Collapse Assessment of Steel Braced
Frames In Seismic Regions
July 9th-12th, 2012
Dimitrios G. Lignos, Ph.D.
Assistant Professor, McGill University, Montreal, Canada
Emre Karamanci, Graduate Student Researcher, McGill University,
Montreal, Canada
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
1
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
2
Motivation
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. Lignos
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
Quake Summit, San Francisco 2010
3
Motivation
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. Lignos
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
Quake Summit, San Francisco 2010
4
Steel Brace Model
Model proposed by (Uriz et al. 2008)
500
Integration
points
2*tG
Rigid Link
Gusset Plates
Initial deformation
from allowable tolerances
to model flexural buckling
2*tG
Rigid Link
Gusset Plate flexibility and yield moment
are modeled with the model proposed by
Roeder et al. (2011)
Stress s [MPa]
Corotational Transformation
0
−500
−0.01
0
0.01
0.02
Strain e [mm/mm]
ei = e o ( N f )
0.03
m
• 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
5
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
LH
LB
LB
LH
LH LB
LH LB
LB
LH
 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
6
Steel Brace Database
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)
Slenderness Parameter
lm =
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
KL Fy
r p 2E
7
Calibration Process of the Brace Model
Mesh Adaptive Search Algorithm (MADS, Abramson et al. 2009)
• Objective Function H
H (eo, m) =
N
åéëFexp. (di ) - Fsimul. (di )ùû
2
i=1
Fexp: Experimentally measured axial force of the brace
Fsimul: Simulated axial force of the brace
δi: Axial displacement of the brace at increment i
• 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.
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
8
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
9
Model Parameter Calibrations
3000
3000
Simulation
Experimental Data
2000
Axial Load [kN]
Axial Load [kN]
2000
Simulation
Experimental Data
1000
0
−1000
1000
0
−1000
−2000
−60
−40
20
0
−20
Brace Elongation [mm]
40
60
(Data from Tremblay et al. 2008)
−2000
−60
−40
−20
0
20
Brace Elongation [mm]
40
60
(Data from Uriz and Mahin 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
10
Validation with a Chevron CBF tested @ E-Defense
•
Chevron CBF, 70%-scale
•
HSS braces: b/t = 19.4, KL/r = 82.5
x: Lateral bracing
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
11
11
E-Defense Chevron CBF: Test Setup
Connecting Beam
Load Cells
Test Bed
Test Bed
Connecting
Beam
N
Shake Table
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
12
12
• JR Takatori
• (1995 Kobe EQ)
•
10, 12, 14,
•
28, 42, 70%
Ground Acceleration (m/s2)
E-Defense Chevron CBF: Test Setup
8
6.56
6
4
2
0
-2
-4
-6
-8
0
5
10
15
20
25
30
Time (sec)
35
Acceleration Response (m/s2)
• Damping h ≈ 0.03
• inherent in test-bed
• system
14%
28%
42%
70%
Takatori
30
25
20
15
10
h = 0.02
5
0
0.1
1
10
Period (sec)
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
13
13
Response of Braces: Comparison @ 70% JR Takatori
East Brace
400
Axial Force (kN)
300
200
100
0
-100
-200
Experiment
42% (a)
-300
-400
-10
0
10
Elongation (mm)
Simulation
-40
-30
-20
(b)
70%
-10
0
10
20
Elongation (mm)
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
14
14
Global Response: Comparison @ 70% JR Takatori
Story Shear (kN)
800
600
Experiment
400
Simula on
200
0
-200
-400
-600
-800
5
6
7
8
9
10
11
13
12
14
15
Time (sec)
(Okazaki, Lignos, Hikino and Kajiyara, 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
15
15
Case Study #2: 2-Story Chevron Braced Frame
6,096
2,743
Beam
W24x117
PL 22
(A572 Gr.50)
2,743
Column
W10x45
PL 22
(A572 Gr.50)
Reaction
Beam
Lateral support
(Uriz and Mahin, 2008)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
16
Case Study #2: 2-Story Chevron Braced Frame
Rigid offset
Rigid offset
Corotational Transformation
Integration
points
Rigid offset
2*tG
Rigid Link
Gusset Plates
Initial deformation
from allowable tolerances
to model flexural buckling
2*tG
Rigid Link
Steel beam & column spring (Bilinear Modified IMK Model)
Shear connection spring (Pinching Modified IMK Model)
