Ductility Capacity Models for Buckling Restrained Braces Blake Andrews Larry Fahnestock Junho Song - PowerPoint PPT Presentation

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Ductility Capacity Models for Buckling Restrained Braces Blake Andrews Larry Fahnestock Junho Song

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Cumulative plastic ductility (CPD) Summary of Predictive Parameters. BRB Force-Deformation Model. An elastic perfectly plastic force-deformation model was assumed ... – PowerPoint PPT presentation

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Title: Ductility Capacity Models for Buckling Restrained Braces Blake Andrews Larry Fahnestock Junho Song


1
Ductility Capacity Models for Buckling Restrained
BracesBlake Andrews Larry FahnestockJunho
Song
bandrew3_at_uiuc.edu
2
What is a Buckling-Restrained Brace (BRB)?
  • Passive energy dissipation device used for
    seismic resistance
  • Yields in both tension and compression
  • Stable, predictable hysteretic behavior

Typical BRB 1
3
2
4
2
5
2
6
2
7
Why is a Capacity Model Important?
  • Within the past 5 years, BRBs have become very
    common in high seismic regions in the U.S.
  • Although
  • Simplified force design methods exist and
  • Analytical force-deformation models are well
    refined,
  • No complete method to determine deformation
    capacity exists.
  • Can we predict capacity (deformation undergone
    without fracture) without the need to test?
  • What about residual capacity after an earthquake?

8
Presentation Outline
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

9
Research Goal
  • To develop a model that can predict BRB core
    fracture due to low-cycle fatigue.
  • Takeuchi 4 has developed a capacity model
    based on force-deformation test data.
  • We seek to develop a model using only deformation
    data only.

10
BRB Test Database
  • 76 BRB specimens
  • 34 failed via tensile rupture
  • 42 did not fail via tensile rupture
  • From researchers around the world
  • Contains following information
  • Geometrical properties
  • Material properties
  • Deformation history
  • Regular cyclic loading (67 specimens)
  • Seismic loading (9 specimens)

11
Predictive Parameters
  • 3 Types of Parameters
  • BRB material properties
  • BRB geometric properties
  • Descriptors of the imposed deformation history
  • General Definitions
  • Ductility
  • Cumulative plastic ductility (CPD)

12
Summary of Predictive Parameters
13
BRB Force-Deformation Model
  • An elastic perfectly plastic force-deformation
    model was assumed to convert deformation history
    into elastic and plastic deformations

14
Plastic Excursions (PEs)
15
Rainflow Cycle Counting
  • Irregular History

Cyclic History
3
16
Presentation Outline
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

17
Bayesian Capacity Modeling Overview
  • Basic Idea Construct capacity models using
    predictive parameters and calibrate the models to
    match the test results
  • Advantages
  • Unbiased
  • Flexibility of form
  • Can take into account both failure and
    non-failure data
  • Able to identify important parameters

18
Bayesian Parameter Estimation Versus Maximum
Likelihood Method
  • A Bayesian methodology uses an informative prior
    distribution (i.e. knowledge known before doing
    parameter estimation) to inform the posterior
    (resulting) distribution.
  • The means of the posterior distributions were
    selected as the model parameter values, while the
    c.o.v.s were used to identify the important
    predictive parameters.
  • Due to the lack of knowledge for prior
    distribution and convenience, we estimated the
    means and standard deviations of the posterior
    distribution approximately by use of the maximum
    likelihood function.

19
Modeling Steps
  • Model form definition
  • Calibration of model parameters
  • Model Reduction
  • Model error analysis
  • NOTE I will present these steps in reference to
    an End-Capacity model formulation.
  • Two other types of models Damage Model and
    Remaining-Capacity Model

20
1. Model Form Definition
  • End-Capacity model takes the form

21
2. Calibration of Model Parameters
Predicted Capacity (from model)
Measured Capacity (from tests)
Iterate ? and s to maximize LIKELIHOOD
Failure points (34) Lower bound points (42)
22
3. Model Reduction
  • Initially, consider a model with many predictive
    parameters
  • The goal of model reduction is to reduce the
    number of predictive parameters in the model
    while maintaining model accuracy.

23
4. Model Error Analysis
24
End-Capacity Modeling Results
Kitchen Sink Model
PE Model
RF Model
Prop. Model (linear)
Prop. Model(exp.)
RF Model (exp.)
25
Issue with the Best Model
  • The CPD is embedded in the model!!!

