[empa] flexural strengthening of reinforced concrete
TRANSCRIPT
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Flexural strengthening of reinforced concreteSwiss Code 166 and other codes/guidelines
ETH Lecture 101-0167-01LFibre Composite Materials in Structural Engineering
Christoph Czaderski
7. November 2012
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2ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Literature
SIA166 (2004) Klebebewehrungen (Externally bonded reinforcement). Schweizerischer Ingenieur- undArchitektenverein SIA.
SIA (2004) D 0209, Dokumentation, Klebebewehrung, Einfhrung in die Norm SIA 166.
Ulaga T (2003) Dissertation ETH Nr. 15062, Betonbauteile mit Stab- und Lamellenbewehrung: Verbund- undZuggliedmodellierung, http://dx.doi.org/10.3929/ethz-a-004525392
Czaderski C (2012) Dissertation ETH No. 20504, Strengthening of reinforced concrete members by prestressed,externally bonded reinforcement with gradient anchorage, http://e-collection.library.ethz.ch/
ACI (2008) ACI440.2R-08, Guide for the design and construction of externally bonded FRP systems for
strengthening concrete structures. American Concrete Institute. CNR (2004) Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing
Structures, CNR-DT 200/2004. CNR - Advisory Committee on Technical Recommendations for Construction, Rome,Italy.
fib (2001) Externally bonded FRP reinforcement for RC structures - Bulletin 14. International Federation forStructural Concrete (fib), Switzerland.
TR55 (2004) Design guidance for strengthening concrete structures using fibre composite materials, SecondEdition. Technical Report No. 55 of the Concrete Society, UK.
Motavalli, M., C. Czaderski, A. Schumacher, and D. Gsell, Fibre reinforced polymer composite materials for buildingand construction, in Textiles, polymers and composites for buildings, G. Pohl, Editor. 2010, Woodhead PublishingLimited: Cambridge UK. p. 69-128.
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3ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Overview
Introduction
Failure modes debonding according to SIA 166 End-anchorage
Debonding at shear cracks and/or discontinuities
Debonding at flexural cracks
Several additional topics according to SIA 166 e.g. Action effects M and V
Resistance factors
Cross-section analysis
etc. Summary, debonding failure modes treated in SIA 166
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4ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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5ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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6ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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7ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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8ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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9ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
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10ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Debonding failure modes
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11ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Debonding failure modes
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12ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
End anchorage failure
Short beams
Cracks near the supports
Anchorage in free length
Small internal steel reinforcement cross-section
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13ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Anchorage resistance
concrete
adhesive
strip
F
F
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14ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Lap shear test (pull-off test, pull test on FRP-
to-concrete-bonded joint)
see: Czaderski, C., K. Soudki, et al. (2010). "Front and Side View Image Correlation Measurements on FRP to Concrete Pull-OffBond Tests." Journal of Composites for Construction, ASCE 14(4): 451-463.
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15ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Lap shear test on the strong floor
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16ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0.0
0.5
1.0
1.5
2.0
2.5
0 50 100 150 200 250
distance [mm]
StraininCFRP[]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 50 100 150 200 250
distance [mm ]
shearstres
s[MPa]
Longitudinal strain
Shear stress betweenstrip and concrete
hyperbolic shape
hyperbolic shape
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17ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0.0
0.5
1.0
1.5
2.0
2.5
0 50 100 150 200 250
distance [mm]
S
traininCFRP[]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 50 100 150 200 250
distance [mm]
shearstress
[MPa]
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18ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0.0
0.5
1.0
1.5
2.0
2.5
0 50 100 150 200 250
distance [mm]
S
traininCFRP[]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 50 100 150 200 250
distance [mm]
shearstress
[MPa]
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19ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0.0
0.5
1.0
1.5
2.0
2.5
0 50 100 150 200 250
distance [mm]
S
traininCFRP[]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 50 100 150 200 250
distance [mm]
shearstress
[MPa]
trigonometric shape
trigonometric shape
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20ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0.0
0.5
1.0
1.5
2.0
2.5
0 50 100 150 200 250
distance [mm]
S
traininCFRP[]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 50 100 150 200 250
distance [mm]
shearstress
[MPa]
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21ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Bond behavior depends on
Elastic deformation
shear modulus of adhesive and concrete
thickness of adhesive plus a layer of concrete
Bond damage (Entfestigungsbereich, Verbundschdigung)
concrete quality
Additionally, the stiffness (Eltl)of the strip influences also thebond behaviour.
