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Strengthening precast-prestressed hollow core slabs to resist negative moments using carbon fibre reinforced polymer strips: an experimental investigation and a critical review of Canadian Standards Association S806-02 Abdelhadi Hosny, Ezzeldin Yazeed Sayed-Ahmed, Amr Ali Abdelrahman, and Naser Ahmed Alhlaby
Abstract: Behaviour of precast-prestressed hollow core slabs has been extensively studied when these slabs are subjected to positive bending moments, a practical application typical of hollow core slabs. However, in many projects it may be required to have an overhanging part of the roof to act as a cantilever. In doing so, and using precastprestressed hollow core slabs, the slabs would be subjected to negative moments, atypical for hollow core slabs. In this paper, the behaviour of precast-prestressed hollow core slabs is experimentally investigated when they are subjected to negative bending moments. A proposed strengthening detail to increase the negative moment resistance of hollow core slabs using bonded carbon fibre reinforced polymer (CFRP) strips is presented. The CFRP strips were bonded to the top side of full-scale precast-prestressed hollow core slabs in the negative moment zone in different configurations. In two of the tested slabs the bond between the prestressing strands and the concrete was initially broken (during casting of the slabs) in the negative moment zone. The slabs with the bonded CFRP strips were tested to failure and the load– deflection behaviour was recorded. The results of the tests are presented and the strength enhancement of the hollow core slabs using the proposed technique is reported. The increase in the negative moment resistance of the CFRPbonded hollow core slabs experimentally determined is also compared with the CSA-S806-02 prediction for the moment resistance of concrete elements with bonded CFRP strips. Key words: carbon fibre reinforced polymer (CFRP) strips, hollow core slab, flexure strengthening, prestressed concrete, precast slabs, prestressing strands. Résumé : Le comportement des dalles à noyau 967 creux précontraintes et préfabriquées a été étudié en détail lorsque ces dalles sont soumises à des moments de flexion positifs : une utilisation pratique typique des dalles à noyaux creux. Cependant, plusieurs projets peuvent demander qu’un avant-toit agisse comme un porte-à-faux. En agissant ainsi, et en utilisant des dalles à noyau creux précontraintes et préfabriquées, les dalles seraient soumises à des moments négatifs, ce qui est peu typique des dalles à noyau creux. Le présent article présente une étude expérimentale du comportement des dalles à noyau creux précontraintes et préfabriquées lorsqu’elles sont soumises à des moments de flexion négatifs. Un détail de renforcement est proposé pour accroître la résistance au moment négatif des dalles à noyau creux en utilisant des bandes de polymères renforcés de fibres de carbone (PRFC). Les bandes de PRFC ont été liées sur le dessus de dalles à noyau creux précontraintes et préfabriquées pleine grandeur dans la zone de moment négatif selon différentes configurations. Dans deux de ces dalles mises à l’épreuve, le lien entre les torons de précontrainte et le béton a été brisé initialement (durant le coulage des dalles) dans la zone de moment négatif. Les dalles munies des bandes de PRFC liées ont été rendues à la rupture et le comportement charge-déflection a été mesuré. Les résultats de ces essais sont présentés et l’augmentation de la résistance dans les dalles à noyau creux, par l’utilisation de la technique proposée, est indiquée. L’augmentation de la résistance au moment négatif des dalles à noyau creux liées par des PRFC, déterminée par les essais, est également comparée aux prévisions de la norme CSA-S806-02 quant à la résistance au moment des éléments de béton munis de bandes de PRFC liées.
Received 31 October 2005. Revision accepted 23 February 2006. Published on the NRC Research Press Web site at http://cjce.nrc.ca on 26 September 2006. A. Hosny, E.Y. Sayed-Ahmed,1,2 A.A. Abdelrahman, and N.A. Alhlaby. Structural Engineering Department, Ain Shams University, Cairo, Egypt. Written discussion of this article is welcomed and will be received by the Editor until 31 December 2006. 1 2
Present address: University of Qatar, Civil Engineering Department, P.O. Box 2713, Doha, Qatar. Corresponding author (e-mail:
[email protected]).
Can. J. Civ. Eng. 33: 955–967 (2006)
doi:10.1139/L06-040
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Can. J. Civ. Eng. Vol. 33, 2006 Mots clés : bandes de PRFC, dalle à noyau creux, renforcement en flexion, béton précontraint, dalles préfabriquées, torons de précontrainte. [Traduit par la Rédaction]
Hosny et al.
