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fib Task Group 4.5 „Bond Models“
– 8th Meeting, November 4, 2005, Stuttgart, Germany –
Treatment of
Headed Rebars
University of Stuttgart
Institute of Construction Materials (IWB)
1/21
Investigations by Hofmann
Improvement of the CC – method for single bolts at the edge
CC - method
Nu ,cb  15  c1.0  AH0.5   w0.5
New equation
Nu ,cb  18,5  c0.75  AH0.5   w0.75  , Nb
Influence of edge distance is taken into account more accurately
Influence of the slope of the head is taken into account
Equation is based on tests and theoretical considerations
Calculation of the average blow out failure load of single anchors at the edge:
N u0,cb  18,5  c0.75  AH0.5   w0.75   , Nb
University of Stuttgart
Institute of Construction Materials (IWB)
2/21
Influence of a ribbed bar
Basic concept:
Nu,m = Nu,cb + Nu,v
Nu,v
?
Nu,cb
Nu ,v    d s  lb  fb ,m ?
N u ,cb
according to the modified CC - method
Average resistance of ribbed headed
bars:
N u ,m  Nu ,v  Nu ,cb
University of Stuttgart
Institute of Construction Materials (IWB)
3/21
Investigations by Hofmann
Behaviour of the head (Furche):
s1s
s1h
d
ka = (5/a)0,5
a
steel
sk
d s2
d
kA 
 m  a  (d s  a )  s  a
4
2
Head displacement sk
Head displacement versus steel stress
0,25 mm
0,20 mm
dH = 3ds
0,15 mm
 w  25 N / mm²
435 N/mm²
Steel stress steel
k A  ka  uk 2
sk  (
)(
)
600
w
University of Stuttgart
Institute of Construction Materials (IWB)
4/21
Investigations by Hofmann
Behaviour of bond (Hofmann):
2 [N/mm²] = head
1 [N/mm²]
2 [N/mm²] = head
Bond slip curves
Bond slip curves
6
6
5
4 3
2
1
lb
Bond slip curves
6
bond
1 [N/mm²]
6
6
Nu,m
 max  (0.36 
5
5
4 3
2
1
lb
c
 1.28)  (  w ) 0.5
ds
4
12
3
Nu,cb
sk,cb
(According to Furche)
Slip
University of Stuttgart
Institute of Construction Materials (IWB)
5/21
Investigations by Hofmann
Nu,cb
fb.m  Nu /   d s  lb
Nu,cb+ Nu,v
Calculations for:
H [N/mm²]
sk,cb
s1
8 mm < ds < 32 mm
1.5 < ds / dk < 3
5 ds < lb < 20 ds
10
8 mm < ds < 32 mm
5 ds < lb < 20 ds
Min.bond
fb,mvalue
[N/mm²]
Mean
[N/mm²]
9
8
dk/ds = 1.5
dk/ds = 2.0
dk/ds = 2.5
dk/ds = 3.0
min fb.m
7
6
5 w
5
4
3
fb,m = 3.0 N/mm²
for uk < 5 w
fb,m = 1.5 N/mm²
for uk > 5 w
2
1
 w  25 N / mm²
0
0
50
100
150
200
Pressure under the head [N/mm²]
H [N/mm²]
University of Stuttgart
Institute of Construction Materials (IWB)
6/21
Investigations by Hofmann
Behaviour of bond:
Mean bond strength of straight bars:
fb.m ( EC 2)  5.4 N / mm²
fb.m ( EC 2)  4.0 N / mm²
( fck  25N / mm²)
( f cm  25N / mm²)
Mean bond strength of headed bars:
puk  5 w  fb.m  3N / mm²
puk  5 w  fb.m  1.5N / mm²
( f cm  25N / mm²)
puk  5 w  fb.m  0.5  fb.m, EC 2 ( 1.0  fbd , EC 2 )
puk  5 w  fb.m  0.25  fb.m, EC 2 ( 0.5  fbd , EC 2 )
University of Stuttgart
Institute of Construction Materials (IWB)
7/21
Investigations by Hofmann
Improvement of the CC – method: Calculation of the average
resistance in non - cracked concrete in case of blow out failure
A0c, Nb  s , Nb  g , Nb  ec , Nb  Nv , m
Nu ,cb  Nu ,cb  Ac, Nb
0
(1)
N u0,cb  18,5  c0.75  AH0.5   w0.75  a , Nb
(2)
 a , Nb  ( / 40)  1, 0
1
(3)
 ec , Nb 
(4)
 s , Nb  0, 7  0, 3 
(5)
(6)
 g , Nb 
1  2  eN /(2  ccr , Nb )
n
s1
c1
 1, 0
 1, 0