GFb
maximum slip
constant (~0.2 mm)
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22ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Comparison with reinforcement
Internal steel reinforcement is surrounded
Deflection perpenticular to longitudinal direction is not possible
Normal (confinement) stresses due to interlocking and friction
the longer the anchor length, the higher the anchor force up toyielding of the steel reinforcement
Externally applied strip is free on one side
Deflection perpenticular to longitudinal direction is possible maximum anchorage force (anchorage resistance) withcorresponding length (active bond length)
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23ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
2/3l0 ct c4
= f =0.4 f 3
gl0 l0
g
ts = G
Ggtg1
l0 = 4.5 MPa
CFRP strip
according to Ulaga:
2/3s0 ctm ck=2f =0.6 f s0 = 5.8 MPa
s1 = 2.9 MPa
with fck = 30MPa (fc = 38MPa), tg=1mm, Gg=4GPa
sl0 = 0.001 mm
Reinforcement
according to Sigrist and Marti:
(Skript Stahlbeton Marti 2009)
sl1 0.225 mm
GFb = 0.51 N/mm
2/3
s1 ctm ck=f =0.3 f
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24ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
fl0 f,meanf,max
G= =
s
l0 = f,max = 4.1 MPa
CFRP strip
according to Czaderski(Diss ETH No. 20504):
with fck = 30MPa, dmax=32mm
slo = sf,el = 0.02 mm
sl1 = sf,max = 0.2 mm
2/3 1/4
f ck maxG =0.018 f d [N/mm]
GFb = Gf= 0.41 N/mm
ctHFb
fG =8
2/3
ctH ctm ckf f =0.3 f
CFRP strip
according to SIA 166
with
with fck = 30MPa, dmax=32mm
GFb = 0.36 N/mm
2/3l0 ctH ck4
= f 0.4 f 3
l0 = f,max = 3.9 MPa
2/3Fb ckG =0.0375 f [N/mm]
(fctH should better be
tested on site)
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25ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
l
f,mean
sl1
sl
Simplified bond shear stress-slip relation
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26ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
F = 5 kN
Ef= 165 GPa, bf= 50mm, tf= 1.2 mm, f,mean = 2.25 MPa
parabolic shape of slip
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27ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
F = 10 kN
Ef= 165 GPa, bf= 50mm, tf= 1.2 mm, f,mean = 2.25 MPa
parabolic shape of slip
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28ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
F = 15 kN
Ef= 165 GPa, bf= 50mm, tf= 1.2 mm, f,mean = 2.25 MPa
parabolic shape of slip
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29ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
F = 20 kN
Ef= 165 GPa, bf= 50mm, tf= 1.2 mm, f,mean = 2.25 MPa
parabolic shape of slip
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30ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
2
ll
l l
xs x =
E t 2
lll l
x = x
E t
l f,meanx =
b0,R
b0
f,mean l
Fl =
b
l b0 l1s x=l =s2
b0,R
l1 2
l l l f,max
Fs =
2Etb
with and we get from Eq. (1) and (3):
(1)
(2)
(3)
and withFb l1 f,maxG =s we get b0,R l Fb l lF =b 2G E t
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31ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Equations for maximum anchorage resistance
ctHb0,R l Fb l l l l l l l l ctHf
F =b 2 G E t =b 2 E t =0.5b E t f 8
SIA 166
f i b Bulletin 14 ctmfffbc1maxfa, ftEbkkcN
ctmfffbmaxk, ftEbk0.5T TR55
1
400
b1
b
b2
1.06kf
f
b
please note: without safety factors!!
Italian CodectmckbFkFkffffdffk.;tE2bF 030
Take care to symbols. They depend on the reference. l in SIA: Lamelle, Gewebe or Gelege
see lecture of Prof. Motavalli, EBR flex. strength.
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32ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Active bond length
(the length which is actively involved in the force transfer from the strip to the concrete)
b0,R l Fb l lF =b 2 G E t
b0,R
b0
l f,mean
F
l b
Fb l l Fb l lb0 2
f,mean f,mean
2 G E t G E tl
with
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33ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Equations for active bond length(minimum necessary length for maximum anchor resistance Fb0,R)
SIA 166
f i b Bulletin 14
TR55
please note: without safety factors!!
Italian Code
; ;Fb l l l lb0 l0 ctH b02l0 ctH
G E t E t4 3l 2 f l
2 3 16 f
ctm2
ffmaxb,
fc
tEl
ctm
ffmaxb,
f
tE0.7l
ctm
ffef2
tEl
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34ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Units in equations in SIA 166
Equations for maximum anchorage resistance and active bond length
Please note, that the units are not conform!
