BondBond--SP01: BondSP01: Bond--slip model slip model

to Capture Strain Penetration to Capture Strain Penetration

Effects in OpenSeesEffects in OpenSees

Sri SritharanSri Sritharan

Associate professorAssociate professor

Iowa State UniversityIowa State University

Jian ZhaoJian Zhao

Assistant professorAssistant professor

University of Wisconsin University of Wisconsin --MilwaukeeMilwaukee

PrePre--NEESR ProjectNEESR Project

Design and

Practitioner

input/feedback

Remote participation,

Education/Outreach

Design,

Instrumentation

and Testing

Simulation

and Remote

control of

test

�� 3 T3 T--wallswalls

2 at 50% scale2 at 50% scale

1 at 75% scale1 at 75% scale

�� Specimen Specimen

under under

constructionconstruction

�� Testing Testing ––

October 2005October 2005

Test PlanTest Plan

OpenSees AnalysesOpenSees Analyses

�� Examine capabilities using existing test dataExamine capabilities using existing test data

-100

-50

0

50

-4 -2 0 2 4

Top Displacement (in,)

Late

ral L

oad (kip

s)

Experimental Data

openSEES 90

openSEES 270

�� Make improvements as neededMake improvements as needed

�� Modeling of bond slip resulting from strain Modeling of bond slip resulting from strain

penetration into the footingpenetration into the footing

Flange in

compression

Flange in

tension

Plot by Jon Waugh at ISUPlot by Jon Waugh at ISU

Strain PenetrationStrain Penetration

Building frame Bridge bentStructural wall

1

1

11

22

Existing Models of Bond SlipExisting Models of Bond Slip

Rotational

spring 1D springs Special interface element

ZeroZero--length Section Elementlength Section Element

Element Section

ZeroLength

Structure

σ

s

Fibers

Bar stress vs.

bar slip

relationship

Strain Penetration ModelStrain Penetration Model

yf

sy

bar @ yield

sy

slip (s) bond stress (τ)

Anchorage

length

la

α

τ

1

1s

s

Previous means:

•Assume effective

anchorage length

• Assume constant

bond stress

distribution

•Assume material

model for steel

•Integrate bar

strain over la

Bar Stress vs. Slip ModelBar Stress vs. Slip Model

σ

σy

σu

ssy

su

K

bK

Ks=σ

( )yyu σσσσσ +−×= ~

( )yy ssss −=~

ReReRe

s

s

b

s

s

1

~

~1

~

~

~

−+

⋅

−=

µµ

µσ

Bar stress

Bar slip

Bridge b

1

Slip at Bar Yield (Slip at Bar Yield (ssyy))

0 0.1 0.2 0.3 0.4 0.5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07L

oad

ed-e

nd s

lip a

t b

ar y

ield

ing (

s y)

( )α

α

1

12'4

+

c

yb

f

fd

( ) 013.012'4

1.0

1

+

+=

α

α

c

yby

f

fds

db: bar diameter

fy: yield strength in ksi

fc': concrete strenght in psi

a : parameter in local bond model (0.4 from MC9018,23)

Model ValidationModel Validation

0 0.2 0.4 0.6 0.8 1Loaded-End Slip (s)

0

20

40

60

80

100B

ar S

tres

s (σ

)

Experiment

Prediction

model parameters:

s y = 0.0264in. f y = 68ksi

s u = 0.98in. f u = 100ksi

b = 0.45 R c = 1.01

Cyclic ModelCyclic Model

(maxrs, maxrl)

(minrs, minrl)

minrl×= *σσ

( ) ysrsvgss '* −=

RcRc

uy

Rc

uy

uy

ss

s

s

ss

s

1

*

*1

*

*

*

−+

−=σ

σ

s

: (rsvg, 0)K

KK

s'y

s'ys'

y

maxrl×= *σσ

Simulation of a Short ColumnSimulation of a Short Column

(a) F @ Dy (b) F @ 4Dy

0 0.50

10

20

30

40

Co

lum

n H

eig

ht

(in

.)

0 1 2 3Column Deflection (in.)

Measured deflection (no shear)

Analysis w/ strain penetration

Analysis w/o strain penetration

Simulation of a Circular ColumnSimulation of a Circular Column

(a) at Dy (b) at 1.6Dy

gaged bar

loading

1000 2000 3000 4000 50000

20

40

60

Co

lum

n H

eig

ht

(in

.)

2000 4000 6000 8000Bar Strain x 106 (in/in)

Measured strain

w/ strain pene.

w/o strain pene.

Simulation of a Bridge JointSimulation of a Bridge Joint

-4 -2 0 2 4Column Displacement (in.)

-100

-50

0

50

100

Ap

pli

ed F

orc

e (k

ips)

Measured response

Analysis w/o strain penetration

Analysis w/ strain penetration

cap beamcolumn

Simulation of a Bridge Joint (con.)Simulation of a Bridge Joint (con.)

-0.004 -0.002 0 0.002 0.004Curvature at Column End (1/in.)

-600

-400

-200

0

200

400

600

Mom

ent

at

Colu

mn

En

d (

kip

s-ft

)

Measured response

Analysis w/o strain penetration

Analysis w/ strain penetration

critical

section

ConclusionsConclusions�� Strain penetration has impact on the behavior of RC Strain penetration has impact on the behavior of RC

membersmembers

�� Strain penetration effects can be modeled in fiberStrain penetration effects can be modeled in fiber--based based analysis using a zeroanalysis using a zero--length section element length section element

�� Proposed bar stress vs. slip model can represent the Proposed bar stress vs. slip model can represent the behavior of bars with ample anchorage behavior of bars with ample anchorage

�� With the proposed model, strain penetration effects on With the proposed model, strain penetration effects on RC member behavior can be capturedRC member behavior can be captured

�� Source code and user manual for BondSource code and user manual for Bond--SP01:SP01:

Email Email jzhao@uwm.edujzhao@uwm.edu

Will be uploaded to OpenSees RepositoryWill be uploaded to OpenSees Repository