ccr , Nb
(1 
(6)
(7)
N v ,m    d s  lb  fbm, Nb
fbm, Nb = 1.5N/mm² if uk  5 w
fbm, Nb = 3.0N/mm² if uk  5 w
(8)
5  ds  lb  20  ds 
n )  1, 0
scr , Nb
 scr , Nb  2  ccr , Nb  4  c1 
University of Stuttgart
Institute of Construction Materials (IWB)
8/21
2,0
N cb0  18 ,5  c 0 ,75  AH0 ,5  f cc0 ,5   ,Nb
1,8
Nu,test/Nu,calc, Hof/Eli [-]
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
2000
4000
6000
8000
10000
12000
AH(net bearing Area) [mm²]
2,0
N cb0  15  c 0 ,75  AH0 ,5  f cc0 ,5   ,Nb
1,8
Nu,test/Nu,calc, Hof/Eli [-]
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
2000
4000
University of Stuttgart
Institute of Construction Materials (IWB)
6000
8000
10000
12000
AH(net bearing Area) [mm²]
9/21
Investigations by Hofmann
2,0
N cb0  18 ,5  c 0 ,75  AH0 ,5  f cc0 ,5   ,Nb
1,8
Nu,test/Nu,calc, Hof/Eli [-]
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
50
100
150
200
250
c1 [mm]
2,0
1,8
N cb0  15  c 0 ,75  AH0 ,5  f cc0 ,5   ,Nb
Nu,test/Nu,calc, Hof/Eli [-]
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
50
100
150
200
250
c1 [mm]
University of Stuttgart
Institute of Construction Materials (IWB)
10/21
Investigations by Hofmann
Introduction:
Reduction of the development length with headed bars
forces are transmitted into the
concrete by bond and
mechanical interlock
Failure mechanism
Local failure
Tensile force
Behaviour of mechanical
interlock
Behaviour of bond
?
?
University of Stuttgart
Institute of Construction Materials (IWB)
11/21
Investigations by Hofmann
Factor considering confining reinforcement:
Mimimum
Minimum
Maximum
Maximum
Mittelwert
Arverage
1,8
Numerical simulation with confining
reinforcement
Höchstlast mit Rückhängebewehrung
Höchstlast ohne Rückhängebewehrung
2,0
1,6
1,4
1.25
1,2
1,0
0,8
Baschandy
(2)
DeVries
Varga
Wright / McCabe
FEM
(3)
(3)
(1)
(1)
Small effect
10 cm
No effect
As
As
(1)
No effect
As
(2)
(3)
University of Stuttgart
Institute of Construction Materials (IWB)
12/21
Investigations by Hofmann
Necessary development length for headed reinforcing bars
lb,net  (
with
A s ,req
A s , prov
 stag 
)  lb  3.0 
1  0.6

n0.30  0.45
 stag   re  c10.75  Ah  f cd0.75
d s  fbd
 re  1.25 2.5 
dk
4
ds
n: number of staggered t- headed bars
Simplification
lb,net  (
lb,net
A s ,req
A s , prov
( stag  0.5) (c1  cmin  d k / 2)
)  lb  8 
d 1.5
k
ds

f cd
fbd
f cd
d k1.5
(
)  lb  11

A s , prov
ds
fbd
A s ,req
Without special
reinforcement
With special
reinforcement
University of Stuttgart
Institute of Construction Materials (IWB)
13/21
Investigations by Appl (Splices with Headed Rebars)
Side view
Front view
260
c= 20mm
500
180
180
90
90
50
40
90
40 50
60 60
60 60
University of Stuttgart
Institute of Construction Materials (IWB)
14/21
Investigations by Appl (Splices with Headed Rebars)
University of Stuttgart
Institute of Construction Materials (IWB)
15/21
Investigations by Appl (Splices with Headed Rebars)
ls
[mm]
ds
[mm]
dk
[mm]
cx
[mm]
fcc
[N/mm²]
Fmax
[kN]
su,m2)
[N/mm²]
Failure3)
H
25ds
20
60
ds
27
371,3
590,9
LB
2
H
25ds
20
60
ds
27
384,0
611,1
LB
1
H
15ds
20
60
ds
27
379,87
604,4
LB
2
H
15ds
20
60
ds
27
368,87
586,9
LB
1
R
25ds
20
-
ds
27
213,46
339,0
S
2
R
25ds
20
-
ds
27
206,63
328,8
S
Test
No.
