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Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 1
Collapse Assessment of Steel Braced Frames In Seismic Regions
Dimitrios G. Lignos, Ph.D.Assistant Professor, McGill University, Montreal, Canada
Emre Karamanci, Graduate Student Researcher, McGill University, Montreal, Canada
July 9th-12th, 2012
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 2
Outline
• Motivation• A Database for Modeling of Post-Buckling Behavior
and Fracture of Steel Braces• Calibration Studies• Case #1: E-Defense Dynamic Testing• Case #2: 2-Story Chevron Braced Frame• Collapse Assessment• Summary and Observations
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 33
In the context of Performance-Based Earthquake Engineering, collapse constitutes a limit state associated with complete loss of a building and its content.
Understanding collapse is a fundamental objective in seismic safety since this failure mode is associated with loss of lives.
Therefore, there is a need for reliable prediction of the various collapse mechanisms of buildings subjected to earthquakes.
Dimitrios G. LignosQuake Summit, San Francisco 2010
Motivation
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 44
1. In the case of steel braced frames, one challenge for reliable collapse assessment is to accurately model the post-buckling behavior and fracture of steel braces as parts of a braced frame.
2. Another challenge is to consider other important deterioration modes associated with plastic hinging in steel components that are part of local story mechanisms that develop after the steel braces fracture This could be an issue for steel braced frames designed in moderate or high seismicity regions.
3. The emphasis is on a common collapse mode associated with sidesway instability in which P-Delta effects accelerated by cyclic deterioration in strength and stiffness of structural components fully offset the first order story shear resistance of a steel braced frame and dynamic instability occurs.
Dimitrios G. LignosQuake Summit, San Francisco 2010
Motivation
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 5
Steel Brace Model
Gusset Plate flexibility and yield moment are modeled with the model proposed by Roeder et al. (2011)
?
Model proposed by (Uriz et al. 2008)
• εo indicates the strain amplitude at which one complete
Cycle of a undamaged material causes fracture• m material parameter that relates the sensitivity of a total strain amplitude of the
material to the number of cycles to fracture
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 6
LH LB LB LH LH LBLH LB
LH
LB
Steel Brace Database for Model Calibration• Collected Data from 20 different experimental programs from the
1970s to date• 143 Hollow Square Steel Sections• 51 Pipes• 50 W Shape braces• 37 L Shape Braces
Digitization of axial load axial displacement relationships (Calibrator JAVA software , Lignos and Krawinkler 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 7
Steel Brace Database
Slenderness Parameter
Based on the local slenderness ratios (b/t), the majority of the braces are categorized as Class 1 based on CISC (2010) requirements (Same conclusions based on AISC 2010 Highly ductile braces)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 8
Calibration Process of the Brace Model
• Objective Function H
Mesh Adaptive Search Algorithm (MADS, Abramson et al. 2009)
• Non-differentiable Optimization problem lacks of smoothness.
• MADS does not use information about the gradient of H to search for an optimal point compared to more traditional optimization algorithms.
Fexp: Experimentally measured axial force of the braceFsimul: Simulated axial force of the braceδi: Axial displacement of the brace at increment i
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 9
Calibration Process of the Brace Model
Based on a sensitivity study with a subset of 30 braces:• Offset of 0.1% of the brace length is adequate• Eight elements along the length of the steel brace• Five integration points per element• Section level:
• Stress strain relationship:• Strain hardening of 0.1%• Radius that defines Bauschinger effect Ro=25
Based on the calibration study of the entire set of braces• Exponent m =0.3• Strain amplitude εo is a function of KL/r, b/t, fy
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 10
Model Parameter Calibrations
(Data from Tremblay et al. 2008) (Data from Uriz and Mahin 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 1111
x: Lateral bracing• Chevron CBF, 70%-scale• HSS braces: b/t = 19.4, KL/r = 82.5
Validation with a Chevron CBF tested @ E-Defense
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 1212
Load CellsConnecting Beam
ConnectingBeam
Test Bed
Test Bed
Specimen
Shake Table
Direction of Shaking
N
E-Defense Chevron CBF: Test Setup
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 13
-8
-6
-4
-2
0
2
4
6
8
0 5 10 15 20 25 30
Gro
und
Acc
eler
atio
n (m
/s2 )
Time (sec)
0
5
10
15
20
25
30
35
0.1 1 10
Acc
eler
atio
n R
espo
nse
(m/s
2 )
Period (sec)
14%28%42%70%Takatori
6.56
h = 0.02
13
E-Defense Chevron CBF: Test Setup
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
• JR Takatori• (1995 Kobe EQ)• 10, 12, 14, • 28, 42, 70%
• Damping h ≈ 0.03 • inherent in test-bed• system
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 1414
-40 -30 -20 -10 0 10 20Elongation (mm)
