An extensive literature review is carried out to investigate the accuracy of the proposed equation of the FRP axial strain of shear-strengthened beams with experimental results.
Shear-strengthened beams that failed by FRP fracture are not reported here. Table 7.2 and Table 7.3 includes shear-strengthened beams that failed by FRP debonding for both strengthening schemes (side-bonded and U-wrap). This database gathers all relevant data, such as the section type, scheme of strengthening and depth size. The specimens designation correspond to those used in the original references. Table 7.2 and Table 7.3 show the effective FRP axial strain and contribution of the FRP to the shear resistance, respectively. Further details can be found from the original sources. Tests that were not sufficiently well documented are excluded.
For the 61 beams listed in Table 7.2 and Table 7.3, they were tested under symmetric three-point bending or four-point bending. The beams have the following parametric ranges: beam height is between 200 to 600 mm; web thickness is between 100 to 300 mm; concrete compressive strength is between 25 to 52 MPa; shear steel stirrups ratio is between 0 to 1.2(%); FRP elastic modulus is between 35 to 210 GPa, FRP thickness is between 0.165 to 2 mm; width ratio between the FRPs width to concrete beam width is between 0.25 to 1.
After the above-presented database of experimental results of shear-strengthened beams, it is of interest to see how the proposed design equation compares with predictions from available design guidelines ACI, ISIS, FIB, BS. The various approaches are briefly de- scribed in Chapter 2. In all these design guidelines, their approaches will be adopted individually to obtain the effective FRP axial strain of each of shear-strengthened beams showed in Table 7.2. However, the FRP shear contribution (V/) is calculated by consid- ering the equation of ACI. According to ACI, the shear capacity contributed by FRP can be calculated by the following equation:
Vf = Af£feEf(sin a + cos a)df/sf (7.5)
Then, the predicted values from each approach will be compared with experimental results.
7.3. DESIGN EQUATIONS
Table 7.2: Comparison of FRP axial strain of shear-strengthened beams controlled by debond- ing
Author Ma]eketal.(1996)
Neôisằtal.l997 Cha&llal et ô1. (199$) Adey and Bruhwiler 1999
Khalifa and Hanni(2000) Deniuad and Chen (2001)
Specimen S2 S3 IE RS90 RS135 2 3 BT2 BT4 BT5 T6S4-C9Q T6S4-G90 T6S2-C90
Section type R-section R-section R- section R-section T-section
T-section Sir Details Side-bonded
U-tmp Side- bonded Side-bonded
U-shape
U-shape
depth sne strain (mm/mm) (mm) Exp- ACI
300 203 250 400 405
600
*
oxô36
0 0 0 4 8 0.0055 0.0055 0XC55
0.0013 0.0016 0.0045 0.0009 0.0009 0.0048 0X1048 0.0042 0.0042 0.0032 0.0059 0X1070 0.0059
ISIS 0.0013 0.0016 0.0045 OJ30C9 0D009 0.0048 0.0048 0 0 0 4 2 0,0042 0X1032
II I
FIB
0.0054
" " " • " • " " " "
0.0042 0 0 0 6 0 0.0062 0.0062
BS 0X1031 0.0049 0,0013 0,0017 0.0067 0JM67
il l
0.0052 0 0084 0.0052
Godat 0.0016 0 0 0 3 5 00051 0.0012 0.0012 0XH19 00016 0 0 0 3 2 0.0036 0 0 0 1 6
H i
Khalifa a n d Nanni(2O02)
Carlo and M o d e n a ( 2 0 0 2 )
A d h i k a r y a n d M u t s u v o s h i ( 2 O 0 3 )
U et al. (2003)
A d h i k a t y a n d M u t $ u y o s h i ( 2 0 0 4 )
B o u s s e l h a m a n d Chaallal(2004)
