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Modeling issues for OpenSees
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Performance Modeling Strategies Performance Modeling Strategies for Modern Reinforced Concrete for Modern Reinforced Concrete
Bridge ColumnsBridge Columns
Michael P. BerryMarc O. Eberhard
University of Washington
Project funded by the Pacific Earthquake Engineering Research Center (PEER)Pacific Earthquake Engineering Research Center (PEER)
UWUW--PEER Structural PEER Structural Performance DatabasePerformance Database
Nearly 500 Columns spiral or circular hoop-reinforced columns (~180) rectangular reinforced columns (~300)
Column geometry, material properties, reinforcing details, loading
Digital Force-Displacement Histories
Observations of column damage
http://nisee.berkeley.edu/spd
Users Manual (Berry and Eberhard, 2004)
Objective of ResearchObjective of Research
Develop, calibrate, and evaluate column modeling strategies that are capable of accurately modeling bridge column behavior under seismic loading.
Global deformationsLocal deformations (strains and rotations)Progression of damage
Advanced Modeling StrategiesAdvanced Modeling Strategies
F
Force-Based Fiber Beam Column Element (Flexure)
Lumped-Plasticity
Force-Based Fiber Beam Column Element (Flexure)
Fiber Section at each integration point with Aggregated Elastic Shear
Zero Length Section (Bond Slip)
Elastic Portion of Beam(A, EI )
to Plastic Hinge
eff
Lp
Distributed-Plasticity
CrossCross--Section ModelingSection Modeling
CrossCross--Section Modeling ComponentsSection Modeling Components
Concrete Material Model
Reinforcing Steel Material Model
Cross-Section Discretization Strategy
Concrete Material ModelConcrete Material Model
Popovics Curve with Mander et. al. Constants and Added Tension Component (Concrete04)
Reinforcing Steel Material ModelsReinforcing Steel Material Models
Giufre-Menegotto-Pinto(Steel02)
0 0.05 0.1 0.150
0.5
1
1.5
/
f
y
s
BilinearMeasured
Es * b
0 0.05 0.1 0.150
0.5
1
1.5
s
/
f
y,
MeasuredKunnath
Mohle and Kunnath(ReinforcingSteel)
Section Fiber Section Fiber DiscretizationDiscretization
Objective: Use as few fibers as possible to eliminate the effects of discretization
Cover-Concrete Fibers
Core-Concrete Fibers
Longitudinal Steel Fibers
0 1 2 3 4x 10-4
0
1
2
3
4
5
6
7
8x 105
(1/mm)
M
o
m
e
n
t
(
K
N
-
m
m
)
RadialUnilateral
y Ratio
M5 y Ratio M10 y
Ratio
CrossCross--Section Fiber Section Fiber DiscretizationDiscretization
Uniform (220 Fibers)
1020
r
c
tc
n
n
=
=
120
r
u
tu
n
n
=
=
Confined Unconfined
Reduced Fiber Reduced Fiber DiscretizationDiscretization
Uniform (220 Fibers)
Nonuniform Strategies
CrossCross--Section Fiber Section Fiber DiscretizationDiscretization
5
20
210
r
finetfiner
coarse
tcoarse
n
n
n
n
=
=
=
=
120
r
u
tu
n
n
=
=
Confined Unconfined
Uniform (220 Fibers) Reduced (140 Fibers)
1020
r
c
tc
n
n
=
=
120
r
u
tu
n
n
=
=
Confined Unconfined
r/2
Modeling with DistributedModeling with Distributed--Plasticity ElementPlasticity Element
Model ComponentsModel Components
Force-Based Fiber Beam Column Element (Flexure)
Fiber Section at each integration point with Aggregated Elastic Shear
Zero Length Section (Bond Slip)
Flexure Model (Force-Based Beam-Column)
nonlinearBeamColumn Fiber section Popovics Curve (Mander constants) Giufre-Menegotto-Pinto (b) Number of Integration Points (Np)
Anchorage-Slip Model zeroLengthSection Fiber section Reinforcement tensile stress-
deformation response from Lehman et. al. (1998) bond model ()
Effective depth in compression (dcomp) Shear Model
section Aggregator Elastic Shear ()
Model OptimizationModel Optimization Objective: Determine model parameters such that the error between
measured and calculated global and local responses are minimized.
