-
Crack Spacing of Overlay Crack Spacing of Overlay Strengthened
RC Beam Strengthened RC Beam
Zhang Dawei (PD)Zhang Dawei (PD)Lab of Engineering for
Maintenance SystemLab of Engineering for Maintenance System
2010080420100804 2
1. Research Background
3. Problem with Current Standard Specifications
4. Analytical approach for Crack spacing
2. Average Crack Spacing
5. Next research plan
3
Research Background
Deterioration problems of highways or bridgesDeterioration
problems of highways or bridges
Continuous increase in traffic amount
Insufficient slab thickness in the past design
Repair or strengthening of deteriorated concrete structures are
necessary
FRP BondingSteel Plate bonding
Traffic Safety
Overlay Strengthening4
Overlay StrengtheningStrengthening
RC beam
overlay
A
ASection A-A
h
tlRlE
Typical view of overlay strengthening method
Overlay materials
Cover materials Reinforcement materials
PCM HPFRCC Steel bars FRP Grid
-
5
Crack Spacing
Serviceability and durability
Pre-mature failure
Shear, tensile and bending stiffnessEnergy absorption
capacityDuctilityCorrosion resistance
Transferred shear stress-----IC or end zone debonding
Transferred normal stress-----Concrete cover separation
Prediction of Average Crack
Spacing
Prediction of Average Crack
Width
Scr Scr Scr Scr Scr Scr ScrScr ScrScr
6
Current prediction equations
hh
t
Overlay strengthened beam Multiplayer reinforced beam
PredictionPredictionequationsequations
BB
EE
CC
DD
AACSA S474 2004
NS 3473 E 1992
Eurocode EC2
JSCE, 2007 CEB-FIP 1990
7
Current prediction equations
CEB-FIP 1990
JSCE, 2007
Eurocode EC2
NS 3473 E 1992
C: concrete cover (mm)
S: bar spacing (mm)Ф: Bar diamater
(mm) (External layer)
Ast: Bar area (mm2)Act: Effective
concrete tension area (mm2)
CSA S474 2004
MainParameters
EquationCode
( ) tNscr kkSCS ρφ /.. 211002 ++=
( ) tNscr kkSCS ρφ /.. 211002 ++=
st
ctcr A
AkkCS
φ212 +=
efscrS
,. ρφ
45=
( ){ }φ−+= SckkkScr 70411 321 ..
ctsttNs AA /=ρ
8
Comparison-1
Scal/Sexp
Mean: 0.79
Standard Deviation: 0.17
Scal/Sexp
Mean: 0.78
Standard Deviation: 0.18
28 Overlay Strengthened Beams
0
50
100
150
200
0 50 100 150 200
Scal(mm)
Sexp
(mm
)
CSA
Scal=Sexp0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
NS
Scal=Sexp
-
9
Comparison-2
Scal/Sexp
Mean: 0.79
Standard Deviation: 0.22
Scal/Sexp
Mean: 0.87
Standard Deviation: 0.32
28 Overlay Strengthened Beams
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
EC2Scal=Sexp
0
50
100
150
200
0 50 100 150 200
Scal (mm)Se
xp (m
m)
CEB-FIPScal=Sexp
10
Comparison-328 Overlay Strengthened Beams
Scal/Sexp
Mean: 1.22
Standard Deviation: 0.30
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
JSCE 2007Scal=Sexp
The current design specifications can not
predict the crack spacing of overlay strengthened
beam satisfactorily
11
Initiation of Crack
Arc
ArAs
hodr
b
ds
ε’cc
εtc
xgdrc
hc
εto
tcgc
ccc fxh
IM−
=
( ) togoc
o
cco fxh
IEEM
−=
Crack at substrate concrete
Crack at overlay material
( )
( )( ) togcc
tcgoo
togo
c
o
c
tcgc
c
co
ccc fxhE
fxhE
fxh
IEE
fxh
I
MM
R−
−=
−
−==
