- Email: [email protected]
Analysis of the CFRP flexural strengthening reinforcement approaches proposed in Fib bulletin 14
Available online at www.sciencedirect.com
Construction and Building
MATERIALS
Construction and Building Materials 22 (2008) 2130–2140
www.elsevier.com/locate/conbuildmat
Analysis of the CFRP flexural strengthening reinforcement approaches proposed in Fib bulletin 14 J. Alexandre Bogas *, Augusto Gomes DECivil/ICIST, Instituto Superior Te´cnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Received 17 January 2006; received in revised form 20 July 2007; accepted 21 July 2007 Available online 11 September 2007
Abstract The main aim of this article is to evaluate, argue and criticise the design models and methods concerning the use of CFRP external flexural strengthening of concrete structures proposed in Fib bulletin 14 – Task Group Fib TG9.3 ‘‘External bonded reinforcement’’ [Fib bulletin 14, FIB TG 9.3 FRPEBR. Externally bonded FRP reinforcement for RC structures. Fe´de´ration Internacionale du be´ton (Fib), Task Group 9.3 FRP, 2001. p. 130]. The three different approaches of flexural strengthening suggested in the above-mentioned document are checked by comparative studies based on different experimental works published by other researchers and analytical applications. By comparing analytical values with experimental results, we draw important conclusions related to: the evaluation of the suggested approaches in terms of complexity; adaptability to real case studies; accuracy of design models proposed in different approaches, and efficiency and general behaviour of CFRP flexural strengthening reinforcement. 2007 Elsevier Ltd. All rights reserved. Keywords: Structural strengthening; Carbon fiber reinforced polymer; Design and structural safety evaluation; Strain limit values; Reinforced concrete
1. Introduction CFRP systems are relatively recent in the construction market. Therefore, the analysis methods and the design guidelines for these materials are almost inexistent and fairly vague. The existing models are not consensual and in general either extremely simplified or very theoretical and complex, with no practical application. The interest in CFRP reinforcement leads to a great development of the research activities in this field. However, the knowledge is still very limited and dispersed, with a lack of guidance code that stipulates accuracy design rules of externally bonded CFRP reinforcement for concrete structures. Due to the lack of normalization, an extensive research program has been conducted to evaluate and criticise the main design models and methods concerning the use of *
Corresponding author. Tel.: +351 218418226; fax: +351 218418380. E-mail address: [email protected] (J.A. Bogas).
0950-0618/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2007.07.025
CFRP external flexural strengthening of concrete structures proposed in Fib bulletin 14 [1]. This paper presents analytical comparative studies based on different experimental works published by other researchers and on the different approaches proposed in Fib bulletin 14 [1], evaluating the complexity, accuracy, adaptability to real case studies and general behaviour of those recent materials in flexural strengthening reinforcement. It is still suggested a simplified design method for flexural strengthening and new values are proposed for the design effective strains depending on the type of CFRP system used (laminates or sheets). 2. Flexural reinforcement 2.1. Cross section analysis for the ultimate limit state in bending Fib bulletin 14 proposes, for the ultimate limit state (ULS) section analysis, a simplified safety evaluation
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
approach based on the traditional equivalent rectangle method, used in steel reinforced concrete with a simplified stress distribution at the section. The proposed model is of simple application when the crush failure first occurs at the concrete, but becomes iterative and too complex when the failure by CFRP debonding is premature, which is the most usual situation [2–4]. In Bogas [5], there is a comparative study for different steel reinforcement ratios, using the simplified traditional method and the rigorous iterative method proposed in Fib bulletin 14, for typical situations of premature CFRP debonding. The study concluded that the use of the traditional method instead of the iterative one, conduces to non-conservative but approximated results with no meaningful round-off errors. Obviously, in an advanced level of a project, it is recommended to use an ‘‘exact method’’ based on the constitutive laws of materials, easy to implement with the current computer systems. However, for brief analysis of flexural strengthening the use of simplified expressions is important to draft designs and to evaluate complex models. In these cases, the following simplified expression is recommended as a better alternative to the method proposed in Fib bulletin 14 [1]: M rd ¼ Aseq zeq fsyd ¼ As zs fsyd þ Af zf ff
ð1Þ
where As and Af are the area of longitudinal steel and the area of CFRP reinforcement, zs and zf are the internal lever arm of steel reinforcement and of CFRP reinforcement, and fsyd and ff are the design value of steel yield strength and the tensile strength of CFRP, respectively. Aseq is the equivalent area of tensile reinforcement and zeq is the equivalent lever arm of internal forces that can be assumed equal to 0.95 dm for usual cases or 0.9 dm for high loaded sections, where dm is the mean effective depth of steel and CFRP reinforcement. As it is concluded in Bogas [5], for current concrete sections, this expression leads to reasonable results and to strengthening levels close to the ones obtained with the simplified methods proposed in Fib bulletin 14 [1]. 2.2. Safety evaluation approaches for CFRP flexural strengthening reinforcement proposed in Fib bulletin 14 While other documents, like ACI 440 [6], only suggest one approach for ULS verification of flexural strengthening reinforcement, the guidance document Fib bulletin 14 proposes three different approaches, which are summarised below. 2.2.1. Approach 1 – CFRP strain limitation This approach consists in restricting the ultimate tensile strain to a conservative value, based upon several experimental results. Therefore, this approach lacks a solid theoretical or analytical basis. Experimental results (Section 3), show that the CFRP tensile strain depends on a wide range of factors, such as
2131
Table 1 Strain limit values Fib bulletin 14 [1] ef,lim (&)
a
6.5–8.5
Japanese Standard [7]
ACI 440 [6]
4.0–8.0
e = f(n; Ef; tf)b
a
For bonding stresses in concrete higher than 1.5 MPa. Strain depends on the number of sheets (n), thickness (tf) and stiffness (Ef). b
CFRP and concrete properties, internal steel yielding and deformation, relation between bonding area and thickness of the CFRP system, etc. Hence, a global strain limit must be conservative to represent the whole range of applications. Its simplicity and suitability for brief calculations is the most attractive advantage of this method. Table 1 shows the strain limit values proposed in different guidance documents. In relation to the table above, it is important to note the following: ACI 440 [6] is the only document that stipulates the strain limit values based on the total thickness and stiffness. In fact, the reinforcements with higher stiffness are much suitable to early premature CFRP debonding, and correspond to much lower values of strain limits [3,8]; None of these documents make the distinction between prefabricated and in situ systems; Although the sheets systems are associated with high dispersion of final application conditions, it is demonstrated that, in general, the premature debonding occurs for higher strain values (Section 3). This can be explained by two factors: the stronger relationship between bonded area and thickness of sheet systems; and the bond advantages of the primaries usually applied.
2.2.2. Approach 2 – calculation of the envelope line of tensile stress The aim of this approach is to calculate the maximum admissible increase in tensile stress between two subsequent flexural cracks, whose equations are presented in Appendix. Approach 2 is based on more solid concepts such as bond stress-slip relation at the interface CFRP-concrete, development of tensile stresses along the CFRP system or spacing of flexural cracks. The calculation of flexural spacing cracks is determinant in this approach, and it is observed by Bogas [5] that the expression proposed by Niedermeier [1] for the calculation of spacing cracks is too conservative when compared with other proposed methods. A study comparing the expression proposed by Niedermeier [1] to the one proposed for the verification of crack width by Fib bulletin 14 [1], is illustrated in Bogas [5]. Differences of about 60% between both expressions in the determination of spacing cracks can be observed. These significant differences can be explained by comparing the expressions of bond stresses proposed
2132
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
by Niedermeier [1] (sfm = 0.44 fctm), and Holzenkampfer in Fib bulletin 14 [1], (sfm = 1.25 fctm). Since the method proposed in Fib bulletin 14 to determine the service limit states (SLS) is relatively well documented by several authors (as an adaptation of the method defined in Eurocode 2 [9]), and concluding that it gives a good estimation of the spacing cracks [5], this method is preferable to that proposed by Niedermeier [1]. Approach 2 potentially provides a better estimation of the real behaviour of CFRP flexural strengthening reinforcement, as it is based on analytical calculations. Nevertheless, one should note that, as this method depends on aleatory and uncertain parameters (such as cracking position and spacing cracks), the tendency will be to replaced it with more realistic and adequate methods.
Experimental tests program of CFRP flexural strengthening reinforcement on reduced slabs models. Juvandes [4]. Experimental tests program of CFRP flexural strengthening of reinforced concrete beams on three models at a real scale, Resende [11]. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates, Oller et al. [12]. Experimental behaviour of RC beams strengthened with CFRP, Ceroni et al. [13]. Strengthening of reinforced concrete beams with CFRP sheets, Bazaa et al. [14]. Flexural strengthening of reinforced concrete beams with externally bonded CFRP systems, Dias et al. [15].
2.2.3. Approach 3 – verification of force transfer between CFRP and concrete This approach is based on a stress distribution along the CFRP considering homogeneous concrete elements without cracking. By using simplified expressions, the shear flow at the interface CFRP-concrete is calculated and the shear stress is restricted to a design bond shear strength, which is considered equal to the bond shear strength of concrete, fcbd. These equations are presented in Appendix. Approach 3 has the advantage of being easy to implement, because it is less complex than Approach 2. In Approach 3 the bonding stress is independent of the level of tension in CFRP, but actually it has been shown that the CFRP systems are more susceptible when the strains are higher, Rostasy and Neaubauer [10]. In comparison with Approach 1, this method involves more bonding parameters namely the area and stiffness of internal steel and CFRP and the bond shear strength of concrete.
The analysis that follows was performed in two steps: (1) observation of experimental works of CFRP flexural strengthening of reinforced concrete beams or slabs; (2) comparison of experimental results to the values obtained by applying Approaches 1, 2 and 3.
