University of StuttgartInstitute of Construction Materials (IWB) 1/21

Treatment ofTreatment of

Headed RebarsHeaded Rebars

fib Task Group 4.5 „Bond Models“– 8th Meeting, November 4, 2005, Stuttgart, Germany –

University of StuttgartInstitute of Construction Materials (IWB) 2/21

0.75 0.5 0.75, ,18,5u cb H w NbN c A

1.0 0.5 0.5, 15u cb H wN c A

CC - method

New equation

Influence of edge distance is taken into account more accurately Influence of the slope of the head is taken into accountEquation is based on tests and theoretical considerations

,

0 0.75 0.5 0.75,18,5

u cb H w NbN c A

Calculation of the average blow out failure load of single anchors at the edge:

Improvement of the CC – method for single bolts at the edge

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 3/21

Influence of a ribbed bar

Basic concept:

Nu,cb

Nu,v

Nu,m = Nu,cb + Nu,v

?

, , ,u m u v u cbN N N

,u cbN

, ,u v s b b mN d l f ?according to the modified CC - method

Average resistance of ribbed headed bars:

University of StuttgartInstitute of Construction Materials (IWB) 4/21

Behaviour of the head (Furche):

sk

2( ) ( )600A a uk

kw

k ks

d

a

2

( )4 2s s

A sd dk m a d a a

ka = (5/a)0,5

Hea

d di

spla

cem

ent s

kSteel stress steel

0,25 mm

0,20 mm

0,15 mm

435 N/mm²

Head displacement versus steel stress

dH = 3ds

s1h

s1s

steel

25 / ²w N mm

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 5/21

Bond slip curves 3 2 1 5 4 6

1 [N/mm²]2 [N/mm²] = head

lb

Behaviour of bond (Hofmann):

23

45

6

1

Slip

bond

Bon

d sl

ip c

urve

s

6Bond slip curves

3 2 1 5 4 6

1 [N/mm²]2 [N/mm²] = head

lb

6

Nu,cb

Nu,m

sk,cb

(According to Furche)

0.5max (0.36 1.28) ( )w

s

cd

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 6/21

0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200Pressure under the head [N/mm²]

dk/ds = 1.5dk/ds = 2.0dk/ds = 2.5dk/ds = 3.0

8 mm < ds < 32 mm5 ds < lb < 20 ds

H [N/mm²]sk,cbs1

. /b m u s bf N d l Nu,cb

H [N/mm²]

Nu,cb+ Nu,v

5 w

fb,m = 1.5 N/mm²

fb,m = 3.0 N/mm² for uk < 5 w

for uk > 5 w

.min b mf

Min

. fb,

m [N

/mm

²]

25 / ²w N mm

Calculations for:8 mm < ds < 32 mm1.5 < ds / dk < 3 5 ds < lb < 20 ds

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 7/21

Mean bond strength of straight bars:

Behaviour of bond:

. ( 2) 5.4 / ²b mf EC N mm ( 25 / ²)ckf N mm

Mean bond strength of headed bars:

.5 3 / ²uk w b mp f N mm

.5 1.5 / ²uk w b mp f N mm

w . . , 2 , 25 0.5 ( 1.0 )uk b m b m EC bd ECp f f f

w . . , 2 , 25 0.25 ( 0.5 )uk b m b m EC bd ECp f f f

( 25 / ²)cmf N mm

. ( 2) 4.0 / ²b mf EC N mm ( 25 / ²)cmf N mm

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 8/21

, ,, ,

0

, ,

0, , su cb u cb Nb v mg Nb ec Nbc Nb c NbN N NA A

Improvement of the CC – method: Calculation of the average resistance in non - cracked concrete in case of blow out failure

,

,

, ( / 40) 1,

11, 0

1 2 /(2

0

)ec Nb

N cr Nb

a Nb

e c

1,

,

0, 7 0, 3 1, 0s Nb

cr Nb

c

c

, , 12 4cr Nb cr Nbs c c

,,

0 0.75 0.70.5 518,5 a Nbu cb H wAN c

1,

,

(1 ) 1, 0g Nb

cr Nb

sn n

s

, ,s bv m bm NbN d l f

, uk

, uk

= 1.5N/mm² if 5

= 3.0N/mm² if 5bm Nb w

bm Nb w

f

f

(1)

(2)

(3)

(4)

(5)

(6)

(6)

(7)

(8) 5 20s b sd l d

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 9/21

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 2000 4000 6000 8000 10000 12000

AH(net bearing Area) [mm²]