Z h a n g e t a l , (2005) S 0 3 - 2 S 0 3 - 3 S 0 3 - 4 S 0 4 - 2 S 0 4 - 3 TR3DC2 TR30C3 TR30D3 TR30D4 TR30D2 CI Al PU1 PU2 FU3 PU4 B2 B4 B7 BS SB-S0-1L SB-S0-2L SB-S1-1L SB-S1-2L Z4-90 Z4-45 Z6-90 Z6-45
R-section
R.section
R-section R-section
R section
T - s e c t i o n
R-section
U - s h a p e
Side- b o n d e d U - s h a p e U-shape
Side- b o n d e d U - s h a p e U - s h a p e
S i d e - b o n d e d 305
300
300 425
200
220
230 0 0 0 3 2
0DO36 0 0 0 3 5
„ 0JJ013 0 0 0 1 6 0 0 0 2 0 0 0 3 2
0 0 0 3 8 0.0022
-~*-i-~~
0.0014 0.0014 0.0035 0.0014 0.0035 0.00345 0,0018 0X102S 0X1023 0JM2 0.0043 0.0046 0.0021 0X1021 0.0021 0.0021 0.0011 0.0033 0.0035 0.002 0.0025 0.0020 0.0025 0.0011 0.0011 0.0011 0.001
0 0 0 1 4 0.0014 0 0 0 3 5 0.0014 0 0 0 3 5 0 0 0 3 5 0.0018 0 0 0 2 8 0XW23 0 0 0 2 0XC43 0 0 0 4 6 0.0021 0 0 0 2 1 0XB21 00021 0.0011 0.0033 0X1035 0.002 0.0025 O0O20 0 0 0 2 5 0 0 0 1 1 00011 00011 0.001
0.0054 0.0044 0.0035 0.0054 0.0035
0.0015 0.0080 0,0080 0.0085 0XB85
0.0036 0.0037 0.0042 0.0028 0.0042 0.0028
™ " ~ ~ "
0.0035 0,0035 0 0035 0 0035 0.0035 0.0022 0,0018 0.0025 0X1021 0.0018 0.0036 0.0039 0.0040 0.0040 013040 0 0040 0X1021 0.0030 0X1030 0XJ032 0.0014 0.0022 0 0 0 1 4 0.0022 0X1017 0.0017 00012 0.0012
0X1030 0,0028 0 0 0 2 8 0X1025 0 0 0 2 4 0X1018 0X1014 0,0013 0.0010 0X1008 0 0 0 3 3 0 0 0 4 5 0X1050 0 0 0 4 8 0.0050 00O48 0.0014 0.0014 0.003 0,003 0.003 0X1027 0.0O28 0X1023 0X1019 0,0019 0X1019 0 0 0 1 9 Q u et al (2005) U4
U5 U6
R-section U - s h a p e 200 400 600
0.003S 0.0028 0.0036 0,0020 0XXB2 0.0017
0002S 0.0020 00017
0.0040 0.0044 0,0012
0 0043 0,0044 0,0038
0.0042 0.0040 00037
H y a s i a n et al. (2006) BST R-section U-shape 380 0.0039 0XO39 0XB42 0.0030
Pellegrino a n d M o d e l s (2006)
A - U l - S - 1 7 A-U2-S-17 A-Ul-S-20 A-U2-S-20
R-section U - s h a p e 300 0.0046
0.0033 0.0046 0.0033
0.0046 0.0033 0JM46 0X1033
0.0070 0.0026 0.007 0,0026
0.0042 0.0031 0X1042 0.0031
C h u a n g e a n d Lu (2008)
SOU-1-1 SGU-2-la
SGU-2-2 SCU-2-1
R-section U-*hape 260
171
0.0066 0,0033 0 0 0 6 2 0.0030 0XB58 0.0030 0XB50 0 0 0 2 0
0.0033 00030 0.0030 OXD20
0X1050 00050 0.0049 OD037
0X1035 0.0031 0.0038 00033
L e u n g et al. (2007) Mosallam et a l 2007
M o n t i a n d U o t t a 2007
SB-U MB-U LB-U B22R UF90 UF45
R-section
R-secUon R-section
U-shape
S i d e - b o n d e d U-wrap
180 360 720 250 450
0.0020 0X3013 0.0092 0JKJ74 0.0016 0.0016
o o o
0XB74 0XB16 0 0 0 1 6
o o o o o o www
0.0018 0.0018
00031 0X1032 0.0024 0.00132 0.0013 0.0014
H i
0.0012 0 0 0 1 2 0X1012 0XXJ55 0X1054 0X1052 0 0 0 3 5
Table 7.3:
debonding
Comparison of FRP shear strength of shear-strengthened beams controlled by
Author Malek et al. (1996)
Nomsetal.1997 Chaallai et al. (1998) Adey and Bruhwiler 1999
Khalifa and Nu3ai(20CKF) Deniu&d and Chen (2001)
Khalifa and Nannt(2002)
Carlo and Mcdena(2002)
Adhikary and Mutsuyoshi(2003)
Li at al (2003)
Adhikary and Mutsuyoshi(2004)
Bousselhun and Chaallai (2004)
Zhang at al (2005)
Qu et al (2005)
Eurasian et al. (2006) PeSegrino and Modena(2006)
Leung et al, (2007) Mosall&m at al. 2007
Monti and Liotta 2007
Specimen 32 S3 IE RS90 RS135 2 5 BT2 BT4 BT5 T6S4-C90 T6S4-G90 T6S2-C90 S03-2 SQ3-3 SQ3-4 S04-2 S04-3 TR30C2 TR30C3 TR3CD3 TR30D4 TR3GD2
CI Al PU1 PU2 PU3 PU4 B2 B4 B7 B8 5B-S0-1L SB-S0-2L SB-S1-1L SB-S1-2L 24-90 Z4.45 26-90 Z6-45 0 4
m m
BST A-Ul-S-17 A-U2-S-17 A-Ul-S-20 A-U2-S-20 SB-U MB-U LB-U B22R UF90 UF45
Exp.