1)
K_500
1
K_300
B_500
1)
2)
3)
K= Headed rebar; R= Rebar with straight end
σ su,m  Fmax / 2  As
LB= Blow out in front of the Head; S= Splitting failure
University of Stuttgart
Institute of Construction Materials (IWB)
16/21
Investigations by Appl (Splices with Headed Rebars)
600
600
500
500
U3 U4
B1
400
U3 U4
B1
B2
B2
Crack 1
Crack 2
Crack 1
Crack 2
300
200
B_500_C1/C2
K_500_C1/C2
K_300_C1/C2
100
Crack 3
Crack 4
U1
B3
0,1
0,2
0,3
0,4
0,5
B4
0,6
0,7
0,8
B4
0,9
Crack 2
Crack 1
Crack 2
B_500_C3/C4
K_500_C3/C4
K_300_C3/C4
Crack 3
Crack 4
Crack 3
Crack 4
U1
1,0
0,0
0,1
0,2
0,3
0,4
U1
U2
B3
0
Crack Opening [mm]
(a) Average splitting crack openings (C1/C2)
Crack 1
200
U2
B3
B2
B2
300
Crack 4
U1
U2
U3 U4
B1
B1
400
100
0
0,0
Crack 3
Steel Stress [N/mm²]
Steel Stress [N/mm²]
U3 U4
0,5
B4
U2
B3
0,6
0,7
0,8
B4
0,9
Crack Opening [mm]
(b) Average splitting crack openings (C3/C4)
University of Stuttgart
Institute of Construction Materials (IWB)
1,0
17/21
600
600
500
500
U3 U4
400
U3 U4
B1
B1
B2
B2
Crack 1
Crack 2
Crack 1
Crack 2
300
200
B_500_B1/B2
K_500_B1/B2
K_300_B1/B2
100
Crack 3
Crack 4
U1
U2
B3
0,2
0,4
U3 U4
400
0,6
0,8
B4
1,0
1,2
B4
B_500_B3/B4
K_500_B3/B4
K_300_B3/B4
1,4
(a) Average load displacement curve (B1/B2)
Crack 2
Crack 1
Crack 2
Crack 3
Crack 4
Crack 3
Crack 4
U1
U2
B3
0
Displacement (Loaded End) [mm]
Crack 1
200
U2
B3
B2
B2
300
Crack 4
U1
U3 U4
B1
B1
100
0
0,0
Crack 3
Steel Stress [N/mm²]
Steel Stress [N/mm²]
Investigations by Appl (Splices with Headed Rebars)
0,0
0,2
0,4
0,6
0,8
U1
B4
U2
B3
1,0
1,2
B4
1,4
Displacement (Loaded End) [mm]
(b) Average load displacement curve (B3/B4)
University of Stuttgart
Institute of Construction Materials (IWB)
18/21
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 1
DMS
DMS
Pos 1
SP3B
SP2B
SP3
SP2
DMS
Pos 1
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 1: Bügel d = 8 mm, l
Transportanker
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 1
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Transportanker
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 1
Pos 1
Pos 2
SP3B
SP3
SP2
Pos
Pos 21
Transportanker
DMS
DMS
DMS
DMS
DMS
DM
DMS
Pos 1
SP3B
SP2B
SP4B
Pos 1: Bügel d = 8 mm, l = 0,750 m
SP4
DMS
DMS
DMS
SP2B
Pos 1
DMS
DMS
Pos 1
SP3
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 1: Bügel d = 8 mm, l
Pos 1: Bügel d = 8 mm, l = 0,90 m
Transportanker
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Transportanke
DMS
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Pos 2
Pos 2
Pos 2
Pos 2
DMS
DMS
DMS
DMS
DMS
DMS
DMS
Confined
DMS
MS
Unconfined
DMS
MS
Investigations by Schmid
SP4B
SP4B
SP4
Pos 1: Bügel d = 8 mm, l = 0,90 m
University of Stuttgart
Institute of Construction Materials (IWB)
Pos 1: Bügel d = 8 mm, l = 0,90 m
19/21
Investigations by Schmid
University of Stuttgart
Institute of Construction Materials (IWB)
20/21
Investigations by Schmid
Test
unconfined
SP2
Nu,calc,18,5
Nu,calc, 15
Nu,test
average value
Nu,test/Nucalc,18,5
Nu,test/Nu,calc,15
151,5
122,7
115,9
0,8
0,9
SP3
168,4
136,4
144,9
0,9
1,1
SP4
329,1
266,6
100,9
130,9
138,9
150,9
153,3
183,5
168,4
0,5
0,6
confined
SP2B
189,38
153,4
165,8
0,9
1,1
SP3B
210,5
170,5
154,8
0,7
0,9
SP4B
411,38
333,2
169,6
161,9
147,8
161,8
245,4
227,6
236,5
0,6
0,7
More research necessary
University of Stuttgart
Institute of Construction Materials (IWB)
21/21
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