3. Study of the proposed approaches and their adequability Comparative studies based on different experimental works published by other researchers were used to evaluate the complexity, accuracy and adaptability of the proposed approaches in Fib bulletin 14. A wide range of experimental works were evaluated, considering different kinds of loadings, geometries, characteristics of materials, types of reinforcements, etc. The following experimental works were analysed:
3.1. CFRP flexural strengthening of reinforced concrete slabs – Juvandes [4] Slabs models and characteristics of materials used in the present experimental work are presented in Fig. 1 and Table 2, respectively. 3.1.1. Results analysis – Approach 1 Tables 3 and 4, show that the analytical results are conservative. Mean values, obtained from the experimental tests of about em,max = 10.5&, are much higher than the strain limits proposed in Fib bulletin 14 [1], (ef,lim. = 6.5– 8.5&). The relation between Pmax (maximum experimental load) and Pt (maximum theoretical load) is Pmax/Pt @ 1.2– 1.45 for series M and Pmax/Pt @ 1.22–1.46 for series L. The difference between Pmax and Pt is lower than the difference between the experimental and theoretical strain limit, due to the strength contribution of internal steel reinforcement. 3.1.2. Results analysis – Approach 2 By analysing and applying the different expressions proposed by Nidermeier [1] and comparing them to the experimental results, one can conclude the following:
Table 2 Characteristics of materials, [4] Steel /3//6 Concrete ( 28 days)
fym (MPa) 330.3/635.6 fcm (MPa)
fum (MPa) 464.6/684.9 fcK (MPa)
eum (&) 56/18.4 fctm (MPa)
Es (GPa) 225 Ecm (GPa)
Class Normal (NL)/Ribbed (NR) Class
Serie M Serie L
56.3 56.3
51.3 51.3
3.8 3.8
36.8 36.8
C50/60 C50/60
Tests
Maker
Type of CFRP
CFRP
fLu (MPa)
eLu (&)
fLu (MPa)
eLu(&)
Ef = 160 GPa/230 GPa
3100/3400
19.4/15
3100/3400
>19/15
S512/sheet Repark 20
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 Table 3 Experimental results, [4] Serie
Models
ef,lim (&)
Pmax (kN)
Srm (cm)
rmax/ffu (%)
Failure mode
M
LC3R
10.92
39.1
6.3
73.9
LC4R
10.3
31.3
6.4
69.7
CFRP failure CFRP failure
LC1S LC2S
10.32 11.83
34.1 37.7
6.4 6.3
53.3 61
L
Debonding Debonding
Table 4 Analytical design values Series
M L
Approach 1a
Approach 2
Approach 3b
ef,lim (&)
Pmax (kN)
ef,lim (&)
Pmax (kN)
6.5 6.5
26.9 25.4
4.7 2.34
22 12
70.5 15.1
a The considered design strain limit was limit = 0.0065 defined in Fib bulletin 14 [1]. b For this approach Pmax = 2P is also defined considering the ultimate crush failure of CFRP, and not only the premature CFRP debonding as it is suggested in Approach 3.
P 0.10 m
0.55 m
P 0.5 m
0.55 m
3φ6 0.08 m
0.45m
Serie M Serie S
3φ3
0.11 m
S512
0.01m
0.1075 m
Repark 20
0.10 m
Série L
Série M
3φ6 0.08 m
0.45m
3φ3
Sheet systems (“Repark20”) – 1 layer 75×0,11+ 1 layer 65×0,11 [mm] Laminate systems (“S512”) – 1 strip 16×1,2 [mm]
Fig. 1. Characteristics of slabs models [4].
As can be verified from the practical examples documented in Bogas [5], this approach is usually very conservative for laminate systems. Analytical results obtained from the proposed expressions are three or four times lower than the experimental values. For sheet systems, usually with lower thickness, values are less conservative, but still about twice as low as the experimental ones. This can be justified by the fact that the expressions derived by Niedermeier [1] strongly depend on thickness. For example, if one layer of sheet systems had been used instead of two, the result values would have been more reasonable and approximate, as shown in the practical example illustrated in Bogas [5]. In Approach 2, for tensile forces slightly above the internal steel yielding stresses, the premature debonding is quickly achieved. Hence, the Niedermeier expressions [1], hardly consider the additional increase of CFRP strain after the steel yielding.
2133
For usual reinforced concrete elements, at real scale, by laminate systems with thickness about 1 mm or more, the Niedermeier expressions lead to maximum strain values about 3&, Bogas [5]. As shown in the practical examples documented in Bogas [5], Approach 2 is not suitable for most of real-life applications of CFRP systems. 3.1.3. Results analysis – Approach 3 By applying the expressions of Approach 3 and comparing them to the experimental results, the following conclusions can be drawn: For laminate systems (series L), the obtained analytical results are too conservative, when compared to the observed experimental values. The premature debonding of the CFRP reinforcement strongly depends on its transmission width, which is not exactly the same as the real width of the laminate (spread adhesive at the borders of the laminate). For current widths of laminate systems (10–30 cm), this difference does not constitute a problem. Nevertheless, for lower widths such as that considered in this experimental work (1.6 cm), differences as small as 1 or 2 cm may conduct to as much as twice the transmission width and load capacity. After a correct adjustment of this effect, the new analytic values are much more accurate and Approach 3 suits the experimental results. Furthermore, the arbitrated bond shear strength was based on concrete tensile tests, which can be different from the real effective bond shear strength at the experimental tests. This has a great influence in the behaviour of the CFRP reinforcement. For sheets (series M), analytical results are higher than the experimental observed values. According to this approach, this means that the premature debonding only occurs for high loading values and the tension failure of CFRP can happen before that, due to the lack of its strengthening capacity. In this case, the analytical Pmax will not be conditioned by the peeling-off as it is considered in Approach 3. Experimental results show that the CFRP rupture occurs earlier than debonding. 3.2. CFRP flexural strengthening of reinforced concrete beams – Resende [11] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 2 and Table 5, respectively. 3.2.1. Results analysis – Approach 1 From the values indicated in Tables 6 and 7, it is observed that the experimental results obtained were about em,max @ 5&, which is lower than the strain limit proposed in Fib bulletin 14 [1]. Therefore, as per the present experimental work, the values proposed in Fib bulletin 14, are
2134
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 P
0.10 m
Table 7 Resume of analytical design values
P
1.0 m
(var.)
(var.)
0.10 m
L = 4.0 m (VGrupo I) / L = 5.0 m (VGrupo II)
VI-2
4φ12
h = 0.50 m
3φ16
2φ8
2φ8
df = 0.35 m
h = 0.40 m
2φ8
Approach 3
ef,lim (&)
Pmax (kN)
VI-1,R VI-2,R VII-1,R
6.5 6.5 6.5
89.3 74.73 72.6
80.8 80.57 221.5
Table 8 Relation between theoretical and experimental load
VII-1 df = 0.45 m
VI-1
Approach 1
b = 0.2 m
lb
lb
Models
Models t
P /Pmax
VI-1,R
VI-2,R
VII-1,R
1.08
1.11
0.83
3φ10 S812 (80×1.2 mm)
Fig. 2. Characteristics of beams models [11].
3.2.2. Results analysis – Approach 3 By applying Approach 3 expressions and comparing its results to the experimental ones, the following can be concluded:
not conservative. Analytical strength reinforcement is inadequate and insufficient. The failure mode occurs earlier than assumed in Fib bulletin 14 [1]. Table 8 summarises the relationship between Pmax and Pt. The strain limits proposed in normative documents are based on usual experimental results. When the cases are slightly different from the usual tests, as it happens in the present experimental work (real scale models with or without side reinforcing strips), failure mode may occur with unexpected ultimate load. In fact, particularly the size of the concrete element has a significant influence at the ultimate strain of the CFRP [3]. From these experimental results one may conclude that there are some strengthening cases where the values proposed in Approach 1 are not conservative.
The obtained numerical values are significantly different from the experimental results, except for beam VI-1,R, where more accurate results are observed. As a matter of fact, for beam VII-1,R, analytical calculations determine a tension failure mode of CFRP, but the experimental ones show a premature debonding of the strengthening reinforcement. That differences of behaviours and results may be related with the following aspects: – Approach 3 was mostly studied for common cases of flexural strengthening of reinforced beams or slabs with bottom externally bonded CFRP systems. On the contrary, in the present experimental work, two of the three beams were tested with side reinforcements, which naturally implicate a different
S812 (80×1.2 mm)
2×S512 (50×1.2 mm)
lb = 1.75 m d = 0.48 m
l b= 1.45 m d = 0.38 m
l b = 1.25 m d = 0.38 m
Table 5 Characteristics of materials [11] Steel reinforcement
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
Class
475
570
23.9
200
A400
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Ec (GPa)
Class
Age – 28 days Age – 108 days
34.8 39.9
29.8 38.3
2.9 3.4
31 32.5
B30
CFRP
Tests
Laminates
flu (MPa)
elu (&)
flu (MPa)
elu (&)
Ef = 160 GPa
3000
–
3050
17
Maker
Type of CFRP
S512/S812
Table 6 Experimental results [11] Models
ef,lim (&)
Pmax (kN)
P0 (kN)b
Srm (m)
Crash failure
Observations
VI-1,R VI-2,R VII-1,Ra
4.19 5.24 6.21 (b), 5.17(L)
82.5 67.5 87.2
47.5 0 20.2
0.125 0.125 0.125
Debonding Debonding Debonding
Initial cracking No initial cracking Initial cracking
a b
(b) – Bottom laminate S812; (L) – side reinforcing laminate S512. P0 – Load when the beams are strengthening.
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
Therefore, the proposed method does not always result in conservative values. The results strongly depend on characteristics and disposition of CFRP systems and on the arbitrated value of the bond shear strength of concrete. 3.3. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates – Oller et al. [12] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 3 and Table 9, respectively. 3.3.1. Results analysis The values in Table 10, show that the experimental results obtained were about em,max @ 4–5&, which is lower than the strain limits proposed in Fib bulletin 14 [1]. As per the experimental work of Resende [11], the estimated values proposed by the normative documents may not be conservative for flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates. The results also depend on the ratio of steel reinforcement, because the
P
2.0 m
Beam type 1
Beam type 2
Stir.φ12//0.15
Stir.φ12//0.10
2φ8
h = 0.20 m
2φ8
h = 0.20 m
distribution of the shear flow at the section. The simplified expression proposed in Fib bulletin 14 [1] has to be changed to take account of different types of reinforcements associated to variable shears stresses distribution along the transversal section height of the beam. The results summarised in Table 8, were obtained assuming the same distribution of shear stress in side and bottom reinforcements, according to Fib equations [1], but in fact, the bottom reinforcement is the most loaded. – The assumed value for the bond shear strength of concrete has great influence in final results. Considering values of about 1.4 MPa for shear strength (experimental value obtained from bond tests) instead of the value proposed in Fib bulletin 14 [1] in the present situation (@2.6 MPa), the results obtained are more accurate. For example, the estimated value of the maximum theoretical load (Pt) for beam V1-2,R, would be of about 63.5 kN instead of 80.57 kN, which is conservative.