Crack always initiates from substrate concreteCrack always
initiates near the bottomRc Max:0.52 Min: 0.33 Mean:
0.45Rc>1
Overlay strengthened RC beamMultilayer reinforced concrete
beam
12
Comparison-1'
Scal/Sexp
Mean: 0.98
Standard Deviation: 0.13
Scal/Sexp
Mean: 0.98
Standard Deviation: 0.13
Ф and S of Internal bars
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sex
p (m
m)
NS (RC)
Scal=Sexp0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)CSA (RC)Scal=Sexp
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13
Comparison-2'
Scal/Sexp
Mean: 1.07
Standard Deviation: 0.13
Scal/Sexp
Mean: 1.35
Standard Deviation: 0.24
Ф and S of Internal bars
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
CEB-FIP (RC)Scal=Sexp
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
CE2 (RC)Sexp=Scal
14
Comparison-3'
Scal/Sexp
Mean: 1.34
Standard Deviation: 0.33
The properties of reinforcementnearest to the initiation
locationof flexure crack predominantly
control the crack spacing of overlay strengthened beam
Ф and S of Internal bars
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
Scal=SexpJSCE (RC)
Mechanism is not clear
15
Analytical Approach -1
SssjAσ
rriAσ
ssiAσ
rrjAσx
Concrete
Overlay dx
bcτ
bpτ
bcτ
bpτ
Overlay
P P
S S
Concrete
FdFF +
bcτ
Overlay
dx
boτb
b
t
ch
( )
( )⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
+−=+
+−=
+++=
∑∑
∑∑∑∑
bosbcroto
ctc
bosbcr
bosbcr
OOAdx
dAdx
d
OOdxdF
dxOdxOdFFF
ττσσ
ττ
ττ
16
Analytical Approach -2
SssjAσ
rriAσ
ssiAσ
rrjAσx
Concrete
Overlay dx
bcτ
bpτ
bcτ
bpτ
bobc ττ or
0
0
oc σσ or
o
o
c
co EE
maxmax σσε ==
( )( )
( )
( )o
oto
cct
bosbcro
t
c
ootct
bosbcrc
bosbcr
S bosbcrotoctc
fA
EE
A
OOS
f
EE
AA
OOS
OOS
dxOOAA
≤
⎟⎟⎠
⎞⎜⎜⎝
⎛+
+=
≤
⎟⎟⎠
⎞⎜⎜⎝
⎛+
+=
+=
+−=+
∑∑
∑∑
∑∑∫ ∑∑
2
2
2
0
2
ττσ
ττσ
ττ
ττσσ
max
max
/maxmax
MIN
Zero-slip point
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17
Analytical Approach -2
( )bosbcrc
ootctt
c OOEE
AAfS
ττ ∑∑ +⎟⎟⎠
⎞⎜⎜⎝
⎛+
=
2
max
( )bosbcrot
o
ccto
o OO
AEE
AfS
ττ ∑∑ +⎟⎟⎠
⎞⎜⎜⎝
⎛+
=2
max
),min( maxmaxmax oc SSS =
),min( maxmaxmax oc SSkkS 21=
ε1
ε2hc+t
ho
xc
Maximum crack spacing of substrate concrete layer
Maximum crack spacing of overlay layer
Uniaxial tension load
Stabilized cracking under flexure load
k2= (ε1 + ε2)/2ε1 (CSA 2004, NS 1992)
k1= 2/3 (CEB-FIP 1990)
18
Verification
0
50
100
150
200
0 50 100 150 200
Scal (mm)
Sexp
(mm
)
New ModelScal=Sexp
Scal/Sexp
Mean: 1.03
Standard Deviation: 0.14
The proposed analytical approach can predict the crack spacing
of overlay strengthened beam satisfactorily
19
Next PlanNext PlanDesign procedure of overlay strengthened RC
members under fatigue loading
1
Visiting Scholar at Technical University of Munich and Technical
University of Braunschweig
3
Design procedure of overlay strengthened damaged RC members
2
Dynamic behavior of strengthening measuresOct, 15-Nov,09TU
Braunschweig
1. Strengthening of RC structures with CFK laminates
2. Concrete to concrete bond3. Joining of ultra-high performance
concrete
(HUPC) by göuing.
Sep,19-Oct,14TU Munich
20
