TOPIC 8 - BOND• Mechanics of Bond• Factors Influencing Bond• Tests to Investigate Bond• Code Provisions for Bond• Anchorage at Precast Girder Ends• Analytical Models for Bond • Modeling Bond in ATENA and DIANA• Modeling for Bond for Cyclic Applications

References for Figures● fib Bulletin No. 10, Bond of reinforcement in concrete, State-of-art report, Pages: 434, 30 tables, 251 illustrations● Lowes, L.N., Moehle, J.P., and Govindjee, S., “Concrete-Steel Bond Model for Use in Finite Element Modeling of Reinforced Concrete Structures, ACI Structural Journal, V. 101, No. 4., July-August 2004

Stages of Bond Resistance

0

AverageBond Stress,

b

1PB

1DB

Plain Bar - Pull-Out Failure

Transverse CrackingPartial SplittingThrough Splitting

Deformed BarConfinement

Pull-Out Failure

Splitting Failure

Residual Strength(Friction)

Bar Slip, (or )t s

0.5 f’c

Stage II

Stage IStage IVa

Stage IVc

Stage III Stage IVb

MECHANICS OF BOND

Splitting Cracks Due to Circumferential Tension

r

l

c

p*

p*

SplittingCrack

F

F F +

Modes of Bond FailureSplitting Failure

A splitting failure occurs when the transverse splitting cracks can extend to a free surface and thereby eliminate the development of confinement.

Pull Out FailureOccurs in more heavily confined concrete. Force transfer mechanism can change from rib bearing to friction after shear resistance of concrete between adjacent ribs is exceeded.

Complex Modes of FailureAt failure, the conditions along the length of a bar can vary, and consist of pull-out with no visible concrete splitting, pull-out induced by partial or thorough splitting, and splitting induced by concrete spalling.

FACTORS INFLUENCING BONDReinforcement Type

– Size and spacing of ribs, plain bars, prestressingstrands

Quality and Stress State of Concrete– Compressive and tensile strength (hsc)– Position of reinforcement in casting

Active and Passive Confinement– Active confinement from support and continuity– Passive confinement from transverse reinforcement

and concrete tensile rings is only mobilized in conjunction with concrete dilation during cracking and thus is a function of bond stress

– Poisson’s effect in strandsOther Factors

– Size and number of bars, spacing of layers– Rusting, temperature extremes

Tests for Bond OF Deformed Bars with Short Embedment Length

RILEM/CEB/FIP (1970) Tassios (1982)

TESTS TO INVESTIGATE BOND• Many factors affect bond resistance• Numerous models developed to describe influence of

various factors• Tests designed to investigate influence of specific factors,

calibrate bond models, and investigate limits of applicability

Tests for Evaluating the Effects of Confinement

TeflonStrain Gauge

Confining RingPlan View

HydraulicJack

ClampingDevice

LVDT(Ring Opening)

Tests for Investigating Long Anchorage Zones

Long Beam Tests

T

P P2

Tension Pullout Tests on Prestressing

Strand

Code Provisions (ACI Code/Deformed Bars)

ACI Design Equations for Bond

(Development Length of Deformed Bars)

(ACI 318-02 Eq. 12-1)

SI Unit

where = reinforcement location factor,

= coating factor,

= reinforcement size factor,

= lightweight aggregate concrete factor,

c = spacing or cover dimension,

Ktr = transverse reinforcement index

b

b

trc

yd d

dKcf

fl

'20

18

snfA

K yttrtr 1500

CODE PROVISIONS FOR BOND Code Provisions (ACI Code/Deformed Bars)

ACI 318-56 (Allowable Stress Design)

or

Ferguson’s recommendation (1965): ub 0.04f ’c.

Therefore, Ld=30 db

for Grade 60 No.8 bar, 4000psi concrete, fs = 24ksi.

d

sb

db

sbb L

fdLdfAu

4area bondforcedesign

b

sbd u

fdL4

30 bar diameter rule of thumb

Code Provisions (ACI Code/Deformed Bars)

Orangun, Jirsa and Breen (1975, 1977)

SI Unit

- empirical relationship

- 2nd term: confining influence of cover and the negative effects of close bar spacing on bond

- 4th term: passive confinement influence

Simplifying this equation gives the following.

SI Unit

'

52.4115.425.01.0 c

b

yttr

d

bb f

sdfA

Ldu

bdC

'

02.0

c

ybd

f

fAL

Code Provisions (ACI Code/Deformed Bars)

ACI 318-95

The bond expressions have been reevaluated and restated in terms of bar diameter.

SI Unit

For standard Configuration, this equation reduces to

SI Unit

b

tr

c

ybd d

Kcf

fdL )(

20

18'

)(20

12'

c

ybd

f

fdL

Code Provisions (CEB Model Code/Def. Bars)

CEB Model Code (1990)

SI Unit

Term fbd represents the design bond stress of concrete,

given by

SI Unit

where n1 is a geometry factor taken as 2.25 for ribbed bars, n2 is an orientation factor for bond (1.0 in most cases), and n3 is a bar size factor set at 1.0 for 32 mm and smaller bars. The term f’td is the design tensile strength of concrete.

bd

ybd f

fdL

4

'321 tdbd ff

Code Provisions (Prestressing Strand)

ACI 318-02

where

fps = stress in prestressed reinforcement at nominal strength

fse = effective stress in prestressed reinforcement after all loss.