2135
2φ16 CFRP b = 0.3 m
2φ20 CFRP b = 0.3 m
Fig. 3. Characteristics of beams models [12].
Table 9 Characteristics of materials [12] Steel reinforcement
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
550
–
–
200
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Ec (GPa)
Age – 28 days
35.2
–
2.76
–
CFRP
flu (MPa) test
Laminated Ef = 150 GPa
1740
Maker elu (&) –
flu (MPa) 2500
elu (&) 16
steel plastification accelerates the stress concentration on the CFRP systems and the subsequent debonding (for example, beam 1/A and 2/A). The result obtained with Approach 3 for the maximum analytical load is about Pmax @ 110 kN, which is a reasonably good estimation considering the experimental data. While, for beams type 1, the estimation is slightly optimistic, for beams type 2 it is conservative. Small differences in the results must be understood by the uncertainty of the real value of the bond shear strength of concrete. 3.4. RC beams strengthened with CFRP – Ceroni F and Prota A [13] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 4 and Tables 11 and 12, respectively.
Table 10 Experimental results [12] Model
Strengthening type
ef,lim (&)
Pmax (kN)
Pmax/Pult (%)
Failure mode
a
Beam type 1
1/D b) 1/C a) 1/C b) 1/B 1/A
2 1 1 1 1
Parallel strips 50 · 1.4 mm Strip 100 · 1.4 mm Strip 100 · 1.4 mmb Strip 100 · 1.4 mm Strip 100 · 1.4 mm
4.112 3.949 4.181 3.646 4.612
100.9 104 121 100.5 109
35 26.8 47.6 22.4 32.9
Peeling Peeling Peeling Peeling Peeling
Beam type 2
2/D a) 2/C 2/B 2/A
1 2 2 1
Strip 100 · 1.4 mm Parallel strips 50 · 1.4 mm Parallel strips 50 · 1.4 mmb Strip 100 · 1.4 mm
3.905 5.509 5.062 5.643
128 118.8 126 155
12.6 25.6 34.6 35.9
Peeling Peeling Peeling Peeling
a b
Length of CFRP – 1.5 m for 1/D a), and 1.8 m for other beams. Additional anchorage by transversal sheets.
2136
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 F/2
For beam D3, Approach 3 leads to conservative and quite accurate estimation, (Pmax @ 34 kN). On the contrary, for beams A2 and A3, the estimation is too optimistic and too far from the reality, (Pmax @ 39 kN). This may be due to both the applying of the strengthening at different distances from the endings of the beam – L1 6¼ L2 (this influence was studied by Li et al. [2]), and the low steel reinforcement ratios. Therefore, it may be concluded that Approach 3 is not adequate for ‘‘A’’ model beams.
F/2
L1
L2 L
Type A-B
Type C-D b = 0.10 m
b = 0.15 m
Αs CFRP(110×0.165 mm2 )
Αs'
h = 0.15 m
h = 0.10 m
Αs'
Αs
3.5. RC beams with CFRP sheets – Bazaa et al. [14]
CFRP(80×0.165 mm 2 )
Fig. 4. Characteristics of beams models [13].
Beams models and characteristics of materials used in the present experimental work are presented in Fig. 5 and Table 14, respectively.
Table 11 Geometrical characteristics of beams [13] Models
L (mm)
L1 (mm)
L2 (mm)
As
As 0
A2 A3 D3
1800 1800 1400
150 300 200
0 200 200
2/8 2/8 2/10
2/8 2/8 2/10
Table 12 Characteristics of materials [13] Steel
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
/8 /10
590 550
690 625
–
200 200
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Es (GPa)
Age – 28 days
29
–
–
–
CFRP sheets
Test
Ef = 230 GPa
flu (MPa) –
3.5.1. Results analysis Table 15, shows a premature failure model of CFRP, with strain limits close to the values proposed in Fib bulletin 14 [1]. Nevertheless, it is important to refer that, as in Ceroni and Prota [13], the use of sheet systems instead of laminate ones decreases the transmission stresses in the interface between CFRP and concrete. The maximum analytical load of Approach 3 is too optimistic and far from the experimental load, (Pmax @ 220 kN).
1000
1000
1000
P/2
P/2
Maker elu (&) –
flu (MPa) 3430
b a
50
elu (&) 15
50
3000
Section Type Beam P111
h = 0.3 m
3.4.1. Results analysis The experimental results in Table 13, indicate a premature failure mode of CFRP, with strain limit values higher than the strain limits proposed in Fib bulletin 14 [1]. This is due to the use of sheet reinforcements instead of laminate systems. With sheet systems the transmission stresses in the interface between CFRP and concrete is much lower than the observed in laminate systems, witch implicates a premature delayed failure mode. Similarly to what had been concluded in other experimental works, the behaviour of the CFRP system also depends on the beam geometry and on the rate of steel reinforcement.
b = 0.20 m
a=2900 mm b=2900 mm Beam P123 a=2400 mm b=1900 mm
A s = 2 cm 2
3×CFRP(167×0.3) mm 2
Fig. 5. Characteristics of beams models [14].
Table 14 Characteristics of materials [14] fym (MPa)
fum (MPa)
eum (&)
E (GPa)
Steel CFRP
430 –
703 –
– –
200 82.03
Concrete
fcm (MPa)
fcK (MPa)
fctk (MPa)
Ec (GPa)
P111
44.3
36.3
2.2
33
Table 13 Experimental results [13] Models
Failure mode
Pmax (kN)
rf (MPa)
ef,lim (&)
A2 A3 D3
Peeling Peeling Peeling
18.5 19.2 40.1
2650 2138 3220
11.5 9.3 14
Table 15 Experimental results [14] Model
Failure mode
Pmax (kN)
rf (MPa)
ef,lim (&)
P111
Peeling
99.8
566
6.9
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
This value indicates that the tension failure mode of CFRP would occur first with no premature debonding. In fact, the strain corresponding to the maximum calculated load of 220 kN is greater than the ultimate strain of the CFRP sheet. 3.6. Flexural strengthening of reinforced concrete beams with externally bonded CFRP systems – Dias et al. [15] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 6 and Table 16, respectively. 3.6.1. Results analysis The values in Table 17, indicate that premature debonding occurs first, for strain limit values within the range proposed in Fib bulletin 14 [1]. As expected, higher strain limits occur in sheet systems with lower thickness than laminates. Adopting Approach 3, the maximum analytical estimated load is conservative for laminate systems and optimistic for sheet systems, (beam V4-Pmax @ 22 kN and
300 P/2
P/2
1740 1800
V2,V3
V4,V5 e V6
b = 0.12 m
b = 0.12 m A s = 2φ6
h = 0.18 m
h = 0.18 m
A s = 2φ6 E st φ6//0.10 A s = 2φ8
E st φ6//0.10 A s = 2φ8
Mbrace laminate HM
Mbrace sheet C1-20 2×(0.111×70)mm2
(1.4×20)mm2
Fig. 6. Characteristics of beams models [15].
Table 16 Characteristics of materials [15] Steel
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
/6//8
555/533
602/543
–
200
Concrete
fcm (MPa)
fcK (MPa)
fctk (MPa)
Ec (GPa)
Age – 28 days
36.7
–
2.9
28.5
CFRP (Maker)
fLu (MPa)
eLu (&)
t (mm)
Ef (GPa)
Laminates-HM Sheets-C1-20
2200 3700
11 15
1.4 0.111
200 240
Table 17 Experimental results [15] Models
Failure mode
Pmax (kN)
rLmax/fLum (%)
ef,lim (&)
V2 V4
Peeling Peeling
37.2 39.22
52.3 62.5
8.07 6.87
2137
beam V2-Pmax @ 76 kN). For beam V2, the rupture of CFRP occurs first for values about Pmax @ 40 kN (based on the ultimate limit strain defined in Table 16). For beam V4, the results strongly depend on the transmission area of the shear stresses in interface between CFRP and concrete, where a collaborative transmission area of ten or more millimetres may double the capacity of CFRP (see also the experimental work of Juvandes [4], previously analysed). 4. Discussion of results The aim of this chapter is to synthesize the main observations and relevant aspects, from the study analysis developed on the present work. According to the obtained experimental results it can be shown that: The expressions of Niedermeier (Approach 2 proposed in Fib bulletin 14 [1]) leads to extremely conservative results and implicates unattractive solutions, with inappropriate and uneconomic levels of strengthening. Approach 2 leads to strain limit values three or four times lower than the observed experimental results. In face of this, the viability and suitability of this method may be contested. On top of that, Approach 2 is complex to implement, implicating a high calculation effort, only justified for detailed and rigorous analysis. Nevertheless, Approach 2 is based on well scientifically fundamentaled concepts. Therefore, it may be pertinent to invest in the calibration and development of this approach in order to make it more attractive and accurate in the future. The other two approaches also have weaknesses. Some of the expressions and values proposed are not suitable to real-life cases. The proposed models are still simplified and too sensitive to any change in the usual characteristics of the reinforcement system or reinforced material. For instance in Approach 1, the premature debonding does not depend on: the steel reinforcement rate; the width and thickness of the CFRP system; the physical characteristics of the CFRP and its application process. Nevertheless, Approach 1 is very easy to implement and therefore, it is quite useful for design purposes. This Approach depends on the experience and sensibility of the engineer, who may be careful in the selection of strain limits for each kind of reinforced case. To conclude, Approach 1 is not suitable for rigorous and advanced analysis, but is a useful method to estimate pre-designed values. It is also a very useful method as a complement of a more detailed analysis to verify the range of the obtained results. The strain limits suggested in Approach 1 of Fib bulletin 14 [1], can be too optimistic in flexural reinforced beams with laminated CFRP systems, mainly for thickness of about 1 mm or more. From the analysed tests of Resende [11] and Oller et al. [12], it was obtained maximum strain limits of about 4–5&, 30–45% less than the values suggested in Fib bulletin 14 [1].
