
Moment (kip-in)
60
50
300
40
30
200
20
100
10
Stress (ksi)
Stress (MPa)
400
0
400
50
Strain
300
Stress (MPa)
0
b) top back
40
30
200
20
100
10
Stress (ksi)
a) top front
0
c) bottom front
0.00
0.02
0.04
0.06
d) bottom back
0.00
0.02
0.04
0
0.06
Strain
Strain
Figure E-44: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
C.
234
Displacement (in)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
a) left beam
-80
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
b) right beam
-80
-4
-2
0
2
4
Displacement (mm)
Figure E-45: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test C.
235
E.4
TEST D
100
4
75
3
50
2
25
1
0
0
-25
-1
-50
-2
-75
-3
-100
-4
-125
0
1000
2000
3000
4000
5000
6000
Time (step)
Figure E-46: Actuator displacement time history for Test D.
236
Displacement (in)
Displacement (mm)
125
Actuator Displacement (in)
-4
-2
0
2
4
100
20
80
15
60
Actuator Force (kN)
20
5
0
0
-20
-5
-40
Actuator Force (kips)
10
40
-10
-60
-15
-80
-20
-100
-100
-50
0
50
100
Actuator Displacement (mm)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-48: M-θ at the column face of the left beam for Test D.
237
Moment (kip-in)
Moment (kN-m)
Figure E-47: Actuator force-displacement for Test D.
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
Figure E-49: M-θ at the column face of the right beam for Test D.
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-50: M-θ at outside of the HSS for column per top strain gauges for Test D.
238
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-51: M-θ at outside of the HSS for column per bottom strain gauges for Test D.
Top of column Displacement (in)
-4
-2
0
2
4
4
100
2
50
1
0
0
-1
-50
Moment (kip-in)
Actuator Displacment (mm)
3
-2
-3
-100
-4
-100
-50
0
50
100
Top of Column Displacement (mm)
Figure E-52: Displacements at the top of the column vs. at the actuator for Test D.
239
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
Gap Opening (mm)
top-front
top-back
bottom-front
bottom-back
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (kip-in)
20
125
Top of Column Displacement (mm)
Figure E-53: Gap openings (LVDT) vs. top of column displacement for Test D.
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Moment (kip-in)
Gap Opening (mm)
left beam
right beam
125
Top of Column Displacement (mm)
Figure E-54: Average gap opening (LVDT) vs. top of column displacement for Test D.
240
80
600
Strain Gauge
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-55: Strain in the top-front tendon vs. Mbeam,avg for Test D.
80
600
Strain Gauge
Extensometer
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-56: Strain in the top-back tendon vs. Mbeam,avg for Test D.
241
Moment (kip-in)
400
40
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-57: Strain (EXT) in the bottom-front tendon vs. Mbeam,avg for Test D.
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-58: Strain (EXT) in the bottom-back tendon vs. Mbeam,avg for Test D.
242
50
300
40
30
200
20
100
10
Stress (ksi)
Stress (MPa)
400
0
400
50
Strain
300
Stress (MPa)
0
b) top back
40
30
200
20
100
10
Stress (ksi)
a) top front
0
c) bottom front
0.00
0.02
0.04
0.06
d) bottom back
0.00
0.02
0.04
0
0.06
Strain
Strain
Figure E-59: Stress (assuming tensile force is transferring through the tendon, thus
neglecting the shear-tab contribution) vs. strain (EXT) of each tendon element for Test
D.
243
Displacement (in)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
a) left beam
-80
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
b) right beam
-80
-4
-2
0
2
4
Displacement (mm)
Figure E-60: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test D.
244
E.5
TEST E
100
4
75
3
50
2
25
1
0
0
-25
-1
-50
-2
-75
-3
-100
-4
-125
0
2000
4000
6000
Time (step)
Figure E-61: Actuator displacement time history for Test E.
245
Displacement (in)
Displacement (mm)
125
Actuator Displacement (in)
-4
-2
0
2
4
100
30
20
10
0
0
-10
Actuator Force (kips)
Actuator Force (kN)
50
-50
-20
-30
-100
-100
-50
0
50
100
Actuator Displacement (mm)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-63: M-θ at the column face of the left beam for Test E.