Introduction Hollow core precast-prestressed concrete slabs have recently been used as the main floor systems for different structures, such as office buildings, condominiums, hotels, commercial buildings, residential dwellings, houses of worship, educational facilities, and high-rise buildings. Besides their superior structural advantage and the ability to cover large spans, hollow core slabs possess many other advantages, such as comparatively low weight, ease in construction, superior thermal and acoustical properties, high fire resistance, and relatively fast construction rate. Hollow core slabs are commonly constructed using lowslump high-strength concrete and prestressed using highstrength prestressing strands (typically seven-wire strands with diameters ranging between 9 and 13 mm). Continuous voids are formed through each unit to reduce its weight and improve its structural performance (Fig. 1). Hollow core slabs are typically 0.9 to 1.25 m wide and 200 mm to 350 mm thick; in Canada they are available 1.217 m wide and 152 to 355 mm thick. The span of hollow core slabs may reach up to 18.0 m. Hollow core slabs are typically designed as simply supported panels. Consequently, the general behaviour of these slabs has been extensively studied when they are subjected to positive bending moments (Euser et al. 1983; Lama et al. 1999; Polania et al. 2004; Paassen 2004; de Castilho et al. 2005). Codes have been developed to cover the behaviour, design, and construction of simply supported precastprestressed hollow core slabs (Canadian Prestressed Concrete Institute 1996; Precast/Prestressed Concrete Institute 1999; Fédération Internationale de la Précontrainte 1988; fib 2000). Frequently, it may be architecturally required to have an overhanging part of the floor system to act as a cantilever. In this case the precast-prestressed hollow core slabs would be subjected to negative moments defying the typical usage of these slabs as simply supported panels. Strengthening of reinforced concrete structural elements using advanced composite materials has become a very important issue. Recently, bonding fibre reinforced polymer (FRP) strips to a reinforced concrete element to increase its flexural strength proved to be an effective and economic strengthening technique. Besides their distinct corrosion resistance, FRP strips have a high strength-to-weight ratio, which leads to great ease in site handling and application procedures. Detailed surveys of field of applications of FRPs are available (Meier et al. 1993; ACI Committee 440 1996; El-Badry 1996). The application of FRPs in strengthening reinforced concrete structural elements has been widely investigated. Flexural strengthening of concrete elements using FRP strips has also been the focus of many studies. Furthermore, flexural strengthening of reinforced concrete slabs using FRP strips was also extensively reported (Ichimasu et al. 1993; Erki and Heffernn 1995; Teng et al. 2000, Teng et al. 2001; Tan and Zhao 2004).
In this study, precast-prestressed hollow core slabs and carbon fibre reinforced polymer (CFRP) strips were coupled to improve the negative moment resistance of the hollow core slabs with a methodology that could be easily applied. The behaviour of hollow core slabs was experimentally investigated, particularly when they are subjected to negative bending moments. Carbon fibre reinforced polymer strips were bonded to the top of full-scale hollow core slabs in the negative moment zone in different configurations. The slabs were then tested in flexure to failure. In some of the tested hollow core slabs, the bond between the prestressing strands and the concrete was initially broken (during casting of the slabs) in the negative moment zone. In this paper, the results of the experimental programme are presented, and the strength enhancement of the hollow core slabs using the proposed technique is reported. The increase in the negative moment resistance of the CFRP-bonded hollow core slabs determined experimentally is compared with the predicted nominal negative moments obtained using the CSA S806-02 (CSA 2002) and the CSA A23.3-94 (R2000) (CSA 2000) provisions.