2138
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
Table 18 Summary of the mean values of strain limit, ef,lim, obtained by the analysed tests Experimental tests
Tests type
ef,lim (&) [tests]
ef,lim (&) [bulletin 14]
Juvandes [4] Resende [11] Oller et al. [12] Ceroni et al. [13] Bazaa et al. [14] Dias et al. [15]
Sheet and laminate systems Laminated systems Laminated systems Sheet systems Sheet systems Sheet and laminate systems
10.3–11.8 4.2–6.2 3.6–5.6 9.3–14 6.9 6.8–8.1
6.5–8.5 6.5–8.5 6.5–8.5 6.5–8.5 65–8.5 6.5–8.5
In Table 18, it is possible to compare the mean values of strain limits obtained for each test analysed with limit values proposed in Fib bulletin 14 [1]. Approach 3, is easy to implement and it is based on more fundamentaled concepts than Approach 1. Although the analytical results obtained by applying Approach 3 were reasonably satisfactory for some of the studied cases, for the others they were too far from the experimental results. In Approach 3 the shear strength of concrete has a very important influence on the failure mode of CFRP. This shear strength strongly depends on the characteristics of the superficial concrete layer where the CFRP system is applied, and its value should be determine by in situ tests, like pull-off. It is very important to distinguish between the different types of analysis adopted in laminate systems and sheet systems. Although the general behaviour of the reinforced elements is similar for both types of systems, the laminates are more susceptible to premature debondings. Laminate systems have a stronger relation between thickness and distribution interface area. Hence, the stress concentration is higher and the peeling occurs faster. Due to the simplicity of the proposed approaches (mainly Approach 1 and 3), they cannot account for some important factors like superficial preparation, fibres stretching, adhesive and primary efficiency, status of the reinforced concrete elements, cracking pattern, ending peeling effects, anchorage systems, bonding areas and internal steel ratios, amongst others. Therefore, it is expected a lack of accuracy for flexural reinforcements that are different from the experimental models used for the methods calibration.
5. Conclusions The elaboration of practical examples in Bogas [5] and the study of several experimental works published by other researchers, allowed the evaluation of the approaches defined in Fib bulletin 14. By applying the expressions proposed in Fib bulletin 14 [1] to real case studies and by comparing the results to experimental data, important conclusions, related to the strengthening design of concrete elements reinforced by CFRP systems, could be made.
It is suggested the implementation of computer programs concerning the constitutive laws of materials, when the design procedure must be detailed and rigorous, as it happens in an advanced stage of any engineer project. For brief calculations, quick estimations of reinforcement quantities and as a useful tool to verify the results of more complex analysis, it is suggested the simplified model proposed in 2.1. From the analysis of previous experimental tests, it can be concluded that Approaches 1 and 3 are very sensitive to the type of reinforcement applied. The obtained results can be conservative or optimistic depending on the thickness and bonding area of reinforcements. In spite of the Approach 2 conservative values, the results achieved with this approach are too pessimistic and lead to non economic solutions. Considering the results of previous studies analysed in chapter 3, it is suggested the following procedure for strengthening design of concrete elements reinforced by CFRP systems: For the most common reinforcement cases, the peelingoff using both Approaches 1 and 3 should be verified. Nevertheless, conservative values for strain limits about @5& should be adopted, when laminate systems with more than about 1 mm of thickness or sheet systems with multiple layers are used. For the remaining cases of common reinforcements, the values proposed by Fib bulletin 14 [1], are satisfactory. For uncommon situations of reinforcement, such as high thickness, high Young’s module, side reinforcements, other types of CFRP systems, etc., specific additional researches and tests, should be performed. To conclude, the reported analytical expressions must be constantly improved, to guarantee that their implementation will comprise a wide range of reinforcement situations with more accurate results. Appendix Approach 2 equations according to Fib bulletim 14 Determination of the most unfavourable spacing of flexural cracks: S rm ¼ 2
M cr 1 P P zm ð sfm bf þ ssm d s pÞ
ðI:1Þ
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
where bf and ds are the width of CFRP and effective depth of steel reinforcement, respectively. Whereas ssm and sfm are the mean bond stress of the internal reinforcement and CFRP, calculated by: ssm ¼ 2:25 fctk0:95 ¼ 1:85 fctm
ðI:2Þ
ssm ¼ 0:44 fctm
ðI:3Þ
M cr ¼
Kf ctk;0:95 bh2 6
ðI:4Þ
where Mcr is the bending moment causing cracking, h is the total depth of the member and zm is the mean lever arm that may be determined taking account the axial stiffness of the different layers of reinforcement: zm ¼ 0:85
ðhEf Af þ dEs As1 Þ ðEf Af þ Es As1 Þ
ðI:5Þ
Ef, Es, Af and As are modulus of elasticity of CFRP, modulus of elasticity of steel, area of CFRP and area of longitudinal steel reinforcement, respectively. Determination of the tensile force within the CFRP between two subsequent cracks: The tensile stress, rfd is calculated taking into account strain compatibility and internal force equilibrium (Section 2.1). The shift rule according to EC2 is applied. Determination of the maximum possible increase in tensile stresses in the CFRP: The maximum tensile force, which can be transferred from the CFRP to the concrete by means of bond stresses at the anchorage zone can be determined as follows: ðAÞ
max rfd
0:23 ¼ cc
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi Ef f ck fctm lb lb 2 ; tf lb; max lb; max
lb 6 lb; max ½MPa
ðI:6Þ
The maximum possible stress is closely related to the effective anchorage length lb,max calculated by: lb; max
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ef tf ¼ 1:44 pffiffiffiffiffiffiffiffiffiffiffiffiffi ½mm f ck fctm
ðI:7Þ
where tf is the thickness of CFRP The maximum increase in tensile stress, max Drfd, in an element between two cracks depends on the tensile stress rfd and may be determined based on the following expressions: If rfd 6 rðBÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi S rm 0:185Ef 0:285 fck fctm S rm 4tf
ðBÞ
where : max Drfd 2sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 4 0:1852 Ef fck fctm ðBÞ ðBÞ ¼ þðrf Þ2 rf 5½MPa cc tf ðI:10Þ ðBÞ
Ifrfd P r ;then : max Drfd 8 9 2sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 pffiffiffiffiffiffiffiffiffiffiffiffiffi <1 = 2 0:185 E f f f ck ctm ¼ min 4 þðrfd Þ2 rf 5;ffd rfd :cc ; tf ðI:11Þ
where ffd is the design tensile strength of the CFRP. Verification of the maximum possible increase in tensile stress within the CFRP: Drfd 6 max Drfd Approach 3 equations according to Fib bulletin 14 Verification of force transfer between CFRP and concrete: V d 6 fcbd es1 < eyd : ðII:1Þ 0:95dbf 1 þ AAs1f EEfs If es1 P eyd :
Vd 6 fcbd 0:95dbf
ðII:2Þ
If where: es1, esf are the tensile steel strain and CFRP strain, respectively; eyd is the design value of the yield strain of the steel reinforcement; As1, Af are area of longitudinal tensile steel reinforcement and of CFRP reinforcement, respectively; Ef, Es are modulus of elasticity of CFRP and modulus of elasticity of steel reinforcement; bf is the width of CFRP; d is the effective depth of the member; Vd is the design shear force, which may be equal to Vd DMd/Dx; where DMd is the difference between the moments in two cross sections at distance Dx. fcbd is the design bond shear strength of concrete, which may be calculated as follows: fctk fcbd ¼ 1:8 ½MPa ðII:3Þ cc where fctk is characteristic value of the concrete tensile strength. In Eq. II.1 it was assumed that es1/ef 1. References
then: max Drfd ¼ max
ðI:8Þ
2139
ðAÞ rfd
ðAÞ
ðBÞ
max rfd max Drfd ðBÞ
rf
rfd ðI:9Þ
[1] Fib bulletin 14, FIB TG 9.3 FRPEBR. Externally bonded FRP reinforcement for RC structures. Fe´de´ration Internacionale du be´ton (Fib), Task Group 9.3 FRP, 2001. p. 130. [2] Li Lj, Guo YC, Liu F, Bungey JH. An experimental and numerical study of the effect of thickness and length of CFRP on performance of
2140
[3]
[4]
[5]
[6]
[7] [8] [9]
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
repaired reinforced concrete beams. Constr Build Mater 2006;20(10):901–9. Maalej M, Leong KS. Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRPstrengthened beams. Compos Sci Technol J 2005;65(7,8):1148–58. Juvandes LFP. Strengthening and rehabilitation of concrete structures with composite materials of CFRP. PhD thesis. Faculdade de Engenharia da Universidade do Porto (FEUP), 1999 [in Portuguese]. Bogas JA. Strengthening of reinforced concrete elements with CFRP – design models and safety evaluation. MSc thesis. Instituto Superior Te´cnico (IST). Technical University of Lisbon, 2003 [in Portuguese]. ACI 440. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American concrete institute, reported by ACI comite´ 440 revised July 2000. p. 148. S&P. 30· less weight than steel for the same tensile force. Clever Reinforcement Company, Scherer& Partener bausystem 1998. p. 30. Triantafillou TC, Pelveris N. Strengthened of RC beams with epoxybonded fibre-composite materials. Mater Struct 1992;25:201–11. Eurocode 2, (EC2). Design of Concrete Structures. European Committee for Standardization 1991.
[10] Neubauer U, Rosta´sy FS. Debonding mechanism and model for CFRP-plates as external reinforcement for concrete members. In: Proceedings of the international conference composites in Construction (CCC2001), Porto, 10–12 October 2001. p. 467–72. [11] Resende N. Flexural strengthening of reinforced concrete beams with fiber reinforced plastic plate. MSc thesis. Instituto Superior Te´cnico (IST). Technical University of Lisbon, 2000 [in Portuguese]. [12] Oller E, Salcedo J, Cobo D, Mari A. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates. In: Proceedings of the international conference composites in Construction (CCC2001), Porto, 10–12 October 2001. p. 473–8. [13] Ceroni F, Prota A, Pecce M. Experimental Behavior of RC Beams strengthened with CFRP systems. In: Proceedings of the international conference composites in construction (CCC2001), Porto, 10–12 October 2001. p. 499–504. [14] Bazza M, Missihaun M, Labossie`re P. Strengthening of reinforced concrete beams with CFRP sheets. In: First International Conference on composites in infrastructure (ICCI’96), Tucson, January 1996. [15] Juvandes LFP, Dias SJE, Figueiras JA. Strengthening of reinforced concrete beams with composite materials of CFRP. Structural concrete 2000, FEUP, Porto, 2000.