246
Moment (kip-in)
Moment (kN-m)
Figure E-62: Actuator force-displacement for Test E.
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
80
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
-700
-80
-0.06
Moment (kip-in)
Moment (kN-m)
Figure E-64: M-θ at the column face of the right beam for Test E.
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-65: M-θ at outside of the HSS for column per top strain gauges for Test E.
247
700
60
525
40
350
20
175
0
0
-20
-175
-40
-350
-60
-525
Moment (kip-in)
Moment (kN-m)
80
-700
-80
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
θconc. (rad)
Figure E-66: M-θ at outside of the HSS for column per bottom strain gauges for Test E.
Top of column Displacement (in)
-4
-2
0
2
4
4
100
2
50
1
0
0
-1
-50
-2
Actuator Displacement (in)
Actuator Displacment (mm)
3
-3
-100
-4
-100
-50
0
50
100
Top of Column Displacement (mm)
Figure E-67: Displacements at the top of the column vs. at the actuator for Test E.
248
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
top-front
top-back
bottom-front
bottom-back
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (in)
Gap Opening (mm)
15
125
Top of Column Displacement (mm)
Figure E-68: Gap openings (LVDT) vs. top of column displacement for Test E.
Top of column Displacement (in)
-4
-3
-2
-1
0
1
2
3
4
20
15
0.6
10
0.4
5
0.2
0
0.0
-125
-100
-75
-50
-25
0
25
50
75
100
Gap Opening (in)
Gap Opening (mm)
left beam
right beam
125
Top of Column Displacement (mm)
Figure E-69: Average gap opening (LVDT) vs. top of column displacement for Test E.
249
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-70: Strain (EXT) in the top-front tendon vs. Mbeam,avg for Test E.
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-71: Strain (EXT) in the top-back tendon vs. Mbeam,avg for Test E.
250
Moment (kip-in)
60
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-72: Strain (EXT) in the bottom-front tendon vs. Mbeam,avg for Test E.
80
600
Strain Gauge
Extensometer
400
Moment (kN-m)
40
200
20
0
0
-20
-200
-40
Moment (kip-in)
60
-400
-60
-600
-80
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain
Figure E-73: Strain (EXT) in the bottom-back tendon vs. Mbeam,avg for Test E.
251
Displacement (in)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
a) left beam
-80
80
600
60
Moment (kN-m)
200
20
0
0
-20
-200
-40
Moment (kip-in)
400
40
-400
-60
-600
b) right beam
-80
-4
-2
0
2
4
Displacement (mm)
Figure E-74: Averaged moment vs. vertical beam displacement for a) left and b) right
beams measured by stringpot at 137.8 cm (54.25 in.) from the outer face of the column
flange for Test E.
252
APPENDIX F
BEAM COLUMN CONNECTION: PHOTOGRAPHS
Figure F-1: Deformation of HSS transfer elements after the completion of Test A.
253
Figure F-2: Experimental test setup with beam-column installed.
Figure F-3: Profile view of Test A.
254
Figure F-4: Profile view of Test B.
Figure F-5: Profile view of Test C.
255
Figure F-6: Profile view of Test D.
Figure F-7: Profile view of Test E.
256
APPENDIX G
ARTICULATED QUADRILATERAL CONCEPTION AND
DEVELOPMENT
One of the main goals of this bracing system is to create an effective way to combine
SMA elements in parallel with supplemental energy dissipating elements. This idea is
rooted in the following result observed in the SDOF Study chapter: a recentering system
with a maximized hysteretic loop will produce the best performance. To dissipate energy
by yielding or by friction, the dissipating element must be subjected to load reversal (i.e.
tension and compression). For a cable bracing system, this is difficult to obtain without a
special arrangement. The AQ configuration accomplishes this requirement in a unique
way and facilitates the use of a variety of dissipating elements.