Specifications of the tested hollow core slabs Fifteen full-scale precast-prestressed hollow core slabs were casted by Qatar Precast Co. (Qatar) to perform this research; nine of these slabs were used in the current experimental investigation. All the slabs were 150 mm thick, 1.20 m wide, and 5.00 m long. The thickness of the slabs (150 mm) was governed by the production schedule of the manufacturer, the slab width (1.20 m) is controlled by the available bed width used to manufacture the slabs,and the length was chosen to be 5.0 m, which is typical for the 150 mm thick slabs. Figure 1 shows a typical cross section and dimensions of the hollow core slabs considered for the current investigation. Material properties and specifications of the tested slabs are summarized in Table 1. The concrete mix used to cast the slab was composed of 370 kg/m3 cement (ordinary Portland cement) with a maximum water/cement ratio of 0.35. It contained 1140 kg/m3 coarse aggregates (10 mm maximum size), 285 kg/m3 fine aggregates (5 to 0 mm), and 500 kg/m3 washed sand. A 3.5 L/m3 Conplast SP2000 was added to the concrete mix. Cubes were taken from the concrete and tested in compression at age 7 and 28 d, which yielded concrete compression strengths of 74 and 89.5 MPa, respectively. The slabs were prestressed using seven 9.3 mm diameter, 1770 MPa low relaxation, seven-wire strands. The strands were placed at 30 mm from the soffit of the slab. Two additional 9.3 mm diameter strands were placed at 30 mm from the top fibres of the slabs to straighten the slabs. Samples of the prestressing strands were tested in direct tension and yielded an ultimate strength of 1769 MPa and a modulus of elasticity of 195 GPa. The seven lower strands were prestressed to an initial strain of 0.556%, which corresponded © 2006 NRC Canada
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Fig. 1. Details of the 150 mm precast-prestressed hollow core slabs adopted in the experimental investigation.
Table 1. Properties of the concrete and the prestressing strands used in the tested hollow core slabs. Concrete
Prestressing strands
Mechanical properties
Values
Mechanical properties
Values
Compressive strength (7 d cube) Compressive strength (28 d cube) Max. water cement ratio Cement content Coarse aggregates Fine aggregates Sand Admixture SP2000
74 MPa 89.5 MPa 0.35 370 kg/m3 1140 kg/m3 285 kg/m3 500 kg/m3 3.5 L/m3
Diameter Nominal cross sectional area Ultimate load Ultimate tensile strength Modulus of elasticity Max elongation% Initial prestressing strain
9.3 mm 52 mm2 92 kN 1770 MPa 195 GPa 3.5% 0.556%
to an initial prestressing stress of 1083 MPa (56.3 kN per strand), about 61% of the ultimate strand strength. The two top strands were prestressed to only 30% of the ultimate strand strength (27 kN per strand).
Specifications of the CFRP strips bonded to the slabs High modulus of elasticity CFRP strips (S&P laminates CFK 200/2000®) that are 100 mm wide by 1.4 mm thick were used in the experimental investigation. The modulus of
elasticity of these CFRP strips is 200 GPa, and the manufacturer guaranteed a tensile strength for the CFRP strips of 2400 MPa at 1.2% strain. The actual tensile strength of the CFRP strips is higher than 2400 MPa and may reach 3500 MPa; the guaranteed strength takes into consideration the gripping effect in the direct tension tests. MBRACE® laminate adhesive HT65 is used to bond the CFRP strips to the concrete surface of the hollow core slabs. It is a two-component epoxy-based adhesive. The properties of both the CFRP strips and the epoxy adhesive are summarized in Table 2 (as provided by their manufacturers). © 2006 NRC Canada
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Can. J. Civ. Eng. Vol. 33, 2006 Table 2. Properties of the CFRP strips and the epoxy adhesive used to strengthen the hollow core slabs. CFRP strips
Epoxy adhesive
Mechanical properties
Values
Mechanical properties
Values
Tensile strength* Tensile modulus (long. dir) Tensile modulus (trans. dir) Interlaminar shear strength Poisson’s ratio (long, trans)
2400 MPa 200 GPa 10 GPa 77 MPa 0.2, 0.02
Tensile strength Tensile modulus Lap shear strength to strips Compressive strength Bond strength to the concrete Poisson’s ratio
32 MPa 11.7 GPa 29.4 MPa 60 MPa 3.5 MPa 0.2
*The defined tensile strength is guaranteed by the manufacturer taking into consideration the effect of grips; the actual tensile strength is much higher than this value and may reach 3500 MPa.
Fig. 2. Tested hollow core slabs: (a) series S1 slabs; (b) series S2 slabs; (c) first slab of series S3; (d) second slab of series S3, (e) third slab of series S3.