Construction and Building
MATERIALS
Construction and Building Materials 22 (2008) 2130–2140
www.elsevier.com/locate/conbuildmat
Analysis of the CFRP flexural strengthening reinforcement approaches proposed in Fib bulletin 14 J. Alexandre Bogas *, Augusto Gomes DECivil/ICIST, Instituto Superior Te´cnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Received 17 January 2006; received in revised form 20 July 2007; accepted 21 July 2007 Available online 11 September 2007
Abstract The main aim of this article is to evaluate, argue and criticise the design models and methods concerning the use of CFRP external flexural strengthening of concrete structures proposed in Fib bulletin 14 – Task Group Fib TG9.3 ‘‘External bonded reinforcement’’ [Fib bulletin 14, FIB TG 9.3 FRPEBR. Externally bonded FRP reinforcement for RC structures. Fe´de´ration Internacionale du be´ton (Fib), Task Group 9.3 FRP, 2001. p. 130]. The three different approaches of flexural strengthening suggested in the above-mentioned document are checked by comparative studies based on different experimental works published by other researchers and analytical applications. By comparing analytical values with experimental results, we draw important conclusions related to: the evaluation of the suggested approaches in terms of complexity; adaptability to real case studies; accuracy of design models proposed in different approaches, and efficiency and general behaviour of CFRP flexural strengthening reinforcement. 2007 Elsevier Ltd. All rights reserved. Keywords: Structural strengthening; Carbon fiber reinforced polymer; Design and structural safety evaluation; Strain limit values; Reinforced concrete
1. Introduction CFRP systems are relatively recent in the construction market. Therefore, the analysis methods and the design guidelines for these materials are almost inexistent and fairly vague. The existing models are not consensual and in general either extremely simplified or very theoretical and complex, with no practical application. The interest in CFRP reinforcement leads to a great development of the research activities in this field. However, the knowledge is still very limited and dispersed, with a lack of guidance code that stipulates accuracy design rules of externally bonded CFRP reinforcement for concrete structures. Due to the lack of normalization, an extensive research program has been conducted to evaluate and criticise the main design models and methods concerning the use of *
Corresponding author. Tel.: +351 218418226; fax: +351 218418380. E-mail address: [email protected] (J.A. Bogas).
0950-0618/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2007.07.025
CFRP external flexural strengthening of concrete structures proposed in Fib bulletin 14 [1]. This paper presents analytical comparative studies based on different experimental works published by other researchers and on the different approaches proposed in Fib bulletin 14 [1], evaluating the complexity, accuracy, adaptability to real case studies and general behaviour of those recent materials in flexural strengthening reinforcement. It is still suggested a simplified design method for flexural strengthening and new values are proposed for the design effective strains depending on the type of CFRP system used (laminates or sheets). 2. Flexural reinforcement 2.1. Cross section analysis for the ultimate limit state in bending Fib bulletin 14 proposes, for the ultimate limit state (ULS) section analysis, a simplified safety evaluation
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
approach based on the traditional equivalent rectangle method, used in steel reinforced concrete with a simplified stress distribution at the section. The proposed model is of simple application when the crush failure first occurs at the concrete, but becomes iterative and too complex when the failure by CFRP debonding is premature, which is the most usual situation [2–4]. In Bogas [5], there is a comparative study for different steel reinforcement ratios, using the simplified traditional method and the rigorous iterative method proposed in Fib bulletin 14, for typical situations of premature CFRP debonding. The study concluded that the use of the traditional method instead of the iterative one, conduces to non-conservative but approximated results with no meaningful round-off errors. Obviously, in an advanced level of a project, it is recommended to use an ‘‘exact method’’ based on the constitutive laws of materials, easy to implement with the current computer systems. However, for brief analysis of flexural strengthening the use of simplified expressions is important to draft designs and to evaluate complex models. In these cases, the following simplified expression is recommended as a better alternative to the method proposed in Fib bulletin 14 [1]: M rd ¼ Aseq zeq fsyd ¼ As zs fsyd þ Af zf ff
ð1Þ
where As and Af are the area of longitudinal steel and the area of CFRP reinforcement, zs and zf are the internal lever arm of steel reinforcement and of CFRP reinforcement, and fsyd and ff are the design value of steel yield strength and the tensile strength of CFRP, respectively. Aseq is the equivalent area of tensile reinforcement and zeq is the equivalent lever arm of internal forces that can be assumed equal to 0.95 dm for usual cases or 0.9 dm for high loaded sections, where dm is the mean effective depth of steel and CFRP reinforcement. As it is concluded in Bogas [5], for current concrete sections, this expression leads to reasonable results and to strengthening levels close to the ones obtained with the simplified methods proposed in Fib bulletin 14 [1]. 2.2. Safety evaluation approaches for CFRP flexural strengthening reinforcement proposed in Fib bulletin 14 While other documents, like ACI 440 [6], only suggest one approach for ULS verification of flexural strengthening reinforcement, the guidance document Fib bulletin 14 proposes three different approaches, which are summarised below. 2.2.1. Approach 1 – CFRP strain limitation This approach consists in restricting the ultimate tensile strain to a conservative value, based upon several experimental results. Therefore, this approach lacks a solid theoretical or analytical basis. Experimental results (Section 3), show that the CFRP tensile strain depends on a wide range of factors, such as
2131
Table 1 Strain limit values Fib bulletin 14 [1] ef,lim (&)
a
6.5–8.5
Japanese Standard [7]
ACI 440 [6]
4.0–8.0
e = f(n; Ef; tf)b
a
For bonding stresses in concrete higher than 1.5 MPa. Strain depends on the number of sheets (n), thickness (tf) and stiffness (Ef). b
CFRP and concrete properties, internal steel yielding and deformation, relation between bonding area and thickness of the CFRP system, etc. Hence, a global strain limit must be conservative to represent the whole range of applications. Its simplicity and suitability for brief calculations is the most attractive advantage of this method. Table 1 shows the strain limit values proposed in different guidance documents. In relation to the table above, it is important to note the following: ACI 440 [6] is the only document that stipulates the strain limit values based on the total thickness and stiffness. In fact, the reinforcements with higher stiffness are much suitable to early premature CFRP debonding, and correspond to much lower values of strain limits [3,8]; None of these documents make the distinction between prefabricated and in situ systems; Although the sheets systems are associated with high dispersion of final application conditions, it is demonstrated that, in general, the premature debonding occurs for higher strain values (Section 3). This can be explained by two factors: the stronger relationship between bonded area and thickness of sheet systems; and the bond advantages of the primaries usually applied.
2.2.2. Approach 2 – calculation of the envelope line of tensile stress The aim of this approach is to calculate the maximum admissible increase in tensile stress between two subsequent flexural cracks, whose equations are presented in Appendix. Approach 2 is based on more solid concepts such as bond stress-slip relation at the interface CFRP-concrete, development of tensile stresses along the CFRP system or spacing of flexural cracks. The calculation of flexural spacing cracks is determinant in this approach, and it is observed by Bogas [5] that the expression proposed by Niedermeier [1] for the calculation of spacing cracks is too conservative when compared with other proposed methods. A study comparing the expression proposed by Niedermeier [1] to the one proposed for the verification of crack width by Fib bulletin 14 [1], is illustrated in Bogas [5]. Differences of about 60% between both expressions in the determination of spacing cracks can be observed. These significant differences can be explained by comparing the expressions of bond stresses proposed
2132
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
by Niedermeier [1] (sfm = 0.44 fctm), and Holzenkampfer in Fib bulletin 14 [1], (sfm = 1.25 fctm). Since the method proposed in Fib bulletin 14 to determine the service limit states (SLS) is relatively well documented by several authors (as an adaptation of the method defined in Eurocode 2 [9]), and concluding that it gives a good estimation of the spacing cracks [5], this method is preferable to that proposed by Niedermeier [1]. Approach 2 potentially provides a better estimation of the real behaviour of CFRP flexural strengthening reinforcement, as it is based on analytical calculations. Nevertheless, one should note that, as this method depends on aleatory and uncertain parameters (such as cracking position and spacing cracks), the tendency will be to replaced it with more realistic and adequate methods.
Experimental tests program of CFRP flexural strengthening reinforcement on reduced slabs models. Juvandes [4]. Experimental tests program of CFRP flexural strengthening of reinforced concrete beams on three models at a real scale, Resende [11]. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates, Oller et al. [12]. Experimental behaviour of RC beams strengthened with CFRP, Ceroni et al. [13]. Strengthening of reinforced concrete beams with CFRP sheets, Bazaa et al. [14]. Flexural strengthening of reinforced concrete beams with externally bonded CFRP systems, Dias et al. [15].
2.2.3. Approach 3 – verification of force transfer between CFRP and concrete This approach is based on a stress distribution along the CFRP considering homogeneous concrete elements without cracking. By using simplified expressions, the shear flow at the interface CFRP-concrete is calculated and the shear stress is restricted to a design bond shear strength, which is considered equal to the bond shear strength of concrete, fcbd. These equations are presented in Appendix. Approach 3 has the advantage of being easy to implement, because it is less complex than Approach 2. In Approach 3 the bonding stress is independent of the level of tension in CFRP, but actually it has been shown that the CFRP systems are more susceptible when the strains are higher, Rostasy and Neaubauer [10]. In comparison with Approach 1, this method involves more bonding parameters namely the area and stiffness of internal steel and CFRP and the bond shear strength of concrete.
The analysis that follows was performed in two steps: (1) observation of experimental works of CFRP flexural strengthening of reinforced concrete beams or slabs; (2) comparison of experimental results to the values obtained by applying Approaches 1, 2 and 3.
