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1/34
University of StuttgartInstitute of Construction Materials (IWB)
Discrete Bond Element for3D Finite Element Analysis
of RC Structures
Steffen LettowInstitute of Construction Materials,
University of Stuttgart, Germany
fib Task Group 4.5 „Bond Models“– 6th Meeting, October 15 - 16, 2004, Edinburgh, UK –
2/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND BEHAVIOUR▫ Requirements & interaction
DISCRETE BOND ELEMENT
▫ Assumptions & implementation
▫ Bond element model (-s relation)
▫ Influencing variables (c, s, cyc)
NUMERICAL EXAMPLES
▫ Pull-out & splitting behaviour
▫ Influence of steel strain and cyclic loading
▫ Tension stiffening effect
▫ Behaviour of lapped splices
▫ Additional applications
OUTLINE
3/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND REQUIREMENTS
Bond requirements for various situations:
(1) SERVICEABILITY LIMIT STATE:
high bond stiffness small crack widths & small deflections
(2) ULTIMATE LIMIT STATE:
low bond stiffness large rotation capacity & low contribution of concrete
high bond stiffness short anchorage lengths
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University of StuttgartInstitute of Construction Materials (IWB)
BOND INTERACTION
Bond behavior is mainly influenced by:
(1) MATERIAL:- rib geometry and diameter of the reinforcement- characteristics of the concrete
(2) GEOMETRY:- concrete cover and bar spacing - confining reinforcement
(3) VARIABLE EFFECTS:- strain state in the reinforcement bar- stress state of the concrete around the bar- loading history
5/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND BEHAVIOUR
Idealisation of the transmission of forces in the bond zone and failure types:
shearing of the concrete lugs pull-out failureexceeding concrete tensile strength splitting failure
6/34
University of StuttgartInstitute of Construction Materials (IWB)
ASSUMPTIONS & IMPLEMENTATION
Simulation of the transmission of forces between reinforcement and concrete finite elements:
longitudinal direction non-linear springslateral direction infinitely stiff connection
7/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND ELEMENT MODEL
1
R
0 R0
0
s 1s b (1 b)
s s1
s
Use of modified MP equation allows for modelling of various materials.
Menegotto-Pinto (MP) formulation:
8/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND ELEMENT MODEL PARAMETERS
Influencing factors for bond model:
(1) INPUT BOND MODEL PARAMETERS:- rib geometry (shape of basic curve)- bond conditions (bond strength/stiffness)
(2) VARIABLE BOND MODEL PARAMETERS:- strain in the reinforcement (decrease of bond stress
with increasing strain)- stress in surrounding concrete (increase of bond stress
with increasing compressive stress)- cyclic loading history (decrease of bond stress with
increasing load cycles)
(3) INTERACTION WITH FE MODEL:- bar spacing & confining reinforcement- concrete cover, concrete tensile strength
(splitting failure - loss of bond)
9/34
University of StuttgartInstitute of Construction Materials (IWB)
TOTAL BOND RESISTANCE
s c cyc
TOTAL BOND RESISTANCE:
s
c
cyc
Influence of the steel strain
Influence of the confinement
Influence of the cyclic loading history
INFLUENCING PARAMETER:
Influence of reinforcement strain
Influence of concrete confinement
Influence of cyclic loading history
max s
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University of StuttgartInstitute of Construction Materials (IWB)
INFLUENCE OF REINFORCEMENT STRAIN
b5 as s1 1 e
s sy
su sy
2
t
y
a ;
fb 2
f
s
s
without influence of reinforcement strain
with influence of reinforcement strain
Influence of s
s≈ 10 %
s ≤ sy
Reduction of bond stress with increasing strain in thereinforcing bar.
11/34
University of StuttgartInstitute of Construction Materials (IWB)
INFLUENCE OF CONCRETE CONFINEMENT
cc c
c
1 tanh0.1 f
c
s
without influence of concrete confinement
with influence of concrete confinement
Influence of c
c ≤ 0 N/mm2
c≈ 15 N/mm2
Increase of bond stress for higher transverse pressure in the confining concrete.