2
0 5
1
ctHb0,R l Fb l l l l l l l l ctH
ctH
Fb
fF b 2 G E t b 2 E t . b E t f
8
N
fN mmG
mm8
mm
ctH
llb0ctHl02
l0
llFbb0
f
tE
16lf
tEG2
2l
3;
3
4;
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35ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Example
mm
N
8
f
GctH
Fb
MPaf3
4ctHl0
18.9kN1.2165'0000.36250tEG2bF llFblRb0,
315MPaA
F
l
Rb0,Rb0, 1.91El
Rb0,
Rb0,
Concrete C30/37
Sika CarboDur S512 tensile strength > 2800 MPatensile strain > 17
for concreteC 20/25 to C 50/60
mm
N
0.368
2.9
GFb
MPa23
4l0 9.39.
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36ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0
50
100
150
200
250
0
5
10
15
20
25
C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
activebond
lengthlb0[mm
]
AnchorageresistanceFb0[kN
]
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37ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
llFb
bl
llFblRb,
bb
tEG2
l
sintEG2bF
llif
22
0
0 :
0
5
10
15
20
25
0 50 100 150 200 250 300
Anchorage
resistanceF[kN
]
bond length l [mm]
C50/60
C45/55
C40/50
C35/45
C30/37
C25/30C20/25
C16/20
C12/15
i hil f i d
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38ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Design philosopy of preventing end
anchorage failure
SIA166: anchorage in the uncracked zone
ACI:
If Vu > 0.67 Vc at strip end, then transverse reinforcement is necessary(they give a design equation for U-wrap reinforcement Af,anchor)
or (instead of detailed analysis)
for simply supported beams: length ldfafter last crack
Elastic solutions for calculating shear and normal stresses at stripend
E d h l t t t i d
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39ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
End anchorage, normal stresses at strip end
Sh d l t t t i d
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40ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Shear and normal stresses at strip end
B4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40
Distance from plate end (mm)
Shearstress(MPa)
Closed-form solution
FEM2(nonlinear)
FEM2(linear)
FEM1
B4
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 10 20 30 40
Distance from plate end (mm)
Normalstress(MPa)
Closed-form solution
FEM2(nonlinear)
FEM2(linear)
see:
Aram, M.R., C. Czaderski, and M. Motavalli, Debonding failure modes of flexural FRP-strengthened RC beams. Composites Part B: Engineering, 2008. 39(5): pp. 826-841.
D b di f il d
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41ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Debonding failure modes
Debonding at shear cracks and/or
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42ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Debonding at shear cracks and/ordiscontinuities
Large shear force, single loads, small distance between load andsupport
Discontinuities: internal stress state
cross-section
reinforcement (joint, ..)
Large compression zone so that no premature concrete crushing
Example
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43ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Example
18.9kN1.2165'0000.36250tEG2bF llFblRb0,
,
,
b0 R
l0 R
l
F315MPa
A
,
, . l0 R
l0 R
l
1 91E
Concrete C30/37
Sika CarboDur S512 tensile strength > 2800 MPatensile strain > 17
According to SIA166,
the maximum allowed strain is 8!
??
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44ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
simple lap shear test
beam
Strain
Simple supported plate
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45ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Simple supported plate
8
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46ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-3
-2
-1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
Str
aininconcreteandCFRP[]
10kN/m
10kN/m
8
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47ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-3
-2
-1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
Str
aininconcreteandCFRP[]
10kN/m
20kN/m
10kN/m
20kN/m
8
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48ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-3
-2
-1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
Str
aininconcreteandCFRP[]
10kN/m
20kN/m
25kN/m
10kN/m
20kN/m
25kN/m
8
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49ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-3
-2
-1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
Str
aininconcreteandCFRP[]
10kN/m
20kN/m
25kN/m
26kN/m
10kN/m
20kN/m
25kN/m
26kN/m
8
10kN/m
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50ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-3
-2
-1
0
1
2
3
4
5
6
7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
StraininconcreteandCFRP[]
10kN/m
20kN/m
25kN/m
26kN/m
27kN/m
10kN/m
20kN/m
25kN/m
26kN/m
27kN/m
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90
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52ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0
10
20
30
40
50
60
70
80
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
Tens
ileForceinoneCF
RPPlate[kN]
30kN/m
100
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53ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
-100
-80
-60
-40
-20
0
20
40
60
80
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
TensileForceCHANGEinone
CFRPplate[N/mm
']
30kN/m
Maximum Tensile Force CHANGE
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54ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
according to SIA 166
ckcliml,
lliml,
R
l
f0.32.52.5
bx
F
(c from SIA 262)
Example
Concrete C30/37
Sika CarboDur S512MPa300.32.52.5
mmNbx
F
climl,
lliml,
R
l
1.4
/205
please note: without safety factors!!