Nu,

test

/Nu,

calc

, Hof

/Eli [

-]

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 2000 4000 6000 8000 10000 12000

AH(net bearing Area) [mm²]

Nu,

test

/Nu,

calc

, Hof

/Eli [

-]Nb,

5,0cc

5,0H

75,00cb fAc5,18N

Nb,5,0

cc5,0

H75,00

cb fAc15N

University of StuttgartInstitute of Construction Materials (IWB) 10/21

Investigations by Hofmann

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 50 100 150 200 250

c1 [mm]

Nu,

test

/Nu,

calc

, Hof

/Eli [

-]

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 50 100 150 200 250

c1 [mm]

Nu,

test

/Nu,

calc

, Hof

/Eli [

-]Nb,

5,0cc

5,0H

75,00cb fAc5,18N

Nb,5,0

cc5,0

H75,00

cb fAc15N

University of StuttgartInstitute of Construction Materials (IWB) 11/21

Introduction:Reduction of the development length with headed bars

Local failure

Tensile force

Failure mechanism

forces are transmitted into the concrete by bond and mechanical interlock

Behaviour of mechanical interlock

Behaviour of bond

??

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 12/21

Investigations by Hofmann

Factor considering confining reinforcement:

(2) (3)(1)

As

Baschandy DeVries Varga Wright / McCabe FEM0,8

1,0

1,2

1,4

1,6

1,8

2,0 Mimimum Maximum Mittelwert

Höc

hstla

st m

it R

ückh

änge

bew

ehru

ng

Höc

hstla

st o

hne

Rüc

khän

gebe

weh

rung

1.25

(1) (1)(3) (3)(2)

MinimumMaximumArverage

No effect

No effect

Small effect

10 cm

Num

eric

al s

imul

atio

n w

ith c

onfin

ing

rein

forc

emen

t

As

As

University of StuttgartInstitute of Construction Materials (IWB) 13/21

1.5,

,,

( ) 8 ks req cdb net b

s prov s bd

dA fl l

A d f

Simplification 1 min( 0.5) ( / 2)stag kc c d

Without special reinforcement

With special reinforcement

1.5,

,,

( ) 11s req cdkb net b

s prov s bd

A fdl lA d f

0.75 0.75, 1

,,

( ) 3.0s req stag re h cdb net b

s prov s bd

A c A fl l

A d f

Necessary development length for headed reinforcing bars

0.30

0.610.45stag n

1.25re with

n: number of staggered t- headed bars

2.5 4k

s

dd

Investigations by Hofmann

University of StuttgartInstitute of Construction Materials (IWB) 14/21

Investigations by Appl (Splices with Headed Rebars)

260

180

c= 20mm

50 40

90

90

5040

500

60

180

90

Side view

60 60 60

Front view260

180

c= 20mm

50 40

90

90

5040

500

60

180

90

Side view

60 60 60

Front view

University of StuttgartInstitute of Construction Materials (IWB) 15/21

Investigations by Appl (Splices with Headed Rebars)

University of StuttgartInstitute of Construction Materials (IWB) 16/21

S328,8206,6327ds-2025dsR2

S339,0213,4627ds-2025dsR1B_500

LB586,9368,8727ds602015dsH2

LB604,4379,8727ds602015dsH1K_300

LB611,1384,027ds602025dsH2

LB590,9371,327ds602025dsH1K_500

Failure3)su,m2)

[N/mm²]Fmax

[kN]fcc

[N/mm²]cx

[mm]dk

[mm]ds

[mm]ls

[mm]1)No.Test

S328,8206,6327ds-2025dsR2

S339,0213,4627ds-2025dsR1B_500

LB586,9368,8727ds602015dsH2

LB604,4379,8727ds602015dsH1K_300

LB611,1384,027ds602025dsH2

LB590,9371,327ds602025dsH1K_500

Failure3)su,m2)

[N/mm²]Fmax

[kN]fcc

[N/mm²]cx

[mm]dk

[mm]ds

[mm]ls

[mm]1)No.Test

1) K= Headed rebar; R= Rebar with straight end2) smsu A2Fσ /max,

3) LB= Blow out in front of the Head; S= Splitting failure

Investigations by Appl (Splices with Headed Rebars)

University of StuttgartInstitute of Construction Materials (IWB) 17/21

0

100

200

300

400

500

600

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Crack Opening [mm]

Stee

l Str

ess

[N/m

m²]

B_500_C1/C2K_500_C1/C2K_300_C1/C2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