3. Study of the proposed approaches and their adequability Comparative studies based on different experimental works published by other researchers were used to evaluate the complexity, accuracy and adaptability of the proposed approaches in Fib bulletin 14. A wide range of experimental works were evaluated, considering different kinds of loadings, geometries, characteristics of materials, types of reinforcements, etc. The following experimental works were analysed:
3.1. CFRP flexural strengthening of reinforced concrete slabs – Juvandes [4] Slabs models and characteristics of materials used in the present experimental work are presented in Fig. 1 and Table 2, respectively. 3.1.1. Results analysis – Approach 1 Tables 3 and 4, show that the analytical results are conservative. Mean values, obtained from the experimental tests of about em,max = 10.5&, are much higher than the strain limits proposed in Fib bulletin 14 [1], (ef,lim. = 6.5– 8.5&). The relation between Pmax (maximum experimental load) and Pt (maximum theoretical load) is Pmax/Pt @ 1.2– 1.45 for series M and Pmax/Pt @ 1.22–1.46 for series L. The difference between Pmax and Pt is lower than the difference between the experimental and theoretical strain limit, due to the strength contribution of internal steel reinforcement. 3.1.2. Results analysis – Approach 2 By analysing and applying the different expressions proposed by Nidermeier [1] and comparing them to the experimental results, one can conclude the following:
Table 2 Characteristics of materials, [4] Steel /3//6 Concrete ( 28 days)
fym (MPa) 330.3/635.6 fcm (MPa)
fum (MPa) 464.6/684.9 fcK (MPa)
eum (&) 56/18.4 fctm (MPa)
Es (GPa) 225 Ecm (GPa)
Class Normal (NL)/Ribbed (NR) Class
Serie M Serie L
56.3 56.3
51.3 51.3
3.8 3.8
36.8 36.8
C50/60 C50/60
Tests
Maker
Type of CFRP
CFRP
fLu (MPa)
eLu (&)
fLu (MPa)
eLu(&)
Ef = 160 GPa/230 GPa
3100/3400
19.4/15
3100/3400
>19/15
S512/sheet Repark 20
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 Table 3 Experimental results, [4] Serie
Models
ef,lim (&)
Pmax (kN)
Srm (cm)
rmax/ffu (%)
Failure mode
M
LC3R
10.92
39.1
6.3
73.9
LC4R
10.3
31.3
6.4
69.7
CFRP failure CFRP failure
LC1S LC2S
10.32 11.83
34.1 37.7
6.4 6.3
53.3 61
L
Debonding Debonding
Table 4 Analytical design values Series
M L
Approach 1a
Approach 2
Approach 3b
ef,lim (&)
Pmax (kN)
ef,lim (&)
Pmax (kN)
6.5 6.5
26.9 25.4
4.7 2.34
22 12
70.5 15.1
a The considered design strain limit was limit = 0.0065 defined in Fib bulletin 14 [1]. b For this approach Pmax = 2P is also defined considering the ultimate crush failure of CFRP, and not only the premature CFRP debonding as it is suggested in Approach 3.
P 0.10 m
0.55 m
P 0.5 m
0.55 m
3φ6 0.08 m
0.45m
Serie M Serie S
3φ3
0.11 m
S512
0.01m
0.1075 m
Repark 20
0.10 m
Série L
Série M
3φ6 0.08 m
0.45m
3φ3
Sheet systems (“Repark20”) – 1 layer 75×0,11+ 1 layer 65×0,11 [mm] Laminate systems (“S512”) – 1 strip 16×1,2 [mm]
Fig. 1. Characteristics of slabs models [4].
As can be verified from the practical examples documented in Bogas [5], this approach is usually very conservative for laminate systems. Analytical results obtained from the proposed expressions are three or four times lower than the experimental values. For sheet systems, usually with lower thickness, values are less conservative, but still about twice as low as the experimental ones. This can be justified by the fact that the expressions derived by Niedermeier [1] strongly depend on thickness. For example, if one layer of sheet systems had been used instead of two, the result values would have been more reasonable and approximate, as shown in the practical example illustrated in Bogas [5]. In Approach 2, for tensile forces slightly above the internal steel yielding stresses, the premature debonding is quickly achieved. Hence, the Niedermeier expressions [1], hardly consider the additional increase of CFRP strain after the steel yielding.
2133
For usual reinforced concrete elements, at real scale, by laminate systems with thickness about 1 mm or more, the Niedermeier expressions lead to maximum strain values about 3&, Bogas [5]. As shown in the practical examples documented in Bogas [5], Approach 2 is not suitable for most of real-life applications of CFRP systems. 3.1.3. Results analysis – Approach 3 By applying the expressions of Approach 3 and comparing them to the experimental results, the following conclusions can be drawn: For laminate systems (series L), the obtained analytical results are too conservative, when compared to the observed experimental values. The premature debonding of the CFRP reinforcement strongly depends on its transmission width, which is not exactly the same as the real width of the laminate (spread adhesive at the borders of the laminate). For current widths of laminate systems (10–30 cm), this difference does not constitute a problem. Nevertheless, for lower widths such as that considered in this experimental work (1.6 cm), differences as small as 1 or 2 cm may conduct to as much as twice the transmission width and load capacity. After a correct adjustment of this effect, the new analytic values are much more accurate and Approach 3 suits the experimental results. Furthermore, the arbitrated bond shear strength was based on concrete tensile tests, which can be different from the real effective bond shear strength at the experimental tests. This has a great influence in the behaviour of the CFRP reinforcement. For sheets (series M), analytical results are higher than the experimental observed values. According to this approach, this means that the premature debonding only occurs for high loading values and the tension failure of CFRP can happen before that, due to the lack of its strengthening capacity. In this case, the analytical Pmax will not be conditioned by the peeling-off as it is considered in Approach 3. Experimental results show that the CFRP rupture occurs earlier than debonding. 3.2. CFRP flexural strengthening of reinforced concrete beams – Resende [11] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 2 and Table 5, respectively. 3.2.1. Results analysis – Approach 1 From the values indicated in Tables 6 and 7, it is observed that the experimental results obtained were about em,max @ 5&, which is lower than the strain limit proposed in Fib bulletin 14 [1]. Therefore, as per the present experimental work, the values proposed in Fib bulletin 14, are
2134
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 P
0.10 m
Table 7 Resume of analytical design values
P
1.0 m
(var.)
(var.)
0.10 m
L = 4.0 m (VGrupo I) / L = 5.0 m (VGrupo II)
VI-2
4φ12
h = 0.50 m
3φ16
2φ8
2φ8
df = 0.35 m
h = 0.40 m
2φ8
Approach 3
ef,lim (&)
Pmax (kN)
VI-1,R VI-2,R VII-1,R
6.5 6.5 6.5
89.3 74.73 72.6
80.8 80.57 221.5
Table 8 Relation between theoretical and experimental load
VII-1 df = 0.45 m
VI-1
Approach 1
b = 0.2 m
lb
lb
Models
Models t
P /Pmax
VI-1,R
VI-2,R
VII-1,R
1.08
1.11
0.83
3φ10 S812 (80×1.2 mm)
Fig. 2. Characteristics of beams models [11].
3.2.2. Results analysis – Approach 3 By applying Approach 3 expressions and comparing its results to the experimental ones, the following can be concluded:
not conservative. Analytical strength reinforcement is inadequate and insufficient. The failure mode occurs earlier than assumed in Fib bulletin 14 [1]. Table 8 summarises the relationship between Pmax and Pt. The strain limits proposed in normative documents are based on usual experimental results. When the cases are slightly different from the usual tests, as it happens in the present experimental work (real scale models with or without side reinforcing strips), failure mode may occur with unexpected ultimate load. In fact, particularly the size of the concrete element has a significant influence at the ultimate strain of the CFRP [3]. From these experimental results one may conclude that there are some strengthening cases where the values proposed in Approach 1 are not conservative.
The obtained numerical values are significantly different from the experimental results, except for beam VI-1,R, where more accurate results are observed. As a matter of fact, for beam VII-1,R, analytical calculations determine a tension failure mode of CFRP, but the experimental ones show a premature debonding of the strengthening reinforcement. That differences of behaviours and results may be related with the following aspects: – Approach 3 was mostly studied for common cases of flexural strengthening of reinforced beams or slabs with bottom externally bonded CFRP systems. On the contrary, in the present experimental work, two of the three beams were tested with side reinforcements, which naturally implicate a different
S812 (80×1.2 mm)
2×S512 (50×1.2 mm)
lb = 1.75 m d = 0.48 m
l b= 1.45 m d = 0.38 m
l b = 1.25 m d = 0.38 m
Table 5 Characteristics of materials [11] Steel reinforcement
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
Class
475
570
23.9
200
A400
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Ec (GPa)
Class
Age – 28 days Age – 108 days
34.8 39.9
29.8 38.3
2.9 3.4
31 32.5
B30
CFRP
Tests
Laminates
flu (MPa)
elu (&)
flu (MPa)
elu (&)
Ef = 160 GPa
3000
–
3050
17
Maker
Type of CFRP
S512/S812
Table 6 Experimental results [11] Models
ef,lim (&)
Pmax (kN)
P0 (kN)b
Srm (m)
Crash failure
Observations
VI-1,R VI-2,R VII-1,Ra
4.19 5.24 6.21 (b), 5.17(L)
82.5 67.5 87.2
47.5 0 20.2
0.125 0.125 0.125
Debonding Debonding Debonding
Initial cracking No initial cracking Initial cracking
a b
(b) – Bottom laminate S812; (L) – side reinforcing laminate S512. P0 – Load when the beams are strengthening.
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
Therefore, the proposed method does not always result in conservative values. The results strongly depend on characteristics and disposition of CFRP systems and on the arbitrated value of the bond shear strength of concrete. 3.3. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates – Oller et al. [12] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 3 and Table 9, respectively. 3.3.1. Results analysis The values in Table 10, show that the experimental results obtained were about em,max @ 4–5&, which is lower than the strain limits proposed in Fib bulletin 14 [1]. As per the experimental work of Resende [11], the estimated values proposed by the normative documents may not be conservative for flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates. The results also depend on the ratio of steel reinforcement, because the
P
2.0 m
Beam type 1
Beam type 2
Stir.φ12//0.15
Stir.φ12//0.10
2φ8
h = 0.20 m
2φ8
h = 0.20 m
distribution of the shear flow at the section. The simplified expression proposed in Fib bulletin 14 [1] has to be changed to take account of different types of reinforcements associated to variable shears stresses distribution along the transversal section height of the beam. The results summarised in Table 8, were obtained assuming the same distribution of shear stress in side and bottom reinforcements, according to Fib equations [1], but in fact, the bottom reinforcement is the most loaded. – The assumed value for the bond shear strength of concrete has great influence in final results. Considering values of about 1.4 MPa for shear strength (experimental value obtained from bond tests) instead of the value proposed in Fib bulletin 14 [1] in the present situation (@2.6 MPa), the results obtained are more accurate. For example, the estimated value of the maximum theoretical load (Pt) for beam V1-2,R, would be of about 63.5 kN instead of 80.57 kN, which is conservative.
2135
2φ16 CFRP b = 0.3 m
2φ20 CFRP b = 0.3 m
Fig. 3. Characteristics of beams models [12].
