4/26/2013

1

ACI WEB SESSIONS

Analysis and Design Issues in Liquid-Containing Concrete

Structures

ACI Fall 2012 ConventionOctober 21 – 24, Toronto, ON

ACI WEB SESSIONS

Armin Ziari is a Structural Engineer at Candu Energy Inc., ON, Canada. He received his BSc from University of Tehran, Tehran, Iran, in 2004; and his MSc and PhD from Ryerson University in 2007 and 2011, respectively. He is a member of subcommittee N287.3, Design Requirements for Concrete Containment Structures for CANDU Nuclear

Power Plants. His research interests include crack and leakage control, and non-linear finite element modeling of RC members.

By

Armin Ziari, M. Reza Kianoush, R. ProticPresenter: Armin Ziari

Ryerson University & Candu Energy Inc.

Research Significance and Scope Proposed Crack Prediction Model Experimental Program Verification Design Guide Conclusions Acknowledgements

Serviceability: Deflection control, Leakage control, ...

Durability: Permeability reduction, Corrosion reduction, ...

Appearance

Simple loading conditions: Pure bending, pure tension,...

No reliable crack control for two‐way members

Ignoring repeated loading effects

Ignoring long term effects

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Experimentally investigating the cracking and leakage behaviour of two‐way panels

Using FE technique to understand different aspects of RC cracking 

Developing a new analytical crack prediction model for two‐way panels

0

1

2

3

4

5

0 50 100 150 200 250

Wal

l Hei

ght (

)

Hoop Tension Force (k/)

0

1

2

3

4

5

-40 -30 -20 -10 0 10 20

Wal

l Hei

ght (

)

Vertical Bending Moment (k./)

T TM

M

M efxseefxccsxspyspyctmrx AtfN ,, 1)(

STABILIZED CRACKING LOAD

csxspyspyctmbxtpxbsp

xbyefxtx f

d

sddS

,II

min

MINIMUM CRACK SPACING

ImaxII

min

IIminII

max 2

oflarger x

x

xy

x SS

SsS

MAXIMUM CRACK SPACING

cscmxsmxxgxx Sw IImaxmax

MAXIMUM CRACK WIDTH AT STABILIZED CRACKING

STABILIZED CRACKING

efxseefxccsxspyspyctmrx AtfN ,, 1)(

STABILIZED CRACKING LOAD

dt,efxdbx

dby

cx

x

spyspyfctm-csx

IImin xS

Imin xS r

sp

y

x

dbx

dbysy

sx

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3

MECHANISM OF BOND

Concrete Elements

Steel Elements

Link Elements

: Concrete Node: Steel Node

Steel Elements

Concrete Elements

-1.5

-1

-0.5

0

0.5

1

-0.2 -0.1 0 0.1 0.2

Force (MN)

Displacement ()

DIAGONAL LINK ELEMENTS

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 0.05 0.1 0.15 0.2 0.25

Con

cret

e T

ensi

le S

tres

s (

)

Crack Opening Displacement ()

0.00

0.01

0.01

0.02

0.02

0.03

0 0.02 0.04 0.06 0.08 0.1 0.12

Con

cret

e T

ensi

le S

tres

s (

)

Crack Opening Displacement ()

/2

Bond Layer

Axis of

Symmetry

cc

BOND LAYER MODEL

A A

Section A-A

Strain Gauge

Transverse Circular Hole for Anchorage

250

300

350

400

450

500

550

0 20 40 60 80 100

Ste

el S

trai

n ()

Distance From Midpoint ()

Kankam TestPerfect Bond45º Link Element30º Link ElementBond Layer

VERIFICATION OF BOND MODELS

KANKAM TEST

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4

Ste

el S

tres

s (

)

)0 0.1 0.2 0.3

11 ()0 0.1 0.2 0.3 0.4 0.5

()

Tammo Test

FE (Bond Layer)

LVDT (wsurf)

LVDT (w11)

Glued Plate

Metal TubeTAMMO TEST

r

sp

Splitting Cracks

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4

db/2 Bond Layer

l

uAxis of

Symmetry

cc

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rad

ial D

ista

nce

/

Splitting tensile stress /

cc = 5

100

200

300

400

-0.2

0

0.2

0.4

0.6

0.8

1

-7.5 -6 -4.5 -3 -1.5 0 1.5 3 4.5 6 7.5

Split

ting

tens

ile s

tres

s/

Bar Axis /

cc = 5

100

200

SPLITTING STRESSES

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350

Ave

rage

Spl

itti

ng te

nsil

e st

ress

/

(%)

