Towards Robust Behavioral Modeling of Reinforced Concrete Membersof Reinforced Concrete Members

K t O k lKutay Orakçal Boğaziçi Universitywith contributions of:

Denizhan Ulugtekin (M.Sc, B.U.) Tevfik Terzioglu (M.Sc. B.U.)S Reza Chowdhury (Ph D B U )S. Reza Chowdhury (Ph.D., B.U.)

International Workshop on“Role of ResearchInternational Workshop on Role of Research Infrastructures in Seismic Rehabilitation”

Structural ModelingStructural Modeling

Modern codes on performance-based i i t d d i iseismic assessment and design require

nonlinear response analysis of structures.

A l i l d l h ld hAnalytical models should represent the behavioral characteristics of the members at both global and local response levels.

gv&&

Examples of novel analytical modeling approaches to be presented for pp pnonlinear response simulation of RC members.

Emphasis on simulation of nonlinear flexural, shear, and bond-slip responses in RC columns and wallsin RC columns and walls

Modeling of Flexural Responses:Modeling of Flexural Responses:Th “MVLEM” f St t l W llTh “MVLEM” f St t l W ll

5 Rigid Beam

The “MVLEM” for Structural WallsThe “MVLEM” for Structural Walls

46 Rigid Beam

m . .

h

(1-c)hk1 k2 knkH. . . . . . .

2

. . . .

ch 1 2

12

3 Rigid Beam RC WALL WALL MODEL

k k k k k k kk1 2 3 4 5 6 7 8

Material Constitutive ModelsMaterial Constitutive Models

C i

( εc ' , f c

' ) E1= bE0σy

Compression

rE0

ss, σ

O (ε0, 0)

εyO

RStre

s

Strain ε

TensionNot to scale(ε0+ εt , ft)

Strain εStrain, εConcrete :• Chang and Mander (1994)

Reinforcing Steel :• Menegotto and Pinto (1973)

Strain, ε

Generalized (can be updated)Allows refined calibrationGap closure and tension

• Menegotto and Pinto (1973)• Filippou et al. (1984)

Simple but effectiveGap closure and tensionstiffeningValidated with extensive data

Simple but effectiveDegradation of cyclic curvature

Experimental Experimental VerificationVerification of the Modelof the Modelpp

• Cyclic test results on slender rectangular and T-shaped wallspecimens (Thomsen and Wallace 1995)(Thomsen and Wallace, 1995)

• Approximately 1/4 scaleA t ti 3• Aspect ratio = 3

• Prototype building design (UBC)• Displacement – based

RW2sp ace e t based

evaluation for detailing• 3.66 m x 122 cm x 10 cm

• Loading:Constant axial loadCCyclic lateral load applied at top of walls

Model PredictionsModel Predictions::

Lateral Flexural Drift (%)

Lateral Load Lateral Load –– Displacement ResponseDisplacement Response

200

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

( )

Test≈Pax 0 07A f '

100

150

at (

kN) Analysis

≈Pax 0.07Ag f c

Plat , Δtop

RW2

0

50

Load

, Pla RW2

-100

-50

Late

ral L

200300400500

(kN

)-200

-150

L

0100200

P ax

-80 -60 -40 -20 0 20 40 60 80

Top Flexural Displacement, Δtop (mm)

Strain Distribution and Strain Distribution and CurvatureCurvaturess

0 05

0.06s) 0.0025RW2

0.04

0.05

(LVD

Ts

TestAnalysis

-0.0025

0RW2

0.02

0.03

Stra

in ( Analysis

0 01

-0.0075

-0.005

0

0.01

cret

e S -0.01

-0.01

0

Con

c

0.5%1.0%2 0%

0 200 400 600 800 1000 1200

Di t l W b ( )

-0.022.0%

Distance along Web (mm)

Modeling of Bond Slip Responses:Modeling of Bond Slip Responses:MVLEM with Bond Slip SpringsMVLEM with Bond Slip Springs

   8

MVLEM with Bond Slip SpringsMVLEM with Bond Slip Springs(Chowdhury, 2011)(Chowdhury, 2011)

 

      

14 818

45 6

12  1016

      

Bond slip spring!

      

  

Rebar element

2 17915   137

M difi d M d l

Column or Wall

Analytical model

1 2 3  11

179 

Rigid BeamConcretemacro-fiber

Modified Model Element

Constitutive Bond Stress vs. Slip Constitutive Bond Stress vs. Slip ModelsModelsSt

ress

Bon

d S

Roman Aqueduct, FranceSplitting Pullout

q19 B.C.