Table 9 Characteristics of materials [12] Steel reinforcement
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
550
–
–
200
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Ec (GPa)
Age – 28 days
35.2
–
2.76
–
CFRP
flu (MPa) test
Laminated Ef = 150 GPa
1740
Maker elu (&) –
flu (MPa) 2500
elu (&) 16
steel plastification accelerates the stress concentration on the CFRP systems and the subsequent debonding (for example, beam 1/A and 2/A). The result obtained with Approach 3 for the maximum analytical load is about Pmax @ 110 kN, which is a reasonably good estimation considering the experimental data. While, for beams type 1, the estimation is slightly optimistic, for beams type 2 it is conservative. Small differences in the results must be understood by the uncertainty of the real value of the bond shear strength of concrete. 3.4. RC beams strengthened with CFRP – Ceroni F and Prota A [13] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 4 and Tables 11 and 12, respectively.
Table 10 Experimental results [12] Model
Strengthening type
ef,lim (&)
Pmax (kN)
Pmax/Pult (%)
Failure mode
a
Beam type 1
1/D b) 1/C a) 1/C b) 1/B 1/A
2 1 1 1 1
Parallel strips 50 · 1.4 mm Strip 100 · 1.4 mm Strip 100 · 1.4 mmb Strip 100 · 1.4 mm Strip 100 · 1.4 mm
4.112 3.949 4.181 3.646 4.612
100.9 104 121 100.5 109
35 26.8 47.6 22.4 32.9
Peeling Peeling Peeling Peeling Peeling
Beam type 2
2/D a) 2/C 2/B 2/A
1 2 2 1
Strip 100 · 1.4 mm Parallel strips 50 · 1.4 mm Parallel strips 50 · 1.4 mmb Strip 100 · 1.4 mm
3.905 5.509 5.062 5.643
128 118.8 126 155
12.6 25.6 34.6 35.9
Peeling Peeling Peeling Peeling
a b
Length of CFRP – 1.5 m for 1/D a), and 1.8 m for other beams. Additional anchorage by transversal sheets.
2136
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140 F/2
For beam D3, Approach 3 leads to conservative and quite accurate estimation, (Pmax @ 34 kN). On the contrary, for beams A2 and A3, the estimation is too optimistic and too far from the reality, (Pmax @ 39 kN). This may be due to both the applying of the strengthening at different distances from the endings of the beam – L1 6¼ L2 (this influence was studied by Li et al. [2]), and the low steel reinforcement ratios. Therefore, it may be concluded that Approach 3 is not adequate for ‘‘A’’ model beams.
F/2
L1
L2 L
Type A-B
Type C-D b = 0.10 m
b = 0.15 m
Αs CFRP(110×0.165 mm2 )
Αs'
h = 0.15 m
h = 0.10 m
Αs'
Αs
3.5. RC beams with CFRP sheets – Bazaa et al. [14]
CFRP(80×0.165 mm 2 )
Fig. 4. Characteristics of beams models [13].
Beams models and characteristics of materials used in the present experimental work are presented in Fig. 5 and Table 14, respectively.
Table 11 Geometrical characteristics of beams [13] Models
L (mm)
L1 (mm)
L2 (mm)
As
As 0
A2 A3 D3
1800 1800 1400
150 300 200
0 200 200
2/8 2/8 2/10
2/8 2/8 2/10
Table 12 Characteristics of materials [13] Steel
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
/8 /10
590 550
690 625
–
200 200
Concrete
fcm (MPa)
fck (MPa)
fctm (MPa)
Es (GPa)
Age – 28 days
29
–
–
–
CFRP sheets
Test
Ef = 230 GPa
flu (MPa) –
3.5.1. Results analysis Table 15, shows a premature failure model of CFRP, with strain limits close to the values proposed in Fib bulletin 14 [1]. Nevertheless, it is important to refer that, as in Ceroni and Prota [13], the use of sheet systems instead of laminate ones decreases the transmission stresses in the interface between CFRP and concrete. The maximum analytical load of Approach 3 is too optimistic and far from the experimental load, (Pmax @ 220 kN).
1000
1000
1000
P/2
P/2
Maker elu (&) –
flu (MPa) 3430
b a
50
elu (&) 15
50
3000
Section Type Beam P111
h = 0.3 m
3.4.1. Results analysis The experimental results in Table 13, indicate a premature failure mode of CFRP, with strain limit values higher than the strain limits proposed in Fib bulletin 14 [1]. This is due to the use of sheet reinforcements instead of laminate systems. With sheet systems the transmission stresses in the interface between CFRP and concrete is much lower than the observed in laminate systems, witch implicates a premature delayed failure mode. Similarly to what had been concluded in other experimental works, the behaviour of the CFRP system also depends on the beam geometry and on the rate of steel reinforcement.
b = 0.20 m
a=2900 mm b=2900 mm Beam P123 a=2400 mm b=1900 mm
A s = 2 cm 2
3×CFRP(167×0.3) mm 2
Fig. 5. Characteristics of beams models [14].
Table 14 Characteristics of materials [14] fym (MPa)
fum (MPa)
eum (&)
E (GPa)
Steel CFRP
430 –
703 –
– –
200 82.03
Concrete
fcm (MPa)
fcK (MPa)
fctk (MPa)
Ec (GPa)
P111
44.3
36.3
2.2
33
Table 13 Experimental results [13] Models
Failure mode
Pmax (kN)
rf (MPa)
ef,lim (&)
A2 A3 D3
Peeling Peeling Peeling
18.5 19.2 40.1
2650 2138 3220
11.5 9.3 14
Table 15 Experimental results [14] Model
Failure mode
Pmax (kN)
rf (MPa)
ef,lim (&)
P111
Peeling
99.8
566
6.9
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
This value indicates that the tension failure mode of CFRP would occur first with no premature debonding. In fact, the strain corresponding to the maximum calculated load of 220 kN is greater than the ultimate strain of the CFRP sheet. 3.6. Flexural strengthening of reinforced concrete beams with externally bonded CFRP systems – Dias et al. [15] Beams models and characteristics of materials used in the present experimental work are presented in Fig. 6 and Table 16, respectively. 3.6.1. Results analysis The values in Table 17, indicate that premature debonding occurs first, for strain limit values within the range proposed in Fib bulletin 14 [1]. As expected, higher strain limits occur in sheet systems with lower thickness than laminates. Adopting Approach 3, the maximum analytical estimated load is conservative for laminate systems and optimistic for sheet systems, (beam V4-Pmax @ 22 kN and
300 P/2
P/2
1740 1800
V2,V3
V4,V5 e V6
b = 0.12 m
b = 0.12 m A s = 2φ6
h = 0.18 m
h = 0.18 m
A s = 2φ6 E st φ6//0.10 A s = 2φ8
E st φ6//0.10 A s = 2φ8
Mbrace laminate HM
Mbrace sheet C1-20 2×(0.111×70)mm2
(1.4×20)mm2
Fig. 6. Characteristics of beams models [15].
Table 16 Characteristics of materials [15] Steel
fym (MPa)
fum (MPa)
eum (&)
Es (GPa)
/6//8
555/533
602/543
–
200
Concrete
fcm (MPa)
fcK (MPa)
fctk (MPa)
Ec (GPa)
Age – 28 days
36.7
–
2.9
28.5
CFRP (Maker)
fLu (MPa)
eLu (&)
t (mm)
Ef (GPa)
Laminates-HM Sheets-C1-20
2200 3700
11 15
1.4 0.111
200 240
Table 17 Experimental results [15] Models
Failure mode
Pmax (kN)
rLmax/fLum (%)
ef,lim (&)
V2 V4
Peeling Peeling
37.2 39.22
52.3 62.5
8.07 6.87
2137
beam V2-Pmax @ 76 kN). For beam V2, the rupture of CFRP occurs first for values about Pmax @ 40 kN (based on the ultimate limit strain defined in Table 16). For beam V4, the results strongly depend on the transmission area of the shear stresses in interface between CFRP and concrete, where a collaborative transmission area of ten or more millimetres may double the capacity of CFRP (see also the experimental work of Juvandes [4], previously analysed). 4. Discussion of results The aim of this chapter is to synthesize the main observations and relevant aspects, from the study analysis developed on the present work. According to the obtained experimental results it can be shown that: The expressions of Niedermeier (Approach 2 proposed in Fib bulletin 14 [1]) leads to extremely conservative results and implicates unattractive solutions, with inappropriate and uneconomic levels of strengthening. Approach 2 leads to strain limit values three or four times lower than the observed experimental results. In face of this, the viability and suitability of this method may be contested. On top of that, Approach 2 is complex to implement, implicating a high calculation effort, only justified for detailed and rigorous analysis. Nevertheless, Approach 2 is based on well scientifically fundamentaled concepts. Therefore, it may be pertinent to invest in the calibration and development of this approach in order to make it more attractive and accurate in the future. The other two approaches also have weaknesses. Some of the expressions and values proposed are not suitable to real-life cases. The proposed models are still simplified and too sensitive to any change in the usual characteristics of the reinforcement system or reinforced material. For instance in Approach 1, the premature debonding does not depend on: the steel reinforcement rate; the width and thickness of the CFRP system; the physical characteristics of the CFRP and its application process. Nevertheless, Approach 1 is very easy to implement and therefore, it is quite useful for design purposes. This Approach depends on the experience and sensibility of the engineer, who may be careful in the selection of strain limits for each kind of reinforced case. To conclude, Approach 1 is not suitable for rigorous and advanced analysis, but is a useful method to estimate pre-designed values. It is also a very useful method as a complement of a more detailed analysis to verify the range of the obtained results. The strain limits suggested in Approach 1 of Fib bulletin 14 [1], can be too optimistic in flexural reinforced beams with laminated CFRP systems, mainly for thickness of about 1 mm or more. From the analysed tests of Resende [11] and Oller et al. [12], it was obtained maximum strain limits of about 4–5&, 30–45% less than the values suggested in Fib bulletin 14 [1].