ExperimentSimulation (b)
-400
-300
-200
-100
0
100
200
300
400
-10 0 10
Axial
For
ce (k
N)
Elongation (mm)
(a)
East Brace
42% 70%
Response of Braces: Comparison @ 70% JR Takatori
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 1515
Global Response: Comparison @ 70% JR Takatori
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 16
□ 152x9
.5
( A500 Gr. B
) □ 152x9.5
(A500 Gr. B)
□ 152x
9.5
( A500 G
r. B) □ 152x9.5
(A500 Gr. B)
ColumnW10x45
BeamW24x117
2,74
32,
743
6,096
ReactionBeam
PL 22(A572 Gr.50)
PL 22(A572 Gr.50)
Lateral support
Case Study #2: 2-Story Chevron Braced Frame
(Uriz and Mahin, 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 17
Rigid offset
Rigid offset
Rigid offset
Steel beam & column spring (Bilinear Modified IMK Model)Shear connection spring (Pinching Modified IMK Model)Gusset plate spring (Menegotto-Pinto model)
Case Study #2: 2-Story Chevron Braced Frame
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 18
Rigid offset
Rigid offset
Rigid offset
Steel beam & column spring (Bilinear Mod. IMK Model)Shear connection spring (Pinching Mod. IMK Model)Gusset plate spring (Menegotto-Pinto model)
Case Study #2: 2-Story Chevron Braced Frame
Liu and Astaneh (2004)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 19
Rigid offset
Rigid offset
Rigid offset
Steel beam & column spring (Bilinear Mod. IMK Model)Shear connection spring (Pinching Mod. IMK Model)Gusset plate spring (Menegotto-Pinto model)
Case Study #2: 2-Story Chevron Braced Frame
-0.05 0 0.05-3
-2
-1
0
1
2
3x 104
Chord Rotation (rad)M
omen
t (k-
in)
(Ibarra et al. 2005, Lignos and Krawinkler 2011)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 20
Case Study #2: 2-Story Chevron Braced Frame
(Lignos and Krawinkler 2011)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 21
Case Study #2: Loading Protocol
(Uriz and Mahin, 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 22
Case Study #2: Quasi-Static Analysis-Global Response
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 23
Case Study #2: Incremental Dynamic Analysis
Collapse Capacities seem a bit high Indicates that a closer look of the individual responses in terms of base shear hysteretic response is needed and not just story drift ratios.
Based on 2% Rayleigh Damping (damping matrix proportional to initial stiffness)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 24
Validation of Simulated Collapse-Small
Scale Tests
0.00
0.04
0.08
0.12
0.16
0.20
0 5 10 15Time (sec)
SDR
1(ra
d)
Analytical Prediction
Experimental Data
(Lignos, Krawinkler & Whittaker 2007)
(NEESCollapse)
Collapse
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 25
Validation of Simulated Collapse-Full
Scale Tests
(Suita et al. 2008)(Lignos, Hikino, Matsuoka, Nakashima 2012)
Collapse
Collapse
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 26
Canoga Park Record: Story Drift Ratio
Histories SF=2.0
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 27
Dynamic Analysis: Base Shear-SDR1
Due to Artificial Damping
Artificial damping is generated in the lower modes with the effective damping increasing to several hundred percent.Following the change in state of steel braces after fracture occurs, large viscous damping forces are generated. This forces are the product of the post-event deformational velocities multiplied by the initial stiffness and by the stiffness proportional coefficient.
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 28
IDA Curves: Damping Based on Current Stiffness
Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 29
Dynamic Analysis: Story Drift Ratios (SF=2.0)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 30
Dynamic Analysis: Brace Response
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 31
Base Shear-First Story SDR @ Collapse Intensity
Collapse
Fracture of East Brace
Fracture of West Brace
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 32
First Story Column Behavior @ Collapse
Intensity
□ 152x9
.5
( A500 Gr. B
) □ 152x9.5
(A500 Gr. B)
□ 152x
9.5
( A500 G
r. B) □ 152x9.5
(A500 Gr. B)
PL 22(A572 Gr.50)
PL 22(A572 Gr.50)
Lateral support
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 33
Summary and Observations1. Modeling of Post-Buckling Behavior and Fracture Initiation of Steel Braces is Critical for Evaluation of Seismic Redundancy of Steel Braced Frames.• Proposed steel brace fracture modeling for different types of steel
braces is based on calibration studies from 295 tests.2. For collapse simulations of sidesway instability, modeling of component deterioration of other structural components is also critical (Beams and Columns)3. Non-simulated collapse criteria could be “dangerous”. Story drift in conjunction with base shear of the system needs to be considered.4. Modeling of damping can substantially overestimate the collapse capacity of steel braced frames For Rayleigh Damping, damping matrix proportional to current stiffness should be considered.
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012 34
Acknowledgments • Dr. Uriz and Prof. Steve Mahin (University of California,
Berkeley) for sharing the digitized data of individual steel brace components and systems that tested over the past few years.
• Professor Benjamin Fell (Sacramento State) for sharing the digitized data of steel brace components that he tested 4 years ago at NEES @ Berkeley.