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