The experimental programme and the test setup Nine of the fifteen precast-prestressed hollow core slabs were tested. They were divided into three series, each with three slabs, as shown in Fig. 2 and listed in Table 3. Series S1 represents the control slabs, while series S2 slabs were
strengthened with three longitudinal CFRP strips bonded along the cantilever part. Series S3 slabs have the same longitudinally bonded CFRP strips and broken bond between the strands and the concrete along 1.5 m from the overhanging edge of the slabs; the bond was broken using duct-tape blanketing on the strands while casting the slabs. Two slabs of series S3 have additional CFRP strips bonded in the © 2006 NRC Canada
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Fig. 3. (a) Marked locations of the CFRP strips on Slab S2-01; (b) mixing the two-component epoxy adhesive.
transverse direction, perpendicular to the main longitudinal CFRP strips, as shown in Fig. 2. The top surfaces of series S2 and S3 slabs were carefully cleaned before bonding the CFRP strips. The locations of the CFRP strips were accurately marked on the top surface of each slab (Fig. 3). For each slab, three CFRP strips (S&P laminates 200/2000®) were cut to 2.0 m in length to cover the 1.0 m long overhang and to extend 1.0 m into the interior span in the negative moment zone. MBRACE® laminate adhesive HT65 (epoxy-based adhesive) was used to bond the CFRP strips to the slabs. The two components of the epoxy adhesive were mixed using an electrical hand mixer (Fig. 3). Before the CFRP strip was applied to the slab, thin layers of the MBRACEHT65 epoxy were applied to the top surface of the slab in the strip locations using a trowel. Another layer (~3 mm) of the epoxy adhesive was applied over the CFRP strips as well, using the tool shown in Fig. 4. The strip was then placed on the surface of the slab. Contact was established at the centre of the strip with the application moving to both outer ends simultaneously. Uniform pressure was ap-
plied to the strip using a roller to squeeze out the excess epoxy adhesive, leaving a thin layer between the concrete and the CFRP strip (Fig. 4). A typical CFRP strengthened hollow core slab is shown in Fig. 5. In this configuration, the CFRP strips were intended to act as an external reinforcement to increase the flexural capacity of the slab in the negative moment zone. The test setup is shown in Fig. 6. It consisted of two loading frames, a loading system (hydraulic rams connected to load cells and load distribution steel beams), dial gauges, and supporting steel beams. One of the loading frames was centered at the interior mid-span, with the other placed at the cantilever tip. The load was applied to the hollow core slabs as a line load across its full width via distribution steel beams (Fig. 6) in a load-controlled fashion. Simultaneous loads were applied incrementally at both the cantilever tip and at the centre of the interior span in a load-controlled fashion. The vertical displacements at the cantilever tip and at the interior span were recorded using simple dial gauges with a 0.01 mm precession. For each load increment, the © 2006 NRC Canada
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Fig. 4. (a) Tool used to apply the epoxy adhesive to the CFRP strips; (b) applying epoxy adhesive to the CFRP strips; (c) fixing the CFRP strips to the Slab S2-01.
load was applied via the hydraulic jacks and kept constant until the readings of the dial gauges were recorded; then the next load increment was applied. The slabs rested on supporting rectangular cross sectional beams (Fig. 6). The supporting beams were transversely placed under the slab across its full width. Greased 4 mm thick neoprene pads were placed between the supporting beams and the hollow core slabs. The supporting beams were arranged to produce a 1.0 m long overhanging cantilever and a 4.0 m interior span for each tested hollow core slab (Fig. 6). Thus, the loading system resulted in a negative moment zone acting on the over-hanging cantilever part and a positive moment in the interior span. The negative moment is coupled with a constant shear force acting along the overhanging cantilever (Fig. 6).
