Collapse Assessment of Steel Braced Frames

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


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


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


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


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


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)


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)


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


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


Model Parameter Calibrations

(Data from Tremblay et al. 2008) (Data from Uriz and Mahin 2008)


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)


Load CellsConnecting Beam

ConnectingBeam

Test Bed

Test Bed

Specimen

Shake Table

Direction of Shaking

N

E-Defense Chevron CBF: Test Setup



-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


• JR Takatori• (1995 Kobe EQ)• 10, 12, 14, • 28, 42, 70%

• Damping h ≈ 0.03 • inherent in test-bed• system


-40 -30 -20 -10 0 10 20

Elongation (mm)

Experiment

Simulation (b)-400

-300

-200

-100

0

100

200

300

400

-10 0 10

Axi

al F

orce

(kN

)

Elongation (mm)

(a)

East Brace

42% 70%

Response of Braces: Comparison @ 70% JR Takatori



Global Response: Comparison @ 70% JR Takatori



□ 152x9.5

（A500 G

r. B) □ 152x9.5

（A500 Gr. B)

□ 152x

9.5

（A50

0 Gr. 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)


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)



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)


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)


-0.05 0 0.05-3

-2

-1

0

1

2

3x 104

Chord Rotation (rad)M

om

ent

(k-i

n)

(Ibarra et al. 2005, Lignos and Krawinkler 2011)



(Lignos and Krawinkler 2011)


Case Study #2: Loading Protocol

(Uriz and Mahin, 2008)


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


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)


Validation of Simulated Collapse-Small

Scale Tests

0.00

0.04

0.08

0.12

0.16

0.20

0 5 10 15Time (sec)

SD

R1(

rad

)

Analytical Prediction

Experimental Data

(Lignos, Krawinkler & Whittaker 2007)

(NEESCollapse)

Collapse


Validation of Simulated Collapse-Full

Scale Tests

(Suita et al. 2008)(Lignos, Hikino, Matsuoka, Nakashima 2012)

Collapse

Collapse


Canoga Park Record: Story Drift Ratio

Histories SF=2.0


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.


IDA Curves: Damping Based on

Current Stiffness

Based on 2% Rayleigh Damping (damping matrix proportional to current stiffness)


Dynamic Analysis: Story Drift Ratios

(SF=2.0)


Dynamic Analysis: Brace Response


Base Shear-First Story SDR @

Collapse Intensity

Collapse

Fracture of East Brace

Fracture of West Brace


First Story Column Behavior @ Collapse

Intensity

□ 152x9.5

（A500 G

r. B) □ 152x9.5

（A500 Gr. B)

□ 152x

9.5

（A50

0 Gr. B

) □ 152x9.5

（A500 Gr. B)

PL 22(A572 Gr.50)

PL 22(A572 Gr.50)

Lateral support


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.


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.

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Collapse Assessment of Steel Braced Frames

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