0

100

200

300

400

500

600

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Crack Opening [mm]St

eel S

tres

s [N

/mm

²]

B_500_C3/C4K_500_C3/C4K_300_C3/C4

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

0

100

200

300

400

500

600

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Crack Opening [mm]

Stee

l Str

ess

[N/m

m²]

B_500_C1/C2K_500_C1/C2K_300_C1/C2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

0

100

200

300

400

500

600

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Crack Opening [mm]St

eel S

tres

s [N

/mm

²]

B_500_C3/C4K_500_C3/C4K_300_C3/C4

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

(a) Average splitting crack openings (C1/C2) (b) Average splitting crack openings (C3/C4)

Investigations by Appl (Splices with Headed Rebars)

University of StuttgartInstitute of Construction Materials (IWB) 18/21

0

100

200

300

400

500

600

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Displacement (Loaded End) [mm]

Stee

l Str

ess

[N/m

m²]

B_500_B1/B2K_500_B1/B2K_300_B1/B2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

0

100

200

300

400

500

600

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Displacement (Loaded End) [mm]

Stee

l Str

ess

[N/m

m²]

B_500_B3/B4K_500_B3/B4K_300_B3/B4

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

Crack 1

Crack 3

Crack 2

Crack 4

B1 B2

B3 B4

U3 U4

U1 U2

(a) Average load displacement curve (B1/B2) (b) Average load displacement curve (B3/B4)

Investigations by Appl (Splices with Headed Rebars)

University of StuttgartInstitute of Construction Materials (IWB) 19/21

Investigations by Schmid

Unconfined Confined

SP4

SP2

DMS

DMS

DMS

DMS

DMS

DMS

SP3

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

Transportanker

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

SP4

SP2

DMS

DMS

DMS

DMS

DMS

DMS

SP3

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

Transportanker

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

SP4

SP2

DMS

DMS

DMS

DMS

DMS

DMS

SP3

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

DMS

Transportanker

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

DMS DMS DMS

Pos 1: Bügel d = 8 mm, l = 0,90 m

Pos 2

Pos 1 DM

S

DM

S

DMS

DMS

DMS

DMS

DMS

DMS

Pos 1: Bügel d = 8 mm, l = 0,750 m

Pos 2

Pos 1

Pos 1

DM

S

DM

S

DMS

DMSDMS

DMS

DMS

DMS

DMSDMS DMS

Pos 1

Transportanker

SP2B SP3B

SP4B

DMSDMS DMS

DMSDMS DMS

DMSDMS DMS

DMSDMS DMS

Pos 1: Bügel d = 8 mm, l = 0,90 m

SP4B

Pos 2

SP2B

Pos 1 DM

S

DM

S

DMS

DMS

DMS

DMS

DMS

DMS

Pos 1: Bügel d = 8 mm, l = 0,750 m

Pos 2

SP3B

Pos 1

Pos 1

DM

S

DM

S

DMS

DMSDMS

DMS

DMS

DMS

DMSDMS DMS

Pos 1

DMSDMS DMS

DMSDMS DMS

DMSDMS DMS

DMSDMS DMS

Pos 1: Bügel d = 8 mm, l = 0,90 m

SP4B

Pos 2

SP2B

Pos 1 DM

S

DM

S

DMS

DMS

DMS

DMS

DMS

DMS

Pos 1: Bügel d = 8 mm, l = 0,750 m

Pos 2

SP3B

Pos 1

Pos 1

DM

S

DM

S

DMS

DMSDMS

DMS

DMS

DMS

DMSDMS DMS

Pos 1

TransportankerDMSDMS DMS

DMSDMS DMS

DMSDMS DMS

DMSDMS DMSD

MS

DM

S

University of StuttgartInstitute of Construction Materials (IWB) 20/21

Investigations by Schmid

University of StuttgartInstitute of Construction Materials (IWB) 21/21

Investigations by Schmid

Test Nu,calc,18,5 Nu,calc, 15 Nu,test average value Nu,test/Nucalc,18,5 Nu,test/Nu,calc,15unconfined

SP2 151,5 122,7 100,9 115,9 0,8 0,9130,9

SP3 168,4 136,4 138,9 144,9 0,9 1,1150,9

SP4 329,1 266,6 153,3 168,4 0,5 0,6183,5

confinedSP2B 189,38 153,4 169,6 165,8 0,9 1,1

161,9SP3B 210,5 170,5 147,8 154,8 0,7 0,9

161,8SP4B 411,38 333,2 245,4 236,5 0,6 0,7

227,6

More research necessary