Title: Ductility Capacity Models for Buckling Restrained Braces Blake Andrews Larry Fahnestock Junho Song
1Ductility Capacity Models for Buckling Restrained
BracesBlake Andrews Larry FahnestockJunho
Song
bandrew3_at_uiuc.edu
2What 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
32
42
52
62
7Why 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?
8Presentation Outline
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
9Research 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.
10BRB 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)
11Predictive Parameters
- 3 Types of Parameters
- BRB material properties
- BRB geometric properties
- Descriptors of the imposed deformation history
- General Definitions
- Ductility
- Cumulative plastic ductility (CPD)
12Summary of Predictive Parameters
13BRB Force-Deformation Model
- An elastic perfectly plastic force-deformation
model was assumed to convert deformation history
into elastic and plastic deformations
14Plastic Excursions (PEs)
15Rainflow Cycle Counting
Cyclic History
3
16Presentation Outline
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
17Bayesian 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
18Bayesian 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.
19Modeling 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
201. Model Form Definition
- End-Capacity model takes the form
212. 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)
223. 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.
234. Model Error Analysis
24End-Capacity Modeling Results
Kitchen Sink Model
PE Model
RF Model
Prop. Model (linear)
Prop. Model(exp.)
RF Model (exp.)
25Issue with the Best Model
- The CPD is embedded in the model!!!
26End-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
27Presentation Outline
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
28Damage Models
- Basic damage model 5
- Calculated at any point in deformation history
29Determination of ß
This yielded
30Augmented Damage Model
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
31Augmented Damage Model Performance
Failure Specimens
32Augmented 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
33Damage 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.
34Presentation Outline
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
35Remaining 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.
36Remaining Capacity Model Form
37Remaining Capacity Equation
Damage evolution
Note
38Model Parameters Calibration
39Parameter Calibration Results
40Remaining Capacity Results
41Best Single Comparison
42Worst Single Comparison
43Remaining 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.)
44Presentation Outline
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
45Research Applications
Performance-Based Design Framework
Random Earthquake Input
BRB Remaining Capacity Model
Likelihood of Damage or Failure
46Summary
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions
47Conclusions 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.
48Acknowledgements
- 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.
49References
- 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.
50QUESTIONS??
- Research Goals
- BRB Test Database
- Predictive Parameters
- Bayesian Modeling Overview
- End-Capacity Models
- Damage Models
- Remaining Capacity Models
- Applications
- Conclusions