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 Average Bond Stress, b 1 PB 1 DB Plain Bar - Pull-Out Failure Transverse Cracking Partial Splitting Through Splitting Deformed Bar Confinement Pull-Out Failure Splitting Failure Residual Strength (Friction) Bar Slip, (or ) t s 0.5 f’ c Stage II Stage I Stage IVa Stage IVc Stage III Stage IVb MECHANICS OF BOND Splitting Cracks Due to Circumferential Tension r l c p* p* Splitting Crack F F F + Modes of Bond Failure Splitting 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 Failure Occurs 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 Failure At 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.
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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
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
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.