26
End-Capacity Modeling Conclusions
  • A large variety of predictive parameters were
    explored.
  • Deformation history predictive parameters were
    more important than BRB properties.
  • The RF distribution parameters were better than
    the PE distribution parameters.
  • Overall, no high-fidelity end-capacity model was
    found, though Model 1 was okay.
  • The end-capacity formulation is awkward.
  • Easy to include the answer in the model when
    using deformation descriptor terms as predictive
    parameters

27
Presentation Outline
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

28
Damage Models
  • Basic damage model 5
  • Calculated at any point in deformation history

29
Determination of ß
  • Solve

This yielded
30
Augmented Damage Model
  • Form

Calibrate ? and s by maximizing the probability
that D (end of history) 1 for all failure
specimens D (end of history) lt 1 for all
non-failure specimens
31
Augmented Damage Model Performance
Failure Specimens
32
Augmented Damage Model Issues
  • Same on as Best End-Capacity Model before the
    answer is embedded in the formulation
  • Behavior over the deformation history is poor

33
Damage Model Conclusions
  • The basic damage model behaves correctly but is
    imprecise.
  • The augmented damage model behaves incorrectly
    but is very precise (due to spurious reasons).
  • The basic damage model may be applied in an
    engineering context, but its imprecision must be
    taken into account.

34
Presentation Outline
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

35
Remaining Capacity Models
  • Remaining capacity models were created to address
    the issues/limitations of the end-capacity and
    damage models.
  • They are somewhat a combination of the two.
  • IDEA Capacity should start at a total value and
    reduce monotonically with the applied deformation
    history.
  • A value of zero means failure.

36
Remaining Capacity Model Form
37
Remaining Capacity Equation
  • End-type-capacity

Damage evolution
Note
38
Model Parameters Calibration
  • Likelihood function

39
Parameter Calibration Results
40
Remaining Capacity Results
41
Best Single Comparison
42
Worst Single Comparison
43
Remaining Capacity Model Conclusions
  • The remaining capacity models are a combination
    of the end-capacity and damage models, having
    their advantages but not their disadvantages
  • Behavior over time (or deformation increment) is
    good.
  • Accuracy is fair considering the variability in
    the inputs (loading, BRBs, etc.)

44
Presentation Outline
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

45
Research Applications
Performance-Based Design Framework
Random Earthquake Input
BRB Remaining Capacity Model
Likelihood of Damage or Failure
46
Summary
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions

47
Conclusions What did we learn?
  • Inferring BRB behavior and fatigue fracture was
    incredibly difficult given our test database.
  • Large variety of specimens
  • Different loadings
  • Mechanisms are complex
  • We learned how to use Bayesian modeling methods
    well.
  • We came up with no high-fidelity models, but the
    remaining capacity model was the most intuitive
    and applicable.
  • To improve BRB CPD capacity modeling, we need a
    more uniform testing program.

48
Acknowledgements
  • Robert Tremblay for his BRB Testing Information
  • Toru Takeuchi for communication regarding his BRB
    CPD capacity modeling concepts.
  • My funding was provdied by the Dwight David
    Eisenhower Transportation Fellowship Program.

49
References
  • Black et al. (2004). Component Testing, Seismic
    Evaluation, and Characterization of Buckling
    Restrained Braces. ASCE Journal of Structural
    Engineering, V. 130, N. 6, Pgs. 880-894.
  • Fahnestock et al. (2006). Analytical and
    Large-Scale Experimental Studies of
    Earthquake-Resistant Buckling-Restrained Braced
    Frame Systems. ATLSS Report No. 06-01. September
    2006, Pgs. 270-275.
  • American Society for Testing and Materials.
    (2005). Standard Practices for Cycle Counting in
    Fatigue Analysis. ASTM 1049-05.
  • Takeuchi, T., Ida M., Yamada, S., and Suzuki K.,
    Estimation of Cumulative Deformation Capacity of
    Buckling Restrained Braces, Journal of
    Structural Engineering, ASCE, In Press.
  • Park, Y.-J., and Ang, A.H.-S., Mechanistic
    Seismic Damage Model for Reinforced Concrete,
    Journal of Structural Engineering, ASCE, Vol 111,
    No 4, 1985, pp. 722-739.

50
QUESTIONS??
  • Research Goals
  • BRB Test Database
  • Predictive Parameters
  • Bayesian Modeling Overview
  • End-Capacity Models
  • Damage Models
  • Remaining Capacity Models
  • Applications
  • Conclusions
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