Results of the experimental investigation The three hollow core slabs series were subjected to monotonic flexure tests to failure. Results of these tests are summarized in Table 3 and reported here. The maximum negative moment acting on the cantilever is plotted versus the cantilever tip vertical deflection in Fig. 7 for the tested slabs. The test setup shown in Fig. 6 was used to test the three series of hollow core slabs. For series S1 slabs (control slabs), sudden failure occurred immediately after the first transverse crack was formed in the negative moment zone across the slab width. This transverse cracking initiated in the negative moment zone for series S2 slabs at a moment ranging between 26.2 and 27.9 kN (Fig. 7 and Table 3). For series S3 slabs, the same cracks started at moments ranging
between 27.5 and 34.1 kN (Fig. 7 and Table 3). The transverse cracks started over the support of the overhanging cantilever on the top surface of the slab. Figure 8 shows a typical example for the crack initiation and propagation process encountered for slab S2-02. The cracks did not immediately cross the CFRP strips after they appeared, but widened and continued to appear in different parts of the negative moment zone as the load increased. At their early stages, the cracks were formed between three strips and they were not aligned as shown in Fig. 8. Failure occurred when the major flexure crack (the one formed over the support) extended to reach the CFRP strips and then ran longitudinally along the interface between the concrete and the CFRP strips in the epoxy adhesive layer, causing debonding of the strips from the concrete surface (Fig. 9a). This mode of failure is referred to as intermediate flexural crack-induced interfacial debonding. For all the slabs (except slabs S3-02 and S3-03), the intermediate crack-induced debonding began over the support (location of the major crack) and propagated toward the ends of the CFRP strips. For slabs S3-02 and S3-03, the transverse strips (shown schematically in Fig. 2) stopped the propagated debonding and delayed this premature debonding failure. For these two slabs (S3-02 and S3-03), failure occurred close to the cantilever tip by shearing simultaneously with debonding of the CFRP strips in this zone (Fig. 9b). Cracking and ultimate moments of all the tested slabs are summarized in Table 3 and graphically presented in Fig. 7. Bonding the CFRP strips to the precast-prestressed hollow core slabs significantly increased the negative moment resistance of the slabs. The cracking moments were increased © 2006 NRC Canada
Hosny et al. Fig. 5. Carbon fibre reinforced polymer strengthened prestressedprecast hollow core slabs: (a) slab S2-01, (b) slab S3-03.
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the CFRP strips, as shown in Fig. 10, which is typical of such mode of failure (e.g., Teng et al. 2000; Tan and Zhao 2004). However, because of the very high concrete strength (89.5 MPa) of the hollow core slabs, the amount of concrete attached to the debonded strips was very small, which agrees with the tests performed earlier on cantilever reinforced concrete slabs with bonded CFRP strips (Teng et al. 2002). The second failure mode (flexure failure) was not encountered in any of the tested slabs, as it was preceded by either the intermediate flexural crack-induced debonding or the shear failure mode of the slab. Failure load causing debonding at the end of the CFRP strips (plate-end debonding) for a cantilever slab is usually higher than the shear strength of the slab itself (Teng et al. 2002). Thus, for CFRP-bonded cantilever slabs, plate-end debonding failure mode is commonly preceded by shear failure of the slab, provided that the first and second modes of failure are not encountered first. For slab S3-02 and S3-03, the transverse CFRP strips stopped the propagating debonding cracks and delayed the premature intermediate crack-induced debonding failure (first failure mode). The slabs did not fail in flexure (second failure mode) but failed in shear as shown in Fig. 9b. Nominal moment predictions for series S2 hollow core slabs The CSA A23.3-94 (CSA 2000) and S806-02 (CSA 2002) specifications are adopted to predict the nominal moments of series S2 CFRP-strengthened hollow core slabs (slabs S2-01, S2-02, and S2-03). These specifications base the nominal moment of concrete elements with surface-bonded CFRP strips on the strain compatibility and the equilibrium of forces assumptions provided that (i) plane sections remain plane, (ii) a perfect bond exists between the CFRP strips and the concrete, (iii) the maximum compressive concrete strain is 0.0035, and (iv) maximum tensile CFRP strain is 0.007. Referring to Fig. 10, the equilibrium of force assumption yields
1.83 to 2.25 times over that of the control slabs, and the ultimate moments were enhanced by 2.77 to 5.74 times over that of the control slabs.