Several options for dissipating elements have been identified including torsional
dissipators (either friction or yielding) at the AQ joints, frictional dissipators on the
diagonals (Pall and Marsh, 1982), flexural yielding of the AQ members (Tyler, 1983), and
c-shaped dissipators on the diagonals (Renzi et al., 2007). The c-shape dissipator was
chosen for this research because of the predictable results shown in experimental work
by Renzi. Nevertheless, the other methods of providing energy dissipation should not be
discounted and have been found to be very successful in research and application.
The options for loading the SMA elements include torsion at the joints and
tension across the diagonal. The latter option was chosen because tension is the most
efficient use of the material. Additionally, superelastic NiTi wires have been shown to
have excellent performance in terms of inherent energy dissipation and recentering. A
257
bundle of NiTi wires was fabricated by Nitinol Technologies Inc. The full details of the
NiTi bundles are described in the component test section of this chapter.
Figure G-1a-b shows a schematic of the complete AQ setup. The SMA bundles
cross in the middle and are anchored to square steel bars at the ends. This steel bar is
then mounted to threaded bars which are inserted into a steel transfer block. This setup
enables tightening of the SMA bundles to either remove slack or to instill some initial
pretension while maintain a configuration that is as compact as possible. The c-shape
members are attached at the corner joints with a large diameter bolt functioning as a pin.
Two c-shaped dissipators were used in the same direction but on opposite faces
of the AQ. Due to the geometry implemented, out-of-plane ties were attached to the cshape along the length. These ties effectively braced the two dissipators together and
forced flexure yielding to occur before lateral torsional buckling.
The dimensions and the material properties of the c-shape determine its strength
and stiffness. When selecting the dimensions, the following criteria were adhered to:
ƒ
The thickness of the c-shape should be minimized to ensure the AQ’s
compactness (12.7 mm (0.5 in.) was selected in this study).
ƒ
The yield strength should be the fraction of the SMA element yield that creates
increased system damping while maintaining good recentering.
The yield
strength was selected to be 22 kN (5 kips), the approximate end of the unloading
plateau seen in mechanical testing of the SMA wire bundle.
ƒ
The stiffness of the c-shape should be greater than or equal to the stiffness that
results in the c-shape yielding at the same deformation as the SMA.
This
criterion ensures the c-shape is pushed beyond its elastic range.
To show the effects of length change, Figure G-1c provides a graphical illustration of
how the dimensions of a c-shape change when thickness, stiffness, and yield force are
held constant and length is varied.
258
For this research, the length is predetermined by the length of the SMA wire
bundles. Because of the length, strength, and stiffness requirements, the c-shape is
rather long. In Figure G-2 the relationship between hole separation, s, and arm rotation,
f, is plotted for a range of m/a ratios (defined on the plot) and the governing equation is:
⎛
m⎞ ⎛φ⎞
s = 2⎜⎜ a + ⎟⎟ sin⎜ ⎟ − m
φ ⎠ ⎝ 2⎠
⎝
(G.1)
This equation and corresponding plot assume that the c-shape body (m portion) is
axially inextensible and that arms (a portions) are rigid. The maximum hole separation
for each m/a gives the limitation of each c-shape geometry. If further hole separation is
induced, the deformation mode will be axial extension rather than flexural bending.
Slotted holes were implemented in the experimental specimen to work-around this
constraint.
To further understand the selection of the AQ setup as the ideal platform of
implementing SMAs in a bracing system, the following benefits are identified:
•
The SMA bundles can be factory installed to a prescribed pretension, thus
reducing or eliminating field installation errors. However, the AQ ties would have
to be designed to prevent buckling from compression due to this pretensioning.
•
The SMA bundles can be combined in parallel with a variety of possible energy
dissipation elements such as torsion elements at the AQ joints, c-shape
dissipators, AQ element deformation dissipator, or friction dissipators across the
diagonal.
•
Shock loading will be minimized because the c-shape dissipator is instantly
activated upon reversal of drift demand.
•
The dimension of the AQ can be adjusted to create a system with a wide range
of force-deformation characteristics.
