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Performance Modeling Strategies Performance Modeling Strategies
for Modern Reinforced Concrete for Modern Reinforced Concrete
Bridge ColumnsBridge Columns
Michael P. Berry
Marc 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
• User’s 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 deformations
–Local 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
Popovic’s 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
σσ σσ/f
y
εεεεs
Bilinear
Measured
Es * b
0 0.05 0.1 0.150
0.5
1
1.5
εεεεs
σσ σσ/f
y,
Measured
Kunnath
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 4
x 10-4
0
1
2
3
4
5
6
7
8x 10
5
φφφφ (1/mm)
Mo
men
t (K
N-m
m)
Radial
Unilateral
φy Ratio
M5 ε
y
Ratio M10 ε
y
Ratio
CrossCross--Section Fiber Section Fiber DiscretizationDiscretization
Uniform (220 Fibers)
10
20
r
c
t
c
n
n
=
=
1
20
r
u
t
u
n
n
=
=
Confined Unconfined
Reduced Fiber Reduced Fiber DiscretizationDiscretization
Uniform (220 Fibers)
Nonuniform Strategies
CrossCross--Section Fiber Section Fiber DiscretizationDiscretization
5
20
2
10
r
fine
t
fine
r
coarse
t
coarse
n
n
n
n
=
=
=
=
1
20
r
u
t
u
n
n
=
=
Confined Unconfined
Uniform (220 Fibers) Reduced (140 Fibers)
10
20
r
c
t
c
n
n
=
=
1
20
r
u
t
u
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 (λ)
– Effective depth in compression (dcomp)
• Shear Model
– section Aggregator
– Elastic Shear (γ)
Model OptimizationModel Optimization
• Objective: Determine model parameters such that the error between measured and calculated global and local responses are minimized.
( )
( )( )
2
1
2
max
n
meas calc
push
meas
F FE
F n
−=∑ ( )
( )( )
2
1
2
max
n
meas calc
strain
meas
En
ε ε
ε
−=∑
Model EvaluationModel Evaluation
. . meas
calc
KS R
K=
_ 4%
_ 4%
. .meas
calc
MM R
M=
mean 14.89 6.73 7.78 14.4 1.02 1.03
cov (%) – – – – 15 8
totalE pushE (0 / 2)D
strainE
− ( / 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, λ = 0.875
• Bond-Compression Depth,
• dcomp =1/2 N.A. Depth at 0.002 comp
strain
• Shear Stiffness γ = 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 1.00
cov (%) 19 16
Stiffness Ratio Stats
effEI = sec sec
calcEIαcalc
g c gE Iα
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-PlasticityDistributed-
Plasticity
Ef orce (%) Ef orce (%)
mean 16.13 15.66
min 6.63 6.47
max 44.71 46.05
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
∆∆∆∆ /∆∆∆∆y
Fo
rce
(K
N)
Lehman No.415
Measured
OpenSees
KunnathKunnath and and MohleMohle
Steel 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, C
f=0.4
• Strength Reduction Constant, Cd=0.4
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
∆∆∆∆/∆∆∆∆y
Fo
rce
(K
N)
Lehman No.415
Measured
OpenSees
-15 -10 -5 0 5 10 15-300
-200
-100
0
100
200
300
∆∆∆∆ /∆∆∆∆y
Fo
rce
(K
N)
Lehman No.415
Measured
OpenSees
Giufre-Menegotto-Pinto (with Bauschinger Effect)
Kunnath and Mohle (2006)
Giufre-Menegotto-
Pinto
Kunnath and
Mohle
Ef orce (%) Ef orce (%)
mean 16.13 11.98
min 6.63 5.15
max 44.71 29.45
Continuing WorkContinuing Work
Imperfect Crack Closure
•Drift Ratio Equations
•Distributed-Plasticity Modeling Strategy
•Lumped-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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