1. 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

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

3. 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
Quake Summit, San Francisco 2010

4. Motivation
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.
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.
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
Quake Summit, San Francisco 2010

5. Steel Brace Model ? Model proposed by (Uriz et al. 2008)
Gusset Plate flexibility and yield moment are modeled with the model proposed by Roeder et al. (2011)
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 ?

6. 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
Digitization of axial load axial displacement relationships
(Calibrator JAVA software , Lignos and Krawinkler 2008)

7. 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

8. Calibration Process of the Brace Model
Mesh Adaptive Search Algorithm (MADS, Abramson et al. 2009)
Objective Function H
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.

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

10. Model Parameter Calibrations
(Data from Tremblay et al. 2008)
(Data from Uriz and Mahin 2008)

11. Validation with a Chevron CBF tested @ E-Defense
x: Lateral bracing
Chevron CBF, 70%-scale
HSS braces: b/t = 19.4, KL/r = 82.5
(Okazaki, Lignos, Hikino and Kajiyara, 2012)

12. E-Defense Chevron CBF: Test Setup
Load Cells
Connecting Beam
Test Bed
Test Bed
Specimen
Connecting
Beam
Direction of Shaking N
Shake Table
(Okazaki, Lignos, Hikino and Kajiyara, 2012)

13. E-Defense Chevron CBF: Test Setup
JR Takatori
(1995 Kobe EQ)
10, 12, 14,
28, 42, 70%
Damping h ≈ 0.03
inherent in test-bed
system
(Okazaki, Lignos, Hikino and Kajiyara, 2012)

14. Response of Braces: Comparison @ 70% JR Takatori
East Brace
42%
70%
(Okazaki, Lignos, Hikino and Kajiyara, 2012)

15. Global Response: Comparison @ 70% JR Takatori
(Okazaki, Lignos, Hikino and Kajiyara, 2012)

16. Case Study #2: 2-Story Chevron Braced Frame
（A500 Gr. B)
□ 152x9.5
Column
W10x45
Beam
W24x117
2,743
6,096
Reaction
PL 22
(A572 Gr.50)
Lateral support
(Uriz and Mahin, 2008)

17. Case Study #2: 2-Story Chevron Braced Frame
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)

18. Case Study #2: 2-Story Chevron Braced Frame
Rigid offset
Rigid offset
Rigid offset
Steel beam & column spring (Bilinear Mod. IMK Model)
Liu and Astaneh (2004)
Shear connection spring (Pinching Mod. IMK Model)
Gusset plate spring (Menegotto-Pinto model)

19. Case Study #2: 2-Story Chevron Braced Frame
Rigid offset
Rigid offset
Rigid offset
Steel beam & column spring (Bilinear Mod. IMK Model)
(Ibarra et al. 2005,
Lignos and Krawinkler 2011)
Shear connection spring (Pinching Mod. IMK Model)
Gusset plate spring (Menegotto-Pinto model)

20. Case Study #2: 2-Story Chevron Braced Frame
(Lignos and Krawinkler 2011)

21. Case Study #2: Loading Protocol
(Uriz and Mahin, 2008)

22. Case Study #2: Quasi-Static Analysis-Global Response

23. Case Study #2: Incremental Dynamic Analysis
Based on 2% Rayleigh Damping (damping matrix proportional to initial stiffness)
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.

24. Validation of Simulated Collapse-Small Scale Tests
(NEESCollapse)
(Lignos, Krawinkler & Whittaker 2007)

25. Validation of Simulated Collapse-Full Scale Tests
(Suita et al. 2008)
(Lignos, Hikino, Matsuoka, Nakashima 2012)

26. Canoga Park Record: Story Drift Ratio Histories SF=2.0

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.

28. IDA Curves: Damping Based on Current Stiffness
Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)

29. Dynamic Analysis: Story Drift Ratios (SF=2.0)

30. Dynamic Analysis: Brace Response

31. Base Shear-First Story SDR @ Collapse Intensity
Fracture of
East Brace
Collapse
Fracture of
West Brace

32. First Story Column Behavior @ Collapse Intensity
（A500 Gr. B)
□ 152x9.5
PL 22
(A572 Gr.50)
Lateral support

33. 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.

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 Berkeley.