Splitting Pull-out

Slip DeformationSlip Deformation

gHarajli et al. (2009)Unconfined and partially-

fi d t

Eligehausen et al. (1983) Confined concrete, in vicinity

f ticonfined concreteExperimentally-validated

of tiesExperimentally-validated

Experimental VerificationExperimental VerificationMelek and Wallace(2006)C l ithColumns with inadequate lap splicesDetailed local responseDetailed local response measurementsAlso verified with

i i t l

Roman Aqueduct, France

various experimental results available in the literature: q

19 B.C.

Harajli and Dagher (2008) Elgawady et al. (2010) Verderame et al. (2008) Yılmaz (2009) (ITU)

Model PredictionsModel Predictions::Lateral Load Lateral Load –– Displacement ResponseDisplacement Response

Specimen 2S10M (Paxial = 10%Agfc )

Lateral Drift (%) Lateral Drift (%)

400-10 -5 0 5 10

T t

400-10 -5 0 5 10

Analysis

Roman Aqueduct, France0

200

Load

(kN

) Test

0

200Analysis

q19 B.C.

-200

0

Late

ral L

2S10M-200

0

2S10M

-200 -100 0 100 200

-400

2S10M

-200 -100 0 100 200

-400

2S10M

00 00 0 00 00Lateral Displacement (mm)

00 00 0 00 00Lateral Displacement (mm)

SteelSteel Strain HistoriesStrain Histories

Specimen 2S20M (at straingauge no. 7)

0.0008Strain Gauge No:7

0.0004

ain

TestAnalysis 2S20M

0

Stee

l Str

a

-0.0004

S

0 200 400 600 800Data No.

-0.0008

Concrete Strain DistributionConcrete Strain Distribution

Specimen 2S10M (at halfway along lap splice length)

0.030.25% Otel.0 75 % Otel

0 01

0.02

Stra

in

0.75 % Otel.1.5% Otel.0.50% Otel.1% Otel2% Ot l

0

0.01

oncr

ete

S 2% Otel

-0.01

Co

TestAnalysis 2S10M

0 200 400 600Distance along width (mm)

-0.02

Columns with Plain Bars and 180Columns with Plain Bars and 180oo HooksHooksSpecimen LS-44φ-N1 by Yılmaz and İlki (2009), İstanbul Tech. Univ.

Plain bar Lap length = 44φ 180-degree hooks

fc = 10 MPa fy = 285 MPa, Paxial = 0

Drift Ratio (%) Drift Ratio (%)

10

15-10 -8 -6 -4 -2 0 2 4 6 8 10

kN)

Drift Ratio (%)

kN)

Drift Ratio (%)

()

0

5

-165 -132 -99 -66 -33 0 33 66 99 132 165al L

oad

(k

al L

oad

(k

-10

-5-165 -132 -99 -66 -33 0 33 66 99 132 165

Late

ra

Test AnalysisLate

raDi l ( )

-15

Lateral Displacement (mm) Lateral Displacement (mm)

Presence of 180-degree hooks prevents slip failure!!

Modeling of ShearModeling of Shear--FlexureFlexure Interaction (SFI):Interaction (SFI):MVLEM ith P l S bMVLEM ith P l S b El tEl t

Load εy

MVLEM with Panel SubMVLEM with Panel Sub--ElementsElementsLoad

(cyclic) γxy

εx

Constitutive

εx

MVLEM(or fiber model)

RCWall

Constitutive“Fixed-Strut-Angle”

Panel Element

A ti

ModelElement

Assumptions:• Plane sections remain plane

Shear strains ( ) are niforml distrib ted along l• Shear strains (γxy) are uniformly distributed along lw• Resultant horizontal stress (σx) is equal to zero for each

panel element (agrees with boundary condition at sides)panel element (agrees with boundary condition at sides)• Assumptions are valid for hw/lw ≥ 1.0

Constitutive RC Panel Model DevelopedConstitutive RC Panel Model Developed(Ul t ki 2010)(Ul t ki 2010)(Ulugtekin, 2010)(Ulugtekin, 2010)Load σc1

compression strut(fixed)

Wall

Panelelement σc - ε

concrete

σc2θεy

γxy

Cracks

Wall

σsyεx

σ ε(direction fixed)σsx

σs - εsteel

• Developed: “fixed-strut-angle” panel modelBased on observed physical behaviorAllows cyclic response predictionsSimple yet robust and flexibleCompression strut

(direction fixed after formation of cracks)

Simple, yet robust and flexible

The FixedThe Fixed--StrutStrut--AAngle Panel Modelngle Panel ModelUncracked Panel Response:

• Rotating principal stress angle approach

• Monotonic stress-strain relationships

εy

• Behavior mostly in the linear elastic range

σc y

ε

γxy

y

σc – εc

softened

σ1, soft

σ2, soft

θε1

ε2

θσ

τc,xy

c,y

εx softened concrete

σy

σc,x

σc y σ

σ

τxy

σy

σ

τc,xy

σc,y

σs,x

σs,y

+ σxσc,x

The FixedThe Fixed--StrutStrut--AAngle Panel Modelngle Panel ModelCracked Panel Response

• ε1 > εcr,mon → θcrA (principal strain direction)

• σ1 and σ2 are || and ┴ to θcrA θcrA

εy

• γx’y’ → τx’y’ = 0 (zero aggregate interlock)

σ’

Compression strut (direction fixed)