6
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55ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0
1
2
3
4
5
C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
Shearstressl,lim
[MPa]
300
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56ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
0
50
100
150
200
250
C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60
Force
ChangeF
l0/x[N/mm]
Shear stress limitations, other guidelines
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57ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
3.7MPa2.90.71.8f1.8f ctkcb
f i b Bulletin 14 (approach 3)
TR55 PaM0.8b
f i b Bulletin 14 (approach 2) f (between cracks )
please note: without safety factors!!
cbb f
Debonding failure modes
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58ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Debonding at flexural cracks
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59ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Less internal steel reinforcement cross-section, so that large strainsin EBR
Small shear load, large spans, continuous force development in thespan
Large compression zone so that no premature concrete crushing
Maximum strain in the strip according to SIA 166
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60ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Local debonding due to compatibility problems between strip andconcrete at flexural cracks
8dlim,l,
supplier of the material
fullliml,llRl, EAEAF
fu
design value!(shall be used also for thecalculation in the exercise)
Maximum strain in strip, other guidelines
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61ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
8.56.5lim,f f i b Bulletin 14 (approach 1)
TR55
Italian Code
ACI
ff
ctmckb
crfddtE
ffk06.0k
With kcr = 3.0
8lim,f
please note: without safety factors!!
fd
f f
0.41n E t
'
cf in SI units
(equation for DFM 2 and 3)
(equation for DFM 2 and 3)
Swiss Pre-Code 166 Externally bondedi f t
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62ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
reinforcement
Design philosophy
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63ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Ultimate limit state (ULS)
Serviceability (SLS) Stresses
Deflections
(Crack width)
Accidential situation
Check of deformation capacity
Ultimate limit state
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64ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
dd RE Design value of effects of action
Design value of ultimate resistance
Hazard Scenario (Gefhrdungsbild)
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65ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
ddki0ik1Q1kPkGd a,X,Q,Q,P,GEE
Ed effects of actions (Auswirkungen) E actions (Einwirkungen)
Gk permanent actions
Pk prestressing
Qk1 leading action (Leiteinwirkung)
Qki accompanying actions (Begleiteinwirkungen)
Xd material properties
ad geometry
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Accidential design situation: Hazard Scenario failure of EBR
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67ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
You have to prove, that the structure does not fail in the case of afailure of the EBR! remaining safety factor >1.0
Determination of action effects M and V(Schnittkrfte)
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68ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
(Schnittkrfte)
Plastic rotation capacity is reduced!
Elastic determination of action effects if FRP are used, e.g. two span
beam
Ultimate resistance
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69ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
d
M
kd a,
XRR
ddlim,d a,RR
Xk = characteristic value of material property
Depending on failure in strengthening material orbond failure:
= conversion factor
M = resistance factor
see Table 3 in SIA166
Table 3 in SIA 166
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70ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Failure of EBR
Steel strip M = 1.05 = 1.0
FRP strip M = 1.30 = 0.8 FRP fabric M = 1.30 = 0.8
Bond failure
in adhesiv M = 1.50 = 0.8
in concrete M = 1.50 see SIA 262 in timber M, see SIA 265
in adhesiv M, see SIA 266
Characteristic values
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71ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
FRP:
l
l
ffd
fud
Ef1
specifications from seller company,
ask also for fraktile values
mixed fibers in strips can havenon-linear behavior
Cross-section analysis
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72ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Bond factor according to SIA166: s=0.7, l=0.9
''
Compatibility with
Equilibrium with
Equations for cross-section analysis
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73ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
D Z
c l
x h x
c
sl
h
x
Equilibrium:
Compatibility:
one equation with unknowns c andx
s ls s l l
s l
Z E A E A
D next slides
d
c s
x d x
Concrete in compression by Hognestad
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74ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
2
1
0.15
0.004 0.003
2
0.003
3
0.003
1
1
3
3
0.15
0.004
2
0.075
0.004
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75ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
13
12
1
3
1
5.1 0.004
0.024
3.925
10.2 0.9
0.016 0.048
0.003
Equations from:
An, W., H. Saadatmanesh, and M.R. Ehsani, RC beams strengthened with FRP plates. II: Analysis and parametric study.