Steel Stress ()

2

3

4

5

),/,( ,crxsybycyctspy dcff

3

22

3

2

,

efxt

cyspy d

c

AVERAGE SPLITTING STRESSES

efxseefxccsxspyspyctmrx AtfN ,, 1)(

Axis of Symmetry

Axis of Symmetry

0

0.04

0.08

0.12

0.16

-50 -40 -30 -20 -10 0 10 20 30 40 50

Con

cret

e S

tres

s at

Sur

face

/

/

= 3 = 4

= 2

SHRINKAGE INDUCED TENSILE STRESSES

efxseefxccsxspyspyctmrx AtfN ,, 1)(

csoxcs

csx 61050

units) (SI )(35.0 5.1, bx

eqxcctcsox d

cf

efxseefxccsxspyspyctmrx AtfN ,, 1)(

EFFECTIVE TENSION AREA

dt,efxdbx

dby

cx

x

spyspyfctm-csx

IImin xS

Imin xS

xbyefxtefxc sddA ,bar)(per ,

cxxxtx

cxefxt

dkddk

hdd

cracks, flexuralfor

5.0 , 5.2 oflesser

cracks,sion direct tenfor

,

Bond Layer Elements

Steel Elements

Concrete Elements

A

AA-A

Pla

ne o

f S

ymm

etry Weaker Plane of

ConcreteWeaker Plane of

Concrete

PARAMETRIC STUDY

Concrete Tensile Stress Crack Pattern

A

A

kd

-225

-150

-75

0

75

150

225

-7 -6 -5 -4 -3 -2 -1 0 1 2 3

Dep

th A

xis

(

)

Concrete Stress )

Actual Normalized Equivalent

= 156

= 240

0.2

0.3

0.4

0.5

0.003 0.005 0.007 0.009 0.011

k't

s

kddkd

ddd

teft

cefteft

,

,,

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dt,efxdbx

dby

cx

x

spyspy

fctm-csx

IImin xS

Imin xS

csxspyspyctmbxtpxbsp

xbyefxtx f

d

sddS

,II

min

csxctmbxtpxbsp

xefxtx f

d

sdS

,I

min

MINIMUM CRACK SPACING

-12-10-8-6-4-202468

1012

-250 -200 -150 -100 -50 0 50 100 150 200 250

She

ar B

ond

Str

ess

(

)

Bar Axis )

FEBest Fit

uradial = 0

500

ccu

6

Axis of Symmetry

Concrete Elements

Steel Elements

Approx. 55 mm, 4-node bilinear axisymmetric quadrilateral elements

Bond Layer Elements

uradial = 0

0.00.40.81.21.62.02.42.83.23.64.04.44.85.2

0 1 2 3 4 5 6 7

t,

peak

/

ct

cc /db

100

200

300

400

s()

BOND SHEAR STRESS

dt,efxdbx

dby

cx

x

spyspy

IImin xS

IImax xS

sy

ImaxII

min

IIminII

max 2

oflarger x

x

xy

x SS

SsS

Imin

Imax

IIminII

max2

2 oflesser

xx

xy

xSS

SsS

MAXIMUM CRACK SPACING

(low probability)

(high probability)

fctm-csx

cscmxsmxxgxx Sw IImaxmax

MAXIMUM CRACK WIDTH AT STABILIZED CRACKING

CracksTension Direct 1

cracks Flexural xx

x

gx kdd

kdh

efxsesxexscmxsmx ,2 1 Shea

r B

ond

Str

ess

Con

cret

e St

rain

Bar Axis

Upper BoundaryActual DistributioinLower Boundary

e = 0.66

e = 0.33

bxs

xtpxbspsx dE

S IImax2

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80 100 120 140

Ste

el S

trai

n ()

Center Jack (kN)

F3T F4Ta F5T

REDUCTION OF BOND STRENGTH DUE TO SPLITTING CRACKS

Steel Elements Bond

Layer

Concrete Elements

z

xy

z = 0

x = 0y = 0

z = 0

y = 0

x = 0

0.0

0.4

0.8

1.2

1.6

2.0

0 1.5 3 4.5 6 7.5

She

ar B

ond

Str

ess

/

Bar Axis/

= 200

without splitting crackwith splitting crack

tp

sptpsp

, c c /d b 100 200

2 15 45 603 15 58 524 15 67 574 30 49 465 30 58 55

tp,sp / tp (%)

s (MPa )

l /d b

BOND STRENGTH REDUCTION DUE TO LONGITUDINAL SPLITTING CRACKS

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EXPERIMENTAL PROGRAM

LOADING SCHEME

SCHEMATIC OF TEST SETUP

(PLAN-VIEW)