12/34
University of StuttgartInstitute of Construction Materials (IWB)
INFLUENCE OF CYCLIC LOADING
1.10( 1.2 / )
cyc e
-20 -10 0 10 20
slip [m m ]
-30
-20
-10
0
10
20
30
aver
age
bond
str
ess
[MP
a]
In fluence of cycw ithout in fluence of cyclic loadw ith in fluence of cyclic load
1
2
3
4
5
6
(Eligehausen et al. (1983))
Deacrese of bond stress with increasing load cycles.
13/34
University of StuttgartInstitute of Construction Materials (IWB)
PULLOUT BEHAVIOUR
FE model of a pull-out test specimen (RILEM) with a short embedement length.
X
Y
Z
X
- 9 0 .- 7 5 .
- 6 0 .- 4 5 .
- 3 0 .- 1 5 .
0 .1 5 .
3 0 .4 5 .
6 0 .7 5 .
9 0 .
Y
- 9 0 .- 7 5 . - 6 0 .- 4 5 .- 3 0 .
- 1 5 . 0 . 1 5 . 3 0 . 4 5 .6 0 . 7 5 . 9 0 .
V 1G 3
Reinforcing bar with large
concrete cover
Realistic results by use of bond elements especially in descending branch (for large deformation).
Dimensions: 200 x 200 x 200 mmEmbedment length: lE = 5∙ds
Material properties of steel & concrete same for both calculations.
14/34
University of StuttgartInstitute of Construction Materials (IWB)
pre-peak load peak load
direction of pull-out
STEEL AND BOND STRESS DISTRIBUTION
WITHOUTBOND ELEMENT:No uniform decrease in steel stress & no constant bond stress distribution.
WITHBOND ELEMENT:Uniform decrease in steel stress & constant bond stress distribution.
15/34
University of StuttgartInstitute of Construction Materials (IWB)
SPLITTING BEHAVIOUR
Dimensions:Ø 60 x 60 mmEmbedment length:lE = 5∙ds = 60 mm
FE model of a pull-out test specimen encased by a steel ring (ringtest)with a short embedement length.(experimental investigationsby Lettow et al. (2001))
1D bar elements (reinforcement) with discrete bond elements
3D solid elements(concrete)
3D solid elements(steel ring)
16/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND STRESS-SLIP DIAGRAM
0
2
4
6
8
10
12
0 2 4 6 8slip s [mm]
bond
str
ess
[N
/mm
2]
experiment
calculation
By use of adequate parameters in the basic bond model the calculated results agree very well with the measured curve.
Comparison of experimental & numerical data
17/34
University of StuttgartInstitute of Construction Materials (IWB)
HOOP STRAINS AS FUNCTION OF SLIP
0,0
0,2
0,4
0,6
0,8
1,0
0 2 4 6 8
slip s [mm]
tens
ile h
oop
stra
ins
[‰
]
experiment pos. 1
calculation pos. 1
experiment pos. 2
calculation pos. 2
Good agreement between measured & calculated hoop strains in the steel ring, which represent the splitting behaviour.
Comparison of experimental & numerical data
18/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND STRESS-SLIP DIAGRAM & CRACK PATTERN
In the calculation with steel ring, failure takes place by pull-out. In the calculation without steel ring, splitting failure occurs due to lack of confinement.
Formation of cracks in the concrete cover due to removal of the steel ring.
0
2
4
6
8
10
12
0 2 4 6 8slip s [mm]
bond
str
ess
[N
/mm
2]
pull out failure
splitting failure
principle tensile strains (11) in the concrete elements
19/34
University of StuttgartInstitute of Construction Materials (IWB)
BOND BEHAVIOR AT INELASTIC STEEL STRAINS
Dimensions:Ø 500 x 1000 mmEmbedment length:lE = 40∙ds = 800 mm
FE model of a pull-out test specimen with long embedment length.(experimental investigationsby Shima et al. (1987))
1D bar elements (reinforcement) with discrete bond elements
3D solid elements(concrete)
20/34
University of StuttgartInstitute of Construction Materials (IWB)
STEEL STRAIN DISTRIBUTION ALONG EMBEDMENT LENGTH
With increase of the distance from the loaded end the inelastic steel strain decreases.
