University of Stuttgart Institute of Construction Materials (IWB) 1/34 Discrete Bond Element for 3D Finite Element Analysis of RC Structures Steffen Lettow

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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 –

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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

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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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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

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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

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ASSUMPTIONS & IMPLEMENTATION

Simulation of the transmission of forces between reinforcement and concrete finite elements:

longitudinal direction non-linear springslateral direction infinitely stiff connection

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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:

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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)

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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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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.

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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.

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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.

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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.

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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.

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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)

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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

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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.


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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

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BOND BEHAVIOR AT INELASTIC STEEL STRAINS


FE model of a pull-out test specimen with long embedment length.(experimental investigationsby Shima et al. (1987))



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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


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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


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INFLUENCE OF CYCLIC LOADING HISTORY


FE model of a pull-out test specimenwith short embedment length under cyclic loading history.(experimental investigationsby Simons (2003))



3D solid elements(steel plate)

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-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.


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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))



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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.


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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.


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CRACK PATTERN & STRAIN DISTRIBUTION

principle tensile strains in 1D bar elements (reinforcement)

principle tensile strains in 3D solid elements (concrete)

test specimen


Localisation of steel strains at the cracks and reduction of the steel strains between two cracks (contribution of concrete) is clearly visible.

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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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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


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)

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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


X

Y

Z

0.01

0.00889

0.00778

0.00667

0.00556

0.00444

0.00333

0.00222

0.00111

0.

V1L1C1



at peak load

STRAIN DISTRIBUTION IN SPLICE REGION



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.

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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:

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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:

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... 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

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… 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

Documents

University of Stuttgart Institute of Construction Materials (IWB) 1/34 Discrete Bond Element for 3D Finite Element Analysis of RC Structures Steffen Lettow