Failure modes and theoretical predictions of failure loads Failure modes of hollow core slabs with bonded CFRP strips Failure of cantilever hollow core slabs with bonded CFRP strips may occur in one of following modes: (i) debonding of the CFRP strip that starts at a major intermediate flexural crack, then propagates towards the ends of the strips; (ii) flexural failure by tensile rupture of the CFRP strips or crushing of concrete; (iii) shear failure of the slab; and (iv) plate-end debonding. The first failure mode is referred to as intermediate flexural crack-induced debonding. It was encountered in all three slabs of series S2 (S2-01, S2-02, and S2-03) and only the first slab of series S3 (S3-01). Figure 9a shows a typical crack-induced debonding failure mode that occurred for slab S3-01. A thin layer of concrete was pulled off the slab by
C = T ⇒ α1 fc ′ (β1c)(b) = Ap1 Fp1 + Ap2 Fp2 + Af Ff [1]
α1 = 0.85 − 0.0015 fc ′ ≥ 0.67 β1 = 0.97 − 0.0025 fc ′ ≥ 0.67
where fc ′ is the concrete compressive strength; b is the slab width; Ap1 and Ap2 are the areas of the bottom and top prestressing strands, respectively; Fp1 and Fp2 are the stresses in the bottom and top prestressing strands, respectively; Af is the area of the CFRP strips; and Ff is the stress in the CFRP strips. The compatibility of strains requires that [2]
εp1 = εcu
dp1 − c c
+ εpi1; εp2 = εcu
dp2 − c c
+ εpi2; εf = εcu
t −c c
where εcu is the maximum compressive (crushing) strain of concrete; εp1 and εp2 are the strains in the bottom and top prestressing strands, respectively; εpi1 and εpi2 are the initial strains in the bottom and top prestressing strands due to © 2006 NRC Canada
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Fig. 6. (a) Schematic of the loading configuration adopted in testing the hollow core slabs; (b) bending moment and shear force diagrams; (c) locations of the loading frames and the dial gauges; (d) loading frame and gauges at the interior span; (e) loading frame and gauges at the cantilever tip.
prestressing, respectively; εf is the strain in the CFRP strips; t is the hollow core slab thickness; dp1 and dp2 are the depths to the bottom and top prestressing strands measured from the soffit of the slab; and c is the depth of the compression part of the cross section (Fig. 10). The stresses in the bottom and top prestressing steel strands and in the CFRP strips are given by
[3]
εp ≤ 0.008:
Fp = Epεp
εp > 0.008:
Fp = 1770 −
0.4 εp − 0.0065
[4]
Ff = Ef εf ≤ Ffu
where Ep and Ef are the elastic moduli of the prestressing strands and the CFRP strips, respectively; Fp and Ff are the stresses in the prestressing strands and the CFRP strips, respectively; and Ffu is the ultimate tensile strength of the CFRP strips. Equations [1] to [4] are solved for the compression zone depth c and the stresses in the prestressing strands and the CFRP strips (a = 13.8 mm, c = 21 mm, Fp1 = 1679 MPa, Fp2 = 1365 MPa, Ff = 1400 MPa). The results reveal that the 3500 MPa tensile strength of the CFRP does not affect the © 2006 NRC Canada
S1-01 S1-02 S1-03 S2-01 S2-02 S2-03 S3-01 S3-02* S3-03*
Slab
15.0 15.7 19.6 53.8 46.1 39.2 88.3 86.4 112.8
13.4 14.0 17.5 47.9 41.0 34.9 78.1 76.9 94.3
—
277%
524% 574%
41.3±6.5
— 85.6±12.3
Increase in ultimate moment (%)
14.9±2.2
Negative failure moment (kN)
*Slabs having transverse CFRP strips bonded on top of the longitudinal strips. † Listed deflections are the average values of the deflections given by gauges G1 and G2.
S3
S2
S1
Series
Failure load P1 (kN)
Table 3. Results of the experimental investigation on the hollow core slabs.
0.5 4.1 2.4 17.8 15.4 11.6 24.6 25.6 24.7
Vertical deflection at failure δ1 (mm)† 13.4 14.0 17.5 27.8 27.9 26.2 27.5 32.9 34.1 — 33.5±0.9
27.3±0.9
14.9±2.2
Negative cracking moment (kN·m)
185% 225%
183%
—
Increase in cracking moment (%)
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Fig. 7. Negative moment versus cantilever deflection: (a) series S1; (b) series S2; (c) series S3.
nominal moment because the specified strain limit (0.007) in the CFRP strips will always be reached first. The nominal moment Mn of the strengthened hollow core slab section is given by
[5]
β c β c M n = Af Ff t − 1 + Ap1 Fp1 dp1 − 1 2 2
β c + Ap2 Fp2 dp2 − 1 2
From eqs. [1] to [5] and with a perfect bond between the CFRP strips and the concrete, the nominal moment of the tested hollow core slabs with bonded CFRP strips is calculated to be 115 kN. The predicted nominal moment is significantly higher (2.8 times) than the experimentally recorded
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Fig. 8. (a) Crack initiation in slab S2-02; (b) crack propagation in slab S2-02.