0,00
0,01
0,02
0,03
0,04
0 100 200 300 400
Distance from loaded end [mm]
Stee
l stra
in [
-]
SD30 - experiment
SD30 - calculation
ds = 19.5 mm
0
200
400
600
800
1000
0 40 80 120 160
Steel strain [‰]
Stee
l stre
ss
[N
/mm
2 ] SD30:ft/fy = 1.54, su = 0.14, ds = 19,5 mm
Comparison of experimental & numerical data
21/34
University of StuttgartInstitute of Construction Materials (IWB)
0,00
0,01
0,02
0,03
0,04
0 100 200 300 400
Distance from loaded end [mm]
Stee
l stra
in [
-]
SD70 - experiment
SD70 - calculation
ds = 19.5 mm
STEEL STRAIN DISTRIBUTION OVER EMBEDMENT LENGTH
The strain gradient is significantly influenced by the shape of the steel stress-strain diagram (ft/fy; εsu).
0
200
400
600
800
1000
0 40 80 120 160
Steel strain [‰]
Stee
l stre
ss
[N
/mm
2 ] SD70:ft/fy = 1.11, su = 0.07, ds = 19,5 mm
Comparison of experimental & numerical data
22/34
University of StuttgartInstitute of Construction Materials (IWB)
INFLUENCE OF CYCLIC LOADING HISTORY
Dimensions:Ø 520 x 200 mmEmbedment length:lE = 5∙ds = 100 mm
FE model of a pull-out test specimenwith short embedment length under cyclic loading history.(experimental investigationsby Simons (2003))
1D bar elements (reinforcement) with discrete bond elements
3D solid elements(concrete)
3D solid elements(steel plate)
23/34
University of StuttgartInstitute of Construction Materials (IWB)
-15
-10
-5
0
5
10
15
20
-2 -1 0 1 2 3slip s [mm]
bo
nd
str
ess
[N/m
m2]
experiment
calculation
BOND STRESS-SLIP RELATION
Good agreement between measured & calculated bond stress-slip curves.
Comparison of experimental & numerical data
24/34
University of StuttgartInstitute of Construction Materials (IWB)
TENSION STIFFENING EFFECT
Dimensions:400 x 400 x 2000 mm
FE model of a tension test specimen for determination of contribution of concrete between cracks.(experimental investigationsby Mayer/Lettow et al. (2003))
1D bar elements (reinforcement) with discrete bond elements
3D solid elements(concrete)
25/34
University of StuttgartInstitute of Construction Materials (IWB)
STEEL STRESS-STRAIN DIAGRAM
0
100
200
300
400
500
600
700
0 20 40 60 80 100Strain sr, sm [‰]
Stee
l stre
ss
s [N
/mm
2]
experiment
calculation
plain steel
Measured & calculated steel stress-strain curves show a smaller deformation capacity compared to the plain steel.
Comparison of experimental & numerical data
26/34
University of StuttgartInstitute of Construction Materials (IWB)
0,0
0,2
0,4
0,6
0,8
1,0
0,00 0,02 0,04 0,06 0,08 0,10Steel strain at the crack sr [-]
Ratio
sm
/sr
[-]
experiment
calculation
BOND COEFFICIENT (εsm/εsr) DIAGRAM
Good agreement between experimental & numerical results over the entire steel strain range.
Comparison of experimental & numerical data
27/34
University of StuttgartInstitute of Construction Materials (IWB)
CRACK PATTERN & STRAIN DISTRIBUTION
principle tensile strains in 1D bar elements (reinforcement)
principle tensile strains in 3D solid elements (concrete)
test specimen
Comparison of experimental & numerical data
Localisation of steel strains at the cracks and reduction of the steel strains between two cracks (contribution of concrete) is clearly visible.
28/34
University of StuttgartInstitute of Construction Materials (IWB)
LAPPED SPLICE BEHAVIOUR
Numerical modell, primary structure and moment diagram(dead load ignored)
X
Y
Z
0.01
0.00889
0.00778
0.00667
0.00556
0.00444
0.00333
0.00222
0.00111
0.
V1L1C1
Output Set: MASA3 Stoss_ds08_b011Contour: Avrg.E11 stra.
FE model of a slab with overlapping reinforcement (welded mesh).(experimental investigations by Bigaj/Lettow (2000))
Dimensions:700 x 200x 4300 mm
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University of StuttgartInstitute of Construction Materials (IWB)
By varying the bond input parameters different failure types can be simulated.