SCHEMATIC OF TEST SETUP (EAST-SIDE-VIEW)

SCHEMATIC OF TEST SETUP (SOUTH-SIDE-VIEW)

TEST SETUP

MC90Error (%)

Proposed Model

Error (%)

MC90Error (%)

Proposed Model

Error (%)

A 200 34000 2.97 -141 756 1166 54 707 -7 92 167 82 103 12B 200 35000 2.79 -107 708 to 744 1078 45 to 52 662 -7 to -11 88 to 105 158 50 to 80 92 5 to -12C 200 33000 2.79 -113 612 to 738 1097 49 to 79 726 19 to -2 86 148 72 97 13

E s , GPa

E c , MPa

f ct , MPa

cs ,

One-WayPanel Two-Way

Flexural Crack

Stabilized Cracking Load (kN)

Experiment (total side jacks)

Direct Tension Crack

Two-WayExperiment

(center Jack)

One-Way

STABILIZED CRACKING LOAD

SII

maxx SII

maxy SII

maxx SII

maxy SII

minx SII

miny SII

maxx SII

maxy

A 677 (57) 374 (-10) 1033 (140) 365 (-12) 503 (39) 503 (64) 217 (-27) 177 (-12) 652 (52) 733 (77) 517 (20) 477 (15) 295 200 430 414B 833 (11) 478 (-12) 1231 (64) 449 (-17) 561 (11) 359 (-11) 212 (-18) 168 (-38) 641 (-15) 724 (34) 512 (-32) 468 (-13) 260 270 750 540C 677 (115) 306 (-13) 1033 (228) 337 (-4) 511 (81) 257 (-21) 237 (-5) 152 (-49) 662 (110) 716 (105) 474 (50) 452 (29) 250 300 315 350

PanelS mx S my S

IIminx S

IIminy

Low Probability High Probability

Crack Spacing (mm) (%Error)MC90 EC2 Rizk&Marzouk Proposed Model

Experiment

S maxx S maxy S maxx S maxy

CRACK SPACING

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600

Cra

ck W

idth

(m

m)

Each Side Jack (kN)

AC

FG

Ab

BbMC90

EC2Proposed

Panel A

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400

Cra

ck W

idth

(m

m)

Each Side Jack (kN)

A

C

D

F

G

Ab

MC90

EC2

Proposed

Panel B

0.000.050.100.150.200.250.300.350.400.450.500.55

0 100 200 300 400

Cra

ck W

idth

(m

m)

Each Side Jack (kN)

ADEFGAbMC90EC2Proposed

Panel C

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 20 40 60 80 100 120 140

Cra

ck W

idth

(m

m)

Center Jack (kN)

E

H

MC90

EC2

Gergely-Lutz

Frosch

ACI 350-06

Nawy

Proposed

Panel A

0.00

0.10

0.20

0.30

0.40

0.50

0 20 40 60 80 100

Cra

ck W

idth

(m

m)

Center Jack (kN)

B

E

MC90

EC2

Gergely-Lutz

Frosch

ACI 350-06

Nawy

Proposed

Panel B

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 20 40 60 80 100 120

Cra

ck W

idth

(m

m)

Center Jack ()

B

MC90

EC2

Gergely-Lutz

Frosch

ACI350-06

Nawy

Proposed

Panel C

MAXIMUM CRACK WIDTH

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

s x=

s y(m

m)

sx,max(MPa)

Wmax,x=0.23mm

100

200

100

200

sy,crx(MPa)

Flexural Cracks

Direct Tension Cracks

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300

s x=

s y(m

m)

sx,max(MPa)

Flexural Cracks, Wmax,x=0.23mm

100

200

ACI350-06

sy,crx(MPa)

DESIGN GUIDE EXAMPLE

New crack prediction model in two‐way RC panels that incorporates: New FE parametric studies of:▪ Bond shear and normal stresses

▪ Average splitting tensile stresses

▪ New factor for effective tension area 

▪ Shrinkage induced tensile stresses

▪ Bond strength reduction due to splitting cracks

Better agreement with experimental results New accurate design guidelines to replace unconservative ACI design guideline

Financial support provided by

Natural Sciences and Engineering Research Council of Canada (NSERC) 

Ryerson University

Candu Energy Inc.

THANK YOU