Fig. 9. (a) Intermediate crack-induced debonding failure mode of dlab S3-01; (b) delayed shear failure of slab S3-03.
Fig. 10. The debonded CFRP strips with a thin layer of concrete on them.
ultimate moment of the series S2 slabs as listed in Table 3 (41.3 ± 6.5 kN), which indicates that the flexural failure mode should not be considered alone. Thus, the intermediate crack-induced debonding mode must be implemented in the previous equations. This is achieved by limiting the stress in the CFRP strips (determined by eq. [4]) to the ultimate intermediate crack-induced debonding strength Fdb. The modified Chen and Teng model (2002) is adopted to determine the debonding strength Fdb (in megapascals) of this mode where [6]
Fdb = α dbβpβL
Ef fc ′ tf
where tf is the thickness of the CFRP strips; α db is a coefficient that was calibrated against test data of beams and slabs and found to be 0.4 for slabs (Teng et al. 2002); and β b and βl are width and bond length coefficients, respectively, determined by βp = [7]
2 − bf /b 1 + bf /b
L ≥ Le = L < Le =
Ef t f fc ′
βL = 1.0
Ef t f fc ′
πL βL = sin 2Le
where Le is the effective bond length, L is the length of the CFRP strip (as shown in Fig. 11), Ef is the modulus of elasticity of the CFRP strips, tf is the thickness of the strip, bf is the width of the CFRP strips (3 × 100 mm for the tested slabs), and b is the hollow core slab width. The stress in the CFRP strips is then obtained using the following equation, which should replace eq. [4] in determining the nominal moment: [8]
Ef εf Ff = minimum of : Edb Efu © 2006 NRC Canada
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Fig. 11. (a) Equilibrium of forces and compatibility of strains for ultimate strength design of slabs; (b) plan of the top surface of the hollow core slab showing CFRP strips parameters of eq. [7].
Adopting the CSA S806-02 (CSA 2000) procedures and limiting the stress in the CFRP strips to the values given by eq. [8], the nominal moment of series S2 slabs is determined to be 67.5 kN. The predicted nominal moment based on this approach is 63% higher than the average experimental ultimate moment. The proposed procedures revealed a significant improvement over the predication of the current CSA S806-02 (CSA 2002) specifications. However, the discrepancy indicates that the crack-induced debonding model is still in need of further refinement. Furthermore, the equations of α l and βl adopted by the CSA S806-02 specifications are valid only when the concrete reaches its ultimate strength. Ultimate strength is another approximation that needs to be revisited, since final failure occurred owing to a premature debonding of the Vci = 0.06 fc ′ bwdp + [9]
Vn = minimum of: Vcw = 0.4 fc ′ 1 +
strips. As well, the concept of full-strain compatibility between the CFRP strips and the rest of the concrete section is another assumption that should be reviewed. Failure load predictions for slabs S3-02 and S3-03 For two of the series S3 slabs, transverse CFRP strips were bonded on top of the main longitudinal strips. The transverse strips stopped the propagating debonding cracks. Thus, they resisted the crack-induced debonding failure and delayed the premature failure. Failure of these two slabs took place by shear (Fig. 9) as opposed to the other three failure modes described earlier. The CSA A23.3-94 (R2000) (CSA 2000) and S806-02 (CAS 2002) specifications are adopted to predict the failure loads of the two slabs (S3-02 and S3-03). The nominal shear force at failure is given by
Vf M cr ≥ 0.17 fc ′ bwdp Mf φpPe /A 0.4φp fc ′
where M and V are the bending moment and the shearing force simultaneously acting on the section under consideration, bw is the reduced width of the slab (at the holes location), d is the depth to the top prestressing reinforcement measured from the bottom concrete fibres, Pe is the effective prestressing force acting on the cross section, A is the crosssection area, Vp is the vertical component of the prestressing force (zero for all the tested hollow core slabs), and Mcr is the cracking moment. Accounting for both the top and bottom prestressing strands, the cracking moment may be given by
bwdp + Vp
[10]
r2 r2 M cr = Pe2 + e2 + Pe1 − e1 + 0.6 fc ′ St ct ct
where Pe2 and Pe1 are the prestressing forces in the top and bottom strands, respectively; e2 and e1 are the eccentricities of the bottom and top strands, respectively; r is the radius of gyration of the slab cross section; ct is the distance from the cross section centre of gravity to the top concrete fibres; and St is the elastic section modulus with respect to the top concrete fibres. © 2006 NRC Canada
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Equations [9] and [10] were applied at the failed sections of S3-02 and S3-03 slabs to yield a predicted failure load of 89.1 kN (M = 79.3 kN). The average failure load experimentally determined was 96.2 1.5 kN, which closely matches the predicted one. It is higher by only 8%.