FE analysis using• no bond elements• low bond strength• high bond strength
LOAD DEFLECTION DIAGRAM
Comparison of experimental & numerical data
deflection [mm]
load
[kN
]
test no. 1 (steel failure)
test no. 2 (concrete failure)
calc. no. 1 (steel failure)
calc. no. 2 (concrete failure)
calc. no. 3 (cocnrete failure)
30/34
University of StuttgartInstitute of Construction Materials (IWB)
X
Y
Z
0 . 0 1
0 . 0 0 8 8 9
0 . 0 0 7 7 8
0 . 0 0 6 6 7
0 . 0 0 5 5 6
0 . 0 0 4 4 4
0 . 0 0 3 3 3
0 . 0 0 2 2 2
0 . 0 0 1 1 1
0 .
V 1L 1C 1
O u t p u t S e t : M A S A 3 S t o s s _ d s 0 8 8 1 4 5C o n t o u r : A v r g . E 1 1 s t r a .
X
Y
Z
0.01
0.00889
0.00778
0.00667
0.00556
0.00444
0.00333
0.00222
0.00111
0.
V1L1C1
Output Set: MASA3 Stoss_ds088139Contour: Avrg.E11 stra.
X
Y
Z
0.01
0.00889
0.00778
0.00667
0.00556
0.00444
0.00333
0.00222
0.00111
0.
V1L1C1
Output Set: MASA3 Stoss_ds08_b181Contour: Avrg.E11 stra.
X
Y
Z
0.01
0.00889
0.00778
0.00667
0.00556
0.00444
0.00333
0.00222
0.00111
0.
V1L1C1
Output Set: MASA3 Stoss_ds08_b136Contour: Avrg.E11 stra.
principle tensile strains (11) in the concrete elements
at peak load
STRAIN DISTRIBUTION IN SPLICE REGION
principle tensile strains (11) in the concrete elements
principle tensile strains (11) in the concrete elements
WITHOUTBOND ELEMENTS:Brittle failure – spalling of top concrete cover.
WITH BOND ELEMENTS (low bond strength):Ductile failure – rupture of reinforcing steel.
WITH BOND ELEMENTS (high bond strength):Brittle failure – spalling of top concrete cover.
31/34
University of StuttgartInstitute of Construction Materials (IWB)
ADDITIONAL APPLICATIONS
... studying the influence of bond on the structuralperformance of thin textile reinforced and prestressedconcrete plates. (by Krüger (2004) at Stuttgart)
... modelling the effects of corrosion on bond betweenplain reinforcement bars and concrete.(by Cairns/Pregartner (2004) at Edinburgh)
... investigating the influence of bond on the behaviourof headed bars spliced with headed bars and headed
barsspliced with reinforcement bars.(by Appl (2004) at Stuttgart)
The new discrete bond element has also been used for:
32/34
University of StuttgartInstitute of Construction Materials (IWB)
SUMMARY
... has been implemented into a nonlinear 3D finiteelement code as a zero-thickness two-node finite
element.
... connects 1D truss/bar finite elements (reinforcement) with 3D solid/volume finite elements (concrete).
... is based on a bond stress-slip relationship which is controlled by basic model parameters.
... accounts for the influence of reinforcement strains, stress state of surrounding concrete and cyclic
loading history.
The discrete bond element:
33/34
University of StuttgartInstitute of Construction Materials (IWB)
... of pull-out tests with short and long embedment length, of tension and bending tests on RC members show a good agreement between experimental and numerical results.
... demonstrate that the discrete bond element is able todistinguish between pull-out and splitting failure
modes.
... indicate that the discrete bond element is able to predict transfer of bond stresses from the reinforcement into the concrete realistically under monotonic and cyclic loading.
The numerical investigations:
CONCLUSION
34/34
University of StuttgartInstitute of Construction Materials (IWB)
… is needed to verfiy the basic bond element modelparameters and the variable influencing factors.
… is needed to check the potential and the accuracyof the discrete bond element model.
… can be very helpful to understand & clarify bondbehaviour between reinforcement and concrete in
detail.
… can be supportive of developing a harmonisedeuropean bond test or improving appraisal factors for bond properties of ribbed reinforcing steel.(proposal for research has been submitted to
)
Further research work:
OUTLOOK