Gusset plate spring (Menegotto-Pinto model)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
17
Case Study #2: 2-Story Chevron Braced Frame
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)
Liu and Astaneh (2004)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
18
Case Study #2: 2-Story Chevron Braced Frame
Rigid offset
Rigid offset
4
3 x 10
Rigid offset
Moment (k-in)
2
1
0
-1
-2
-3
Steel beam & column spring (Bilinear Mod. IMK Model)
Shear connection spring (Pinching Mod. IMK Model)
Gusset plate spring (Menegotto-Pinto model)
-0.05
0
0.05
Chord Rotation (rad)
(Ibarra et al. 2005,
Lignos and Krawinkler 2011)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
19
Case Study #2: 2-Story Chevron Braced Frame
-0.365
æhö
q p = 0.0865 × çç ÷÷
è tw ø
-0.565
æhö
q pc = 5.63× çç ÷÷
è tw ø
æ b
× çç f
è 2× t f
-1.34
æhö
Et
L=
= 495× çç ÷÷
My
è tw ø
-0.140
æ b
× çç f
è2×tf
ö
÷
÷
ø
-0.800
ö
÷
÷
ø
æ b
× çç f
è2×tf
æ Lö
×ç ÷
èd ø
-0.280
æ c1 × d ö
× çç unit ÷÷
è 533 ø
-0.595
ö
÷
÷
ø
-0.721
æ c1 × d ö
× çç unit ÷÷
è 533 ø
0.340
-0.230
æ c2 × F ö
× ç unit y ÷
ç 355 ÷
è
ø
-0.430
æ c2 × F ö
× ç unit y ÷
ç 355 ÷
è
ø
-0.360
æ c2 × F ö
× ç unit y ÷
ç 355 ÷
è
ø
(Lignos and Krawinkler 2011)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
20
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
21
Case Study #2: Quasi-Static Analysis-Global Response
3000
Simulation
Exper. Data
2000
Axial Load [kN]
Base Shear [kN]
2000
1000
0
−1000
Simulation
Exper.Data
1000
0
−1000
−2000
−2000
−3000
−0.06 −0.04 −0.02
0
0.02 0.04
First Story Drift Ratio SDR 1 [rad]
0.06
−50
0
50
Brace Elongation [mm]
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
22
Case Study #2: Incremental Dynamic Analysis
Based on 2% Rayleigh Damping (damping matrix proportional to initial stiffness)
IDA Curves, LMSR−N, 2−Story SCBF T =0.29sec
1
Collapse Fragility Curve, LMSR−N, 2−Story SCBF T =0.29sec
1
1
3
Probability of Collapse
2
1.5
a
1
S (T ,5%)/g
2.5
1
0.6
0.4
0.2
0.5
0
0
0.8
0.02
0.06
0.04
MAX SDR (rad)
0.08
0
0
1
2
Sa(T1,5%) [g]
3
4
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.
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
23
Validation of Simulated Collapse-Small Scale Tests
0.20
SDR1(rad)
0.16
0.12
0.08
Analytical Prediction
0.04
Experimental Data
0.00
0
5
0.4
Normalized Base Shear V/W
10
15
Experimental Data
Simulation
0.3
(NEESCollapse)
Time (sec)
Collapse
0.2
0.1
0
−0.1
−0.2
−0.3
(Lignos, Krawinkler & Whittaker 2007)
−0.4
−0.05
0
0.05
0.1
First Story Drift Angle [rad]
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
0.15
24
Validation of Simulated Collapse-Full Scale Tests
Collapse
Collapse
(Suita et al. 2008)
(Lignos, Hikino, Matsuoka, Nakashima 2012)
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
25
SDR1 [rad]
SDR2 [rad]
Canoga Park Record: Story Drift Ratio Histories SF=2.0
0.08
0.04
0
−0.02
0
5
10
15
Time [sec]
20
25
5
10
15
Time [sec]
20
25
0.08
0.04
0
−0.02
0
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
26
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
27
IDA Curves: Damping Based on Current Stiffness
Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)
IDA Curves, LMSR−N, 2−Story SCBF T1=0.29sec
Collapse Fragility Curve, LMSR−N, 2−Story SCBF T1=0.29sec
3
1
Probability of Collapse
Sa(T1,5%)/g
2.5
2
1.5
1
0.6
0.4
0.2
0.5
0
0
0.8
0.02
0.06
0.04
MAX SDR (rad)
0.08
0
0
1
2
S (T ,5%) [g]
a
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
3
4
1
28
SDR1 [rad]
SDR2 [rad]
Dynamic Analysis: Story Drift Ratios (SF=2.0)
0.08
0.04
0
−0.02
0
5
10
15
Time [sec]
20
25
0.1
0.05
0
−0.05
0
5
10
15
Time [sec]
20
25
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
29
Dynamic Analysis: Brace Response
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
30
Base Shear-First Story SDR @ Collapse Intensity
Fracture of
East Brace
Collapse
Fracture of
West Brace
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
31
First Story Column Behavior @ Collapse Intensity
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
32
Summary and Observations
1. 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
33
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.
Collapse Assessment of Steel Braced Frames in Seismic Regions, Dimitrios G. Lignos, QuakeSummit, Boston, July, 2012
34