Journal of Structural Engineering ASCE, 1991. 117(11): p. 3434-3455.
Proposal
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76ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Make a table e.g. with Excel
c x s1 s2 l M F0
0.00005
0.00010
0.00015
0.00340
0.00345
0.00350
with this table you have l and can make the SIA verifications
Deformation capacity
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77ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
SIA 166 and 262:
For mainly bending load: compression zone x/d 0.35 what limits
reinforcement ratio (If x/d > 0.35 but 0.5 then calculation of deformation capacity)
(on the basis of similar limitation, minimal values of strain in EBR andreinforcement at ultimate are given in fib Bulletin 14)
SLS and evenness
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78ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
SIA 166: Serviceability (SLS)
Stresses in the internal reinforcement should not exceed 90% of yieldstrength.
Deflections should be checked
Evenness of concrete surface
for 2 m measurement length (Messlatte): max. 5 mm tolerance
for 0.3 m measurement length (Messlatte): max. 1 mm tolerance
Deflections
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79ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
If the strains at top and bottom side along the beam is calculated,the curvature can be obtained.
By two times integrating, the deflection can be calculated. (consideralso boundary condition: (L/2)=0)
h
bottomtop
L
dx
0
681 22 mm Lw
Simplified calculation for 4-point beam(see e.g. Ulaga 2003): L
m = curvature between loadsL
L
dxw
0
Longitudinal force from shear force
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80ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Generally, longitudinal force due to shear force shall be carried frominternal steel
If it yields, see SIA 166
)(
2
1),('' VFEAVMF t
l
llll
cot)( VVFt = angle of compression struts
Assessment, some remarks
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81ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Consider existing stresses and deflections in the structure beforestrengthening
Internal reinforcement Good assessment: geometry, strength
Minimum value (brittle behaviour)
Risk of premature concrete crushing if steel is neglected in calculations
Concrete property (tensile strength good enough?)
Static system
See also SIA166 chapter 2.1
Normal design as usual
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82ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Concrete crushing
Bending resistance in the unstrengthened region
Shear resistance of cross-section etc.
Calculation procedure, first step
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83ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Cross-section analysis to determine the strain and forces along thestructure for an assumed maximum load
-3
-2
-1
0
1
2
3
4
5
6
7
8
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
30kN/m
30kN/m
Check debonding failure mode 1:end strip failure
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84ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Determine the location of last crack and define anchorage zone
Compare the existing force in the strip at the last crack with anchorageresistance which can be anchored in the anchorage zone
I: uncracked cross-section
II: cracked cross-section, internal steel in elastic state
III: cracked cross-section, internal steel in yielding state
Check debonding failure mode 2:Debonding at strong strain increase in strip
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85ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Calculation of shear stress between strip and concrete(force change) and comparison with bond shear strength
l
l
bx
F
-100
-80
-60
-40
-20
0
20
40
60
80
100
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
TensileForceCHANGEinoneCFRPplate[N/mm']
30kN/m
Check debonding failure mode 3:at flexural cracks
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86ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
Compare maximum existing strain with maximum admissible strain
0
1
2
3
4
5
6
7
8
0.0 0 .5 1.0 1.5 2 .0 2 .5 3 .0 3 .5 4 .0 4.5 5 .0
Length of beam / plate [m ]
StraininconcreteandCFRP[]
30kN/m
Calculation procedure for a four point beam
1. Calculation crackmoment Mcrand yieldmoment Mywith cross-section analysis (CSA)
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87ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
- Strip strain at last crack and at the point of steel yielding
2. Assumption of a failure load Pult (larger as Py), then:- with CSA calculation of the maximum strain in the strip
- calculation of the location of the last crack lcrand the location ofMy(lyundx)
- with this l and l
3. The three SIA verifications and assumption of a new failure load Pultetc.
l,strip
M
P
l
crM
crl
yM
yl
M P
P
x
ly''
lcr
''
l,Load
''
l ll
l
E A
x b
'' ''
l l ,Load ly
Summary of the three SIA 166 verifications
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88ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012
1. End strip debonding failure at the last crack
2. Debonding at strong strain increase in strip
3. Debonding at flexural cracks
0
10
20
30
40
50
60
70
80
90
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Length of beam / plate [m]
TensileForcein
oneCFRPPlate[kN]
30kN/m
12
3
''
b b,RF F
l
''
l,lim,d 8
l l
R
F F
x x
88