εx

γxy

y

σc – εc

softened

σ’cy,soft

σ cx,soft

θcrA

ε’yε’x

θcrA

ε2

ε1Strain

transformationεx softened concrete

crA

σyσc y σ

t a s o at o

σ

τxy

σy

σ

τc,xy

σc,y

σs,x

σs,y

+ σxσc,x

Experimental Verification of the Panel ModelExperimental Verification of the Panel Model

(Mpa

)Cyclic panel test results by:Mansour and Hsu (2001)

r Str

ess

(Mansour and Hsu (2001)Stevens and Collins (1987)

Accurate response predictions

Shea Test

Analysis

a)

Shear Strain

ress

(Mpa

Shea

r Str

TestAnalysis

Shear Strain

yPanel Tester

at Univ. Of Houston

SFI Model Prediction for Slender Walls:SFI Model Prediction for Slender Walls:L t l L dL t l L d Di l t RDi l t RLateral Load Lateral Load –– Displacement ResponseDisplacement Response

MVLEM – SFI(σx = 0)

Specimen RW2 pThomsen and Wallace (1995)

Strain Distribution and CurvaturesStrain Distribution and Curvatures

SFI Model Prediction for Short Walls:SFI Model Prediction for Short Walls:• Hirosawa (1975)

Cantilever wall• Hidalgo et al. (2002)

Fixed Fixed wall

1200

Cantilever wallShear cap. ≈ Flex. cap.

Fixed–Fixed wallShear cap. ≈ 0.5 Flex. Cap.

150

200

(kN

)

800(kN

)

100

ral L

oad

M/(Vl) = 0.69

800

ral L

oad

M/(Vl) = 1.0

50Late

r

TestAnalysis

M/(Vl) 0.69400

Late

r

Flexural AnalysisTestCoupled Analysis

M/(Vl) 1.0

0 0.4 0.8 1.2 1.6Lateral Displacement (cm)

0Analysis

0 0.5 1 1.5 2Lateral Displacement (cm)

0Coupled Analysis

p ( )p ( )

Short Wall Test Program at B.U.Short Wall Test Program at B.U.(Terzioglu 2011)(Terzioglu 2011)(Terzioglu, 2011)(Terzioglu, 2011)

• 11 short wall specimens

• Aspect ratios: 1, 1/2, 1/3

• Width = 1.5 m

• Thickness = 120 mm

W b i f t ti• Web reinforcement ratios:ρweb = 0.34% or 0.68%

• Boundary reinforcement: 4-φ16 or 2-φ8

• Paxial = 0%, 5%, 10%Agfc

• fc = 20 MPa – 35 Mpac p

• fy = 520 MPa

Different Failure Modes ObservedDifferent Failure Modes Observed

diagonal tension failure diagonal compression failurediagonal tension failure diagonal compression failure

sliding shearshear-flex. interaction(M/Vl = 1)

InstrumentationInstrumentation

• Detailed measurement of flexural and shear deformations• Detailed measurement of flexural and shear deformations, and average transverse normal strain (εx) distribution

Overview of Shear Modeling ApproachesOverview of Shear Modeling Approaches

Load(cyclic)

( y )

C tit ti

MVLEMRC

ModelElement

Constitutive“Fixed-Strut-Angle”

Panel Elementdeveloped a “modified” fiber modeling

Load

(or fiber model)Wall developed a modified fiber modeling approach for shear-flexure interaction

Load(cyclic)

RCWall

Finite ElementModel

Constitutive“Fixed-Strut-Angle”

Panel ElementPanel Elementongoing efforts on a simplified finite element modeling approach for predominant shear (diagonal tension/compression or sliding)

Results and Ongoing EffortsResults and Ongoing Efforts• Flexural response modeling for slender walls

accurate response predictions overalli t i di ti i d i SFIcompressive strain predictions improved via SFI

bar buckling and low-cycle fatigue effects can be adopted

• Bond slip response modeling for lap spliced columns• Bond slip response modeling for lap-spliced columnsaccurate predictions for columns with deformed barsreasonable predictions for columns with plain barsreasonable predictions for columns with plain bars need better constitutive models for 180o hooks

• Shear and shear-flexure interaction response modelingShear and shear flexure interaction response modelingfixed-crack-angle constitutive panel element developed accurate response predictions for M/Vl ratios > 0.7t t lt ill h l i di ti f h t lltest results will help improve predictions for shorter wallsa simple finite element modeling approach underway

• I l t ti i t t ti l l tf• Implementation into computational platformsOpenSees (in progress)

Towards Robust Behavioral Modeling of Reinforced Concrete Membersof Reinforced Concrete Members

K t O k lKutay Orakçal Boğaziçi Universitywith contributions of:

Denizhan Ulugtekin (M.Sc, B.U.) Tevfik Terzioglu (M.Sc. B.U.)S Reza Chowdhury (Ph D B U )S. Reza Chowdhury (Ph.D., B.U.)

International Workshop on“Role of ResearchInternational Workshop on Role of Research Infrastructures in Seismic Rehabilitation”