259
The dimension and further description of the AQ setup tested in this research are given
in the Section 6.3.4 of the main text.
(a)
(b)
(c)
Figure G-1: (a) AQ with SMA bundles and c-shape dissipaters, (b) 3D view of SMA
attachment, and (c) c-shape dimension variation for constant thickness, stiffness, and
yield force.
2
1.0
a
m
m=a
m=2a
0
m=a
m=6a
m=10a
-2
m=6a
m=14a
-4
m=14a
m=22a
φ (+)
-8
-10
0.6
m=10a
m=18a
-6
0.8
m=2a
m=18a
0.4
0.2
m=22a
s/2
-12
Hole Seperation, s (in terms of a)
Hole Seperation, s (in terms of a)
4
0.0
-4
-2
0
2
Rotation, φ (rad)
4 0.0
0.2
0.4
0.6
0.8
1.0
Rotation, φ (rad)
Figure G-2: C-shape kinematic behavior assuming the center of c-shape is axially
inextensible and the arms are completely rigid.
260
APPENDIX H
SMA-BASED BRACING DESIGN
The behavior of a SMA-based bracing system is largely governed by the stiffness of the
attributing parts. The general strategy is to concentrate the inelastic deformations into
the SMA only: thus the remainder of the brace should remain completely elastic. To
illustrate this point, the force-deformation of a SMA element and an elastic element are
combined in series (deformations are additive while the forces are equal) as shown in
Figure H-1.
The following observations can be made from the resulting element’s
behavior:
1) The stiffness of the series spring is:
ks =
1
1 k e + 1 k SMA
(H.1)
which is always less then kSMA unless ke → ∞ .
2) The length of the loading plateau for the series element, βs, is defined as:
βs = βSMA + ΔF k e
(H.2)
where βSMA is the length of the SMA loading plateau and ΔF is the change in
force in the series system (FSMA = Fe = Fs).
3) A plateau ductility parameter, η, is defined as:
η = β Δy
(H.3)
where β is the length of the loading plateau Δy is the yield displacement. The η
value is a measure of the ductility in the element available until the end of the
loading plateau.
261
4) Assuming ηSMA to be predetermined by strength and stiffness requirements, it is
desirable to create a system with a ηs value approaching ηSMA, which is the
upper bound. This is done by making the relative stiffness ratio, ρ, as large as
possible. ρ is defined as:
ρ = kSMA k e
(H.4)
5) For the experimental tests, the ρ was much lower than anticipated (0.4).
Parametric studies need to be conducted to determine an appropriate target ρ.
The “series” arrangement effectively shortens the plateau ductility parameter as defined
in this appendix. The designer of an SMA-base system must pay special attention to
these phenomena. In this experimental work, though the elastic elements were large
relative to the SMA elements, the ρ factor was much smaller than anticipated. For the
analytical study, the general behavior is taken from the experimental results, and the
effect of the relative stiffness is briefly explored.
In terms of practicality, there remain issues with providing the appropriate
amount of SMA at the appropriate length. For example, in the analysis section of this
study, the SMA1 area is defined by the target brace yield force. The SMA length is then
calculated by setting the SMA stiffness equal to the target stiffness while assuming
rigidity in the attaching members. This results in the SMA needing to have a very large
area over a short length (the bottom floor brace is 914 mm (36 in.) long but has an area
of 11900 mm2 (18.45 in2)). The practicality of attaching this amount of SMA to the
bracing elements is challenging.
One potential solution is to spread the SMA braces over more frame lines. For
example, if there were four SMA braces for every one steel brace in the corresponding
design, then the area of the SMA would be much more manageable for the analytical
262
study example’s numbers. However, cost should be factored into the viability of this
option. For the sake of this study, these issues are noted but ignored.
SMA
Elastic
=
SMA + Elastic (series)
β
dF
F / Fy
+
β
1
ksma
u / uy
ke
dF/ke
k
u / uy
u / uy
Figure H-1: The resulting force-deformation characteristics of an SMA element
combined in series with an elastic element.
263
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