Summary Architects frequently require an overhanging part of a roof to act as a cantilever. In this situation precast-prestressed hollow core slabs would be subjected to a negative moment that violates the design concepts of these slabs. A proposed strengthening detail, using bonded CFRP strips to increase the negative moment resistance of hollow core slabs, is presented and experimentally verified. Carbon fibre reinforced polymer strips were bonded to the top of full-scale precastprestressed hollow core slabs in the negative moment zone. The proposed strengthening technique is efficient for in place strengthening of the hollow core slab subject to negative moment, particularly when the addition of negative steel reinforcement becomes impractical or impossible. Six CFRP strengthened slabs and three control specimens were subjected to negative and positive moments and tested monotonically to failure. The results of these tests were presented, and the strength enhancement of the hollow core slabs using the proposed technique was reported. The cracking moment and the negative moment resistance of the CFRP-bonded hollow core slabs was enhanced by 183% to 225% and 277% to 574%, respectively. The failure modes expected to occur for these slabs were summarized and compared with the ones experimentally encountered. The CSA A23.3-94 (R2000) (CSA 2000) and S806–02 (CSA 2002) specifications were adopted to predict the failure loads and moments of the tested slabs. The analyses revealed that crack-induced debonding failure mode should be taken into account in calculating the nominal moments of the CFRP-bonded slabs. A recently proposed debonding model was adopted, together with code provisions in estimating the failure loads. The model showed reasonable agreement with the test results but still needs further refinement. The experimental investigation and the failure load prediction analyses also revealed that shear failure would occur if the crack-induced debonding failure mode is prevented.
Acknowledgements This work was performed under the auspices of University of Qatar (Qatar). In-kind support was received from S&P Clever Reinforcement Co. (Austria), MBT Middle East (United Arab Emirates), and Qatar Precast Co. (Qatar); we are very grateful for this support. We appreciate in particular the great help offered by Mr. J. Scherer (S&P Clever Reinforcement Co.) and Mr. D. McGlashen (Qatar Precast Co.).
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List of symbols A hollow core slab cross sectional area Af area of the CFRP strips Ap1, Ap2 areas of the bottom and top prestressing strands, respectively b hollow core slab width bf width of the CFRP strips (3 × 100 mm for the tested slabs) bw reduced width of the slab at the holes location c depth of the compression part of the cross section ct distance from the cross-section centre of gravity to the top concrete fibres d depth to the prestressing reinforcement dp1, dp2 depths to the bottom and top prestressing strands measured from the soffit of the slab e2, e1 eccentricities of the bottom and top strands, respectively Ef modulus of elasticity of the CFPR strips Ep modulus of elasticity of the prestressing strands
967 fc′ Fdb Ff Fp1, Fp2 Le M Mcr Mn Pe Pe2, Pe1 r St t tf V α, β α db βb , βl εcu εf εp1 , εp2
concrete compressive strength ultimate intermediate crack-induced debonding strength stress in the CFRP strip stresses in the bottom and top prestressing strands, respectively effective bond length between a CFRP strip and concrete bending moment at a section cracking moment of the hollow core slab nominal moment of the cross section effective prestressing force acting on the section prestressing forces in the top and bottom strands, respectively radius of gyration of the hollow core slab cross section elastic section modulus of the hollow core slab with respect to the top concrete fibres hollow core slab thickness thickness of the CFRP strip shearing force at a section concrete compression stress block coefficients a coefficient that calibrated against test data for the determination of intermediate crack-induced debonding strength width and bond length coefficients adopted for the determination of intermediate crack-induced debonding strength crushing stain of concrete strain in the CFRP strips strains in the bottom and top prestressing strands, respectively
© 2006 NRC Canada