63 110 22 35 43 23 90 68 SO 38
_
55 58 65 55 85 45 52 5 44 52 53 43 65 40 89 80 U 24 29 47 12 16 2 6 27 37 21 14 43 100 392 49 49 22 32 5 23 30 25 30 64
FRP shear ACI
104 130 51 27 25 90 18 78 240 26
65 65 S9 65 67 67 104 54 89 116 75 124 65 52 92 73 13 38
ô>
8 18 7 9 32 45 17 24 73 205 398 109 76 125 76 114 20 63 31 119 117 165
ISIS 104 I X 51 27 25 90 18 78 240 26
65 65 59 65 67 67 104
54 89 116
75 124 65 52 92 73 13 38 46 8 18 7 9 32 45 17 24 73 205 398 109 76 125 76 114
20 63 31 119 117 165
strength (kN) FIB
68
78 342
250 203 67 219 67
28 185 261 155 214
42 48 15 21 15 21
114 Aii 1030
117 114 99 114 99 60 283 227 131 185
BS 247 391 24 274
——
90 90 74 217 160
161 161 67 161 67 40 54 48 81 104 100 73 123 174 79 112
16 35 35 41 5 16 5 16 163 231 96 132 117 451 889 SO 116 80 116 31 151
83 217 95 102
Godit 64 142
32 24 20 22 18 38 94 43
67 65 54 58 55 22 52 13 22 30 33 73 77 62 109
87 6 10 20 27 7 It 5 18 23 38:
16 22 55 205 425 42 38 55 38 60 17 66 44 95 43 61
Chuange and Lu (2008)
SOU-1-1 SOU-2-U
SGU-2-2 SCU-2-1
40 35 40
48
"S
82
48 - 55 - 83 — 82 —
— 73 91
— 136 158
40 49 72 70
7.3. DESIGN EQUATIONS In the calculation of the effective FRP axial strain £fe and FRP shear capacity con- tribution Vj, all the necessary safety factors are incorporated. The experimental shear contribution by the FRP is obtained by subtracting the shear capacity of the reference beam, which represents the shear contribution by concrete and steel stirrups. This means that we neglect the superposition effect of the steel stirrups on the FRP shear contribution.
Figure 7.12(a)-(e) show the comparison between the experimental results of the effective FRP axial strain and the ACI, ISIS, FIB, BS and proposed design equation, respectively.
Also, the test data are compared with design equation in terms of FRP shear contribution is shown graphically in Figure 7.13(a)-(e).
According to Figure 7.12, for the FRP axial strain, the proposed design equation is able to give reasonable predictions for various test data, whereas both the ACI and ISIS equation (Figure 7.12 (a) and (b) tends to underestimate the effective FRP axial strain. However, the ACI and ISIS equations can be conservative in some cases, but unconservative in others. Based on the results shown in Figure 7.12(c) and (d), it can be stated that the FIB and BS could not estimate the FRP axial effective strain correctly.
The difference may be attributed to the various volume of shear steel stirrups in the specimens. The contribution of the FRP axial effective strain is lower in a beam containing shear stirrups when compared to a member without steel stirrups, so the presence of shear stirrups influence the effectiveness of FRP. We should note that FIB design practise does not provide an equation for the side-bonded strengthening scheme as well as the for AFRP and GFRP materials in case of debonding.
For the FRP shear contribution shown in Figure 7.13(a)-(e), either the ACI or ISIS equation can give conservative results, as the predicted results are higher than the test results. The proposed design equation actually gives the closest agreement with test data due to the fact that consideration of parameters most influence the behaviour of shear-strengthened beam. The model predicted the experimental results with relatively good accuracy, which is obvious because the model include the parameters most influence the shear behaviour. It is seen that the model proposed by FIB and ISIS could not assess correctly the FRP shear contribution. The model showed poor correlation with experimental results for both side-bonded and U-wrap strengthening schemes.
Finally, since design guidelines were derived from relatively limited experimental database and did not take into account most of factors affecting the FRP shear contribution, they
I
u
<
Exp. FRP axial strain (10 ) (a)
Exp. FRP axial strain (10 ) (b)
Exp. FRP axial strain (10 ) (C)
f >
6
G
•a )-.
1st
CQ
'* Ct
FRP
oo m
o -
6
4
2 •
0 -
•
•
.
• yS
• S
\ / / j * +
j*+*
X
Exp. FRP axial strain (10" ) (d)
Exp. FRP axial strain (10 ) (e)
F i g u r e 7 . 1 2 : Comparison of F R P axial strain results between experimental a n d various design codes: (a) ACI; (b) ISIS; (c) F I B ; (d) BS; (e) new design equation
7.3. DESIGN EQUATIONS
500
PQ
E
O 400 •
1 3 0°"
C/3
S3 2 0 0 -
ftt 100 • OS a.
22 0 i J ( ^ • 100 200 300 400 500
Exp. FRP shear strength (kN)
(a)
100 200 300 400 500
Exp. FRP shear strength (kN) (b)
1200 ^ 1000
800
2 600 400 ft.
ft.
03 200
0 300 600 900
Exp. FRP shear strength (kN)
(C) 500
1200 200 400 600 800
Exp. FRP shear strength (kN)
(d)
1000
100 200 300 400 500
Exp. FRP shear strength (kN)
(e)
F i g u r e 7 . 1 3 : Comparison of FRP shear strength between experimental and various design codes: (a) ACI; (b) ISIS; (c) FIB; (d) BS; (e) new design equation
are not able to predict the experimental results with good accuracy. The proposed design equation is believed to be the most appropriate for practical design.