( )( )( )
2
12
max
n
meas calcpush
meas
F FE
F n
= ( )
( )( )2
12
max
n
meas calcstrain
meas
En
=
Model EvaluationModel Evaluation
. .
meas
calc
KS RK
=
_ 4%
_ 4%
. .
meas
calc
MM R
M=
mean 14.89 6.73 7.78 14.4 1.02 1.03cov (%) 15 8
totalE pushE (0 / 2)DstrainE ( / 2 )D D
strainE
. .S R . .M R
Optimized Model: Strain Hardening Ratio, b = 0.01 Number of Integration Points, Np = 5 Bond-Strength Ratio, = 0.875 Bond-Compression Depth, dcomp =1/2 N.A. Depth at 0.002 comp
strain Shear Stiffness = 0.4
Modeling with LumpedModeling with Lumped--Plasticity ElementPlasticity Element
LumpedLumped--Plasticity ModelPlasticity Model
Fiber Section assigned to Plastic Hinge
Elastic Portion of Beam(A, EI )
Lp
eff
Hinge Model Formulation: beamwithHinges3 Force Based Beam Column Element
with Integration Scheme Proposed by Scott and Fenves, 2006.
Fiber Section Elastic Section Properties
Elastic Area, A Effective Section Stiffness, EIeff
Calculated Plastic-Hinge Length Lp
Section Stiffness CalibrationSection Stiffness Calibration
mean 1.00 1.00cov (%) 19 16
Stiffness Ratio Stats
effEI = sec seccalcEIcalcg c gE I
PlasticPlastic--Hinge Length CalibrationHinge Length Calibration
Cyclic ResponseCyclic Response
Cyclic Material ResponseCyclic Material Response Cyclic response of the fiber-column model depends
on the cyclic response of the material models.
Current Methodologies Do not account for cyclic degradation steel Do not account for imperfect crack closure
Giufre-Menegotto-Pinto (with Bauschinger Effect)Steel02
Reinforcing Steel Confined and Unconfined Concrete
Karsan and Jirsa with Added Tension Component Concrete04
Evaluation of ResponseEvaluation of Response
Lumped-Plasticity Distributed-PlasticityEf orce (%) Ef orce (%)
mean 16.13 15.66min 6.63 6.47max 44.71 46.05
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
/y
F
o
r
c
e
(
K
N
)
Lehman No.415
MeasuredOpenSees
KunnathKunnath and and MohleMohleSteel Material ModelSteel Material Model
Cyclic degradation according to Coffin and Manson Fatigue. Model parameters:
Ductility Constant, Cf Strength Reduction Constant, Cd
Preliminary Study with Preliminary Study with KunnathKunnath Steel Steel ModelModel
Ductility Constant, Cf =0.4 Strength Reduction Constant, Cd=0.4
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
/y
F
o
r
c
e
(
K
N
)
Lehman No.415
MeasuredOpenSees
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
/y
F
o
r
c
e
(
K
N
)
Lehman No.415
MeasuredOpenSees
Giufre-Menegotto-Pinto (with Bauschinger Effect) Kunnath and Mohle (2006)
Giufre-Menegotto-Pinto
Kunnath and Mohle
Ef orce (%) Ef orce (%)mean 16.13 11.98min 6.63 5.15max 44.71 29.45
Continuing WorkContinuing Work
Imperfect Crack Closure
Drift Ratio EquationsDistributed-Plasticity Modeling StrategyLumped-Plasticity Modeling Strategy
Prediction of Flexural Damage
Key Statistics Fragility Curves Design Recommendations
Evaluation of Modeling-Strategies for Complex Loading
Bridge Bent (Purdue, 2006)Unidirectional and Bi-directional Shake Table (Hachem, 2003)
Thank you
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