AASHTO Eq. (9-32)

-1st term: transfer length of strand

- 2nd term: flexural bond length of the strand

bsepsd dffL

32

bsesubsed dffdfL )(3/1 *

Code Provisions (Prestressing Strand)

bsesubsed dffdfL )(3/1 *

Code Provisions (Prestressing Strand)

Transfer Length

A transfer bond stress of 4000psi (2.76MPa) and Grade 250 strand applies to the actual perimeter of seven-wire strand, 4db/3. For equilibrium of a strand over the transfer length:

Solving this yields:

0)4/(725.0

34400.0 2

sebtb

x fdLdF

3bse

tdfL

Code Provisions (Prestressing Strand)

Flexural Bond Length:

Fig. Flexural bond length recommended by ACI Committee 323

bsesutd dffLL )( *

Application LRFD ACI 318-95 Development length for deformed bars, deformed wire in tension

'21

c

ydd

f

fl

b

c

yd

btrd d

f

fdKc

l

'/)(

lap length of bars in tension dmlsp ll dmlsp ll

Development length for prestressing strand

bpepsb

ped dffd

fkl )(

34 or

10

))((4.64''5

c

bpeps

c

pbtd f

dfff

dfl

bsepsb

sed dffd

fl )(

34

Transfer length 60 db or b

pe df3

50 db or b

se df3

Application CEB-FIP MC90 Eurocode2 Local bond stress-slip model

)/( 1max ss

Basic anchorage length ctd

pd

p

pb f

fAl

321 or

efscalsbb AAll ,,1098762 /

22 dll tb

lap length of bars in tension

efscalsbo AAll ,,1110986 /

Transfer length pdpibt fll /141312 pptl 15

Longitudinal Tension Reinforcement: Demand – LRFD

0.5 0.5 cotu u ups ps s y p s

v

M N VA f A f V V

d

ANCHORAGE AT PRECAST GIRDER ENDS Longitudinal Tension Reinforcement:Demand – STM

θcotRfAfA yspsps

Longitudinal Tension Reinforcement: CapacityAt nominal resistance of member

Ef fective prestress

f ps

f pe

Steel Stress

60d b

l px

l d

End of member or

f ree end of strand

b

pxpepx d

lff

60

peps

bd

bpxpepx ff

dl

dlff

60

60

End of transfer length

-800

-400

0

400

800

1200

1600

0 12 24 36 48 60 72Distance From End (inch)

Stra

in (x

10-6

)

14.7 kips/ft18.2 kips/ft21.5 kips/ft23.7 kips/ft26.4 kips/ft27.9 kips/ft32.7 kips/ft

G8W

Bearingplate

Longitudinal Tension Reinforcement: Capacity

ANALYTICAL MODELS FOR BONDIneffectiveRegion

x

s0

s

R Z

s c,

s0

c

s

c0 xR Z

l

F

xR = Z

c

s

xR = Z

l

F

s0

s

s c,

s0

c0

Model for Bondincluded in CEB 1990 Model Code

BondStress

Slip

1

3

S1 S2 S3

Unconfined Concrete*

Confined Concrete**

Good Bond

Conditions

Other Bond

Conditions

Good Bond

Conditions

Other Bond

Conditions

s1 0.6 mm 0.6 mm 1.0 mm 1.0 mms2 0.6 mm 0.6 mm 3.0 mm 3.0 mms3 1.0 mm 2.5 mm clear rib

spacingclear rib spacing

T3

T1 0.15 T3 0.15 T3 0.4 T3 0.4 T3* Failure by splitting, ** Failure by shearing at ribs

ckf25.1ckf0.2 ckf0.1 ckf5.2

Shortcomings of models• Assumption of zero slip• Neglects effects of confinement, cover• Most models assume linear elastic behavior• Most models for monotonic loading Concrete

Reinforcement

Concrete

Reinforcement

Concrete

Reinforcement

Bond behavior models in ATENA Defines the bond strength depending on the value of

current slip between reinforcement and surrounding concrete

ATENA contains three models• CEB-FIP model code 1990, Bigaj model, User defined law

MODELING BOND in ATENA and DIANAReinforcement bars with prescribed slip

Stress in steel Equilibrium condition In equilibrium, the change of stress in rebar is fully transferred

to cohesive stress.

Discretized form If the equilibrium is not satisfied, the slip will occur to reduce

the stress in steel.

1 1i i i ii

i

u uE

l

where :perimeter, :cross-section of barcp p A

x A

11 2

i ii i c

l lA p

How to use in the program (I) How to use in the program (II) Define the behavior model in material

How to use in the program (III) Assign behavior model to discrete rebar Select rebar assign properties of the bar

Bond behavior models in DIANA DIANA contains three models Cubic, Power Law, and Multi-linear

Shear relations for positive and negative values of slip are equal.

The material option is combined with the line interface element.

Figures from DIANA material manual

Line interface element with bond option Bond-slip option is used in the line interface 2-D, L8IF.

Interface element between two lines in a two-dimensional configuration.

The bond-slip is a function of relative displacement.

Finite element implementation The relationship between the normal traction and normal

relative displacement is modeled as linear elastic.

The relationship between the shear traction and the slip is modeled as a nonlinear function.

Tangential stiffness coefficients for relative displacements

t tt f dt

00n

t t

kf d

n n nt k u

ABSTRACTReinforced concrete requires bond between plain concrete and reinforcing steel. Accurate numerical modeling of structures that exhibit severe bond-stress demand requires explicit representation of bond-zone response. A bond element is presented for use in high-resolution finite element modeling of reinforced concrete structures subjected to general loading. The model is defined by a normalized bond stress versus slip relationship and a relationship between maximum bond strength and the concrete and steel stress-strain state. A finite element implementation of the model is proposed that enables a one- or two-dimensional representation of bond-zone action. Nonlocal modeling is used to incorporate the dependence of bond strength on the concrete and steel material state. Comparisons of simulated and observed response for systems with uniform and variable bond-zone conditions are presented.