2138
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
Table 18 Summary of the mean values of strain limit, ef,lim, obtained by the analysed tests Experimental tests
Tests type
ef,lim (&) [tests]
ef,lim (&) [bulletin 14]
Juvandes [4] Resende [11] Oller et al. [12] Ceroni et al. [13] Bazaa et al. [14] Dias et al. [15]
Sheet and laminate systems Laminated systems Laminated systems Sheet systems Sheet systems Sheet and laminate systems
10.3–11.8 4.2–6.2 3.6–5.6 9.3–14 6.9 6.8–8.1
6.5–8.5 6.5–8.5 6.5–8.5 6.5–8.5 65–8.5 6.5–8.5
In Table 18, it is possible to compare the mean values of strain limits obtained for each test analysed with limit values proposed in Fib bulletin 14 [1]. Approach 3, is easy to implement and it is based on more fundamentaled concepts than Approach 1. Although the analytical results obtained by applying Approach 3 were reasonably satisfactory for some of the studied cases, for the others they were too far from the experimental results. In Approach 3 the shear strength of concrete has a very important influence on the failure mode of CFRP. This shear strength strongly depends on the characteristics of the superficial concrete layer where the CFRP system is applied, and its value should be determine by in situ tests, like pull-off. It is very important to distinguish between the different types of analysis adopted in laminate systems and sheet systems. Although the general behaviour of the reinforced elements is similar for both types of systems, the laminates are more susceptible to premature debondings. Laminate systems have a stronger relation between thickness and distribution interface area. Hence, the stress concentration is higher and the peeling occurs faster. Due to the simplicity of the proposed approaches (mainly Approach 1 and 3), they cannot account for some important factors like superficial preparation, fibres stretching, adhesive and primary efficiency, status of the reinforced concrete elements, cracking pattern, ending peeling effects, anchorage systems, bonding areas and internal steel ratios, amongst others. Therefore, it is expected a lack of accuracy for flexural reinforcements that are different from the experimental models used for the methods calibration.
5. Conclusions The elaboration of practical examples in Bogas [5] and the study of several experimental works published by other researchers, allowed the evaluation of the approaches defined in Fib bulletin 14. By applying the expressions proposed in Fib bulletin 14 [1] to real case studies and by comparing the results to experimental data, important conclusions, related to the strengthening design of concrete elements reinforced by CFRP systems, could be made.
It is suggested the implementation of computer programs concerning the constitutive laws of materials, when the design procedure must be detailed and rigorous, as it happens in an advanced stage of any engineer project. For brief calculations, quick estimations of reinforcement quantities and as a useful tool to verify the results of more complex analysis, it is suggested the simplified model proposed in 2.1. From the analysis of previous experimental tests, it can be concluded that Approaches 1 and 3 are very sensitive to the type of reinforcement applied. The obtained results can be conservative or optimistic depending on the thickness and bonding area of reinforcements. In spite of the Approach 2 conservative values, the results achieved with this approach are too pessimistic and lead to non economic solutions. Considering the results of previous studies analysed in chapter 3, it is suggested the following procedure for strengthening design of concrete elements reinforced by CFRP systems: For the most common reinforcement cases, the peelingoff using both Approaches 1 and 3 should be verified. Nevertheless, conservative values for strain limits about @5& should be adopted, when laminate systems with more than about 1 mm of thickness or sheet systems with multiple layers are used. For the remaining cases of common reinforcements, the values proposed by Fib bulletin 14 [1], are satisfactory. For uncommon situations of reinforcement, such as high thickness, high Young’s module, side reinforcements, other types of CFRP systems, etc., specific additional researches and tests, should be performed. To conclude, the reported analytical expressions must be constantly improved, to guarantee that their implementation will comprise a wide range of reinforcement situations with more accurate results. Appendix Approach 2 equations according to Fib bulletim 14 Determination of the most unfavourable spacing of flexural cracks: S rm ¼ 2
M cr 1 P P zm ð sfm bf þ ssm d s pÞ
ðI:1Þ
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
where bf and ds are the width of CFRP and effective depth of steel reinforcement, respectively. Whereas ssm and sfm are the mean bond stress of the internal reinforcement and CFRP, calculated by: ssm ¼ 2:25 fctk0:95 ¼ 1:85 fctm
ðI:2Þ
ssm ¼ 0:44 fctm
ðI:3Þ
M cr ¼
Kf ctk;0:95 bh2 6
ðI:4Þ
where Mcr is the bending moment causing cracking, h is the total depth of the member and zm is the mean lever arm that may be determined taking account the axial stiffness of the different layers of reinforcement: zm ¼ 0:85
ðhEf Af þ dEs As1 Þ ðEf Af þ Es As1 Þ
ðI:5Þ
Ef, Es, Af and As are modulus of elasticity of CFRP, modulus of elasticity of steel, area of CFRP and area of longitudinal steel reinforcement, respectively. Determination of the tensile force within the CFRP between two subsequent cracks: The tensile stress, rfd is calculated taking into account strain compatibility and internal force equilibrium (Section 2.1). The shift rule according to EC2 is applied. Determination of the maximum possible increase in tensile stresses in the CFRP: The maximum tensile force, which can be transferred from the CFRP to the concrete by means of bond stresses at the anchorage zone can be determined as follows: ðAÞ
max rfd
0:23 ¼ cc
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi Ef f ck fctm lb lb 2 ; tf lb; max lb; max
lb 6 lb; max ½MPa
ðI:6Þ
The maximum possible stress is closely related to the effective anchorage length lb,max calculated by: lb; max
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ef tf ¼ 1:44 pffiffiffiffiffiffiffiffiffiffiffiffiffi ½mm f ck fctm
ðI:7Þ
where tf is the thickness of CFRP The maximum increase in tensile stress, max Drfd, in an element between two cracks depends on the tensile stress rfd and may be determined based on the following expressions: If rfd 6 rðBÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffi S rm 0:185Ef 0:285 fck fctm S rm 4tf
ðBÞ
where : max Drfd 2sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 4 0:1852 Ef fck fctm ðBÞ ðBÞ ¼ þðrf Þ2 rf 5½MPa cc tf ðI:10Þ ðBÞ
Ifrfd P r ;then : max Drfd 8 9 2sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 pffiffiffiffiffiffiffiffiffiffiffiffiffi <1 = 2 0:185 E f f f ck ctm ¼ min 4 þðrfd Þ2 rf 5;ffd rfd :cc ; tf ðI:11Þ
where ffd is the design tensile strength of the CFRP. Verification of the maximum possible increase in tensile stress within the CFRP: Drfd 6 max Drfd Approach 3 equations according to Fib bulletin 14 Verification of force transfer between CFRP and concrete: V d 6 fcbd es1 < eyd : ðII:1Þ 0:95dbf 1 þ AAs1f EEfs If es1 P eyd :
Vd 6 fcbd 0:95dbf
ðII:2Þ
If where: es1, esf are the tensile steel strain and CFRP strain, respectively; eyd is the design value of the yield strain of the steel reinforcement; As1, Af are area of longitudinal tensile steel reinforcement and of CFRP reinforcement, respectively; Ef, Es are modulus of elasticity of CFRP and modulus of elasticity of steel reinforcement; bf is the width of CFRP; d is the effective depth of the member; Vd is the design shear force, which may be equal to Vd DMd/Dx; where DMd is the difference between the moments in two cross sections at distance Dx. fcbd is the design bond shear strength of concrete, which may be calculated as follows: fctk fcbd ¼ 1:8 ½MPa ðII:3Þ cc where fctk is characteristic value of the concrete tensile strength. In Eq. II.1 it was assumed that es1/ef 1. References
then: max Drfd ¼ max
ðI:8Þ
2139
ðAÞ rfd
ðAÞ
ðBÞ
max rfd max Drfd ðBÞ
rf
rfd ðI:9Þ
[1] Fib bulletin 14, FIB TG 9.3 FRPEBR. Externally bonded FRP reinforcement for RC structures. Fe´de´ration Internacionale du be´ton (Fib), Task Group 9.3 FRP, 2001. p. 130. [2] Li Lj, Guo YC, Liu F, Bungey JH. An experimental and numerical study of the effect of thickness and length of CFRP on performance of
2140
[3]
[4]
[5]
[6]
[7] [8] [9]
J.A. Bogas, A. Gomes / Construction and Building Materials 22 (2008) 2130–2140
repaired reinforced concrete beams. Constr Build Mater 2006;20(10):901–9. Maalej M, Leong KS. Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRPstrengthened beams. Compos Sci Technol J 2005;65(7,8):1148–58. Juvandes LFP. Strengthening and rehabilitation of concrete structures with composite materials of CFRP. PhD thesis. Faculdade de Engenharia da Universidade do Porto (FEUP), 1999 [in Portuguese]. Bogas JA. Strengthening of reinforced concrete elements with CFRP – design models and safety evaluation. MSc thesis. Instituto Superior Te´cnico (IST). Technical University of Lisbon, 2003 [in Portuguese]. ACI 440. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American concrete institute, reported by ACI comite´ 440 revised July 2000. p. 148. S&P. 30· less weight than steel for the same tensile force. Clever Reinforcement Company, Scherer& Partener bausystem 1998. p. 30. Triantafillou TC, Pelveris N. Strengthened of RC beams with epoxybonded fibre-composite materials. Mater Struct 1992;25:201–11. Eurocode 2, (EC2). Design of Concrete Structures. European Committee for Standardization 1991.
[10] Neubauer U, Rosta´sy FS. Debonding mechanism and model for CFRP-plates as external reinforcement for concrete members. In: Proceedings of the international conference composites in Construction (CCC2001), Porto, 10–12 October 2001. p. 467–72. [11] Resende N. Flexural strengthening of reinforced concrete beams with fiber reinforced plastic plate. MSc thesis. Instituto Superior Te´cnico (IST). Technical University of Lisbon, 2000 [in Portuguese]. [12] Oller E, Salcedo J, Cobo D, Mari A. Flexural strengthening of reinforced concrete beams with externally bonded CFRP laminates. In: Proceedings of the international conference composites in Construction (CCC2001), Porto, 10–12 October 2001. p. 473–8. [13] Ceroni F, Prota A, Pecce M. Experimental Behavior of RC Beams strengthened with CFRP systems. In: Proceedings of the international conference composites in construction (CCC2001), Porto, 10–12 October 2001. p. 499–504. [14] Bazza M, Missihaun M, Labossie`re P. Strengthening of reinforced concrete beams with CFRP sheets. In: First International Conference on composites in infrastructure (ICCI’96), Tucson, January 1996. [15] Juvandes LFP, Dias SJE, Figueiras JA. Strengthening of reinforced concrete beams with composite materials of CFRP. Structural concrete 2000, FEUP, Porto, 2000.