R / C Structures Strengthened With CFRP – Part II : Analysis of Shear Models

© 2010 IBRACON a Post-Doctoral Researcher, School of Civil Engineering, Architecture and Urbanism, University of Campinas, andre.gamino@gmail.com, Av. Albert Einstein 951, Campinas-SP, CEP 13083-852. b Professor, School of Civil Engineering, Architecture and Urbanism, University of Campinas, jls@fec.unicamp.br, Av. Albert Einstein 951, Campinas-SP, CEP 13083-852. c Associate Professor, São Paulo State University, omanzoli@feb.unesp.br, Av. Luiz Edmundo Carrijo, s/n, Bauru-SP, CEP 17033-360. d Associate Professor, Polytechnical School, University of São Paulo, tulio.bittencourt@poli.usp.br, Av. Prof. Almeida Prado, 271, São Paulo-SP, CEP 05508-900.


Introduction
Reinforced concrete has been established, from the decade of 1950, as the most used structural material in the world.Innumerable researches on concrete technology, constructive techniques and analytical and computational tools capable to provide efficient projects are dedicated to this material.As a result more slender and optimized structures, from the safety and economical points of view, have been produced.However, these structures are more vulnerable to the deterioration processes (Cánovas [1]).In the recent years, research in reinforced concrete has drawn attention on the knowledge of the application techniques concerning its repair and strengthening.According to Figueiras; Juvandes [2], the growing degradation of building structures, bridges and viaducts is due mainly to aging processes, deficiencies in design and construction procedures, lack of maintenance and accidental causes (e.g., .earthquakes.)The incorporation of new materials to the reinforced concrete, as for instance composite materials, can improve the performance of structural elements.Those materials have already been used thousands of years ago: Egyptians used to mix straw to the clay to improve structural performance of bricks and, seven thousand years ago, boats were built by using tar to glue pieces of juncus.In addition, the development of new polymeric materials, such as CFRP-Carbon Fiber Reinforced Polymer, GFRP-Glass Fiber Reinforced Polymer and AFRP-Aramid Fiber Reinforced Polymer has allowed a great flexibility for the strengthening techniques in reinforced concrete structures.Strengthening with polymers aims at increasing stiffness, tensile, compression, fatigue and impact strength (Meier [3]).The CFRP composites are the most indicated for strengthening of reinforced concrete structures since they present characteristics that best fit to this structural type.Optimum mechanical performance when compared with other fibers can be highlighted: high tensile strength, high Young´s modulus in comparison with steel, high strength to fatigue and alkaline resistance (Toutanji;Gómez [4]).In general the composite materials are more durable than the traditional materials.Furthermore, since they are of easy handling and do not require heavy and expensive frameworks, they can be used in adverse operational conditions.Although fibers and resins used in the composite systems are relatively expensive when compared with the traditional strengthening materials (concrete and steel), labor and equipment costs for FRP systems installation are always less expensive (Figueiras;Juvandes [2]).The objective of the this work is to investigate, from experimental laboratory results, the ability of predicting the structural behavior of reinforced concrete beams strengthened to shear with carbon fiber reinforced polymers (CFRP).This work complements another publication entitled "R/C Structures Strengthened with CFRP Part I: Analysis of Flexural Models" (Gamino; Bittencourt; Sousa [5].More details on this work are presented in Gamino [6].

ACI-440 [7]
The contribution in shear of fiber reinforced composites is given by: where: A fv = total FRP area given by: where: The effective stress in FRP is: where f E is the FRP Young´s modulus and e fe is the effective strain: with: e fu = ultimate deformation in FRP; v k = strain reduction factor in FRP; This factor depends on the strengthening scheme:

R/C Structures Strengthened With CFRP -Part II: Analysis of Shear Models
The effective strain can be computed by:

Khalifa et al. [9]
The contribution in shear of fiber reinforced composites is the same expression from the ACI design code but the effective strain is given by: The reduction factor R is the smallest value from the three equations: where: W fe = effective width of the FRP; f ρ = FRP geometric ratio obtained by: The effective width is: where: e L = effective length of the FRP strip given by; The remaining factors can be obtained from:

fib-14 [8]
The contribution in shear of fiber reinforced composites is given by: where: α = inclination angle of FRP; θ = shear crack angle; f ρ = FRP ratio computed by: Finally the effective length can be obtained by:

Chen; Teng [10]
The contribution in shear of fiber reinforced composites is given by: where: The effective stress is: where: f D = distribution factor of the FRP; max , f σ = maximum tensile stress in the FRP; The equations for the determination of maximum tensile stress are: The maximum anchorage length is given by: The other factor can be obtained by: The distribution factor of the FRP is:

Nollet; Chaallal; Perraton [11]
The contribution in shear of fiber reinforced composites is given by: The maximum shear stress in adhesive layer is: The factor 1 k can be obtained by: The factor n k can be obtained by: The average shear stress in adhesive layer is: The contribution in shear of composite fabrics is given by: The final contribution in shear of FRP will be the smaller f V val- ue obtained between Equation (30) and Equation (35).

Täljsten [12]
A simple form for the determination of f V is giving by: where: β = angle between beam axis and a perpendicular line to the FRP orientation;

Experimental Procedure
The experimental program included eight "T" beams strengthened to shear with carbon fiber reinforced polymer (CFRP) with f s equal to 15 cm (Figure 1-b) and f s equal to 17.5 mm (Figure 1-c).
The remaining beams were strengthened with one CFRP layer.The beams VTC1 and VTC3 were strengthened with U-wraps (CFRP fabric) without anchorage, VTC2 and VTC4 with U-wraps (CFRP fabric) with anchorage (Figure 2) and VTC5 with two sides only (CFRP sheet) without anchorage.The strain-gages distribution in the reinforcement steel bars (bottom steel or stirrups) for the "T" beams can be observed in Figure 3.The data acquisition system ADS 2000 of the Lynx [13] was used together with the programs AqDados [14] and AqDAnalysis [15], responsible for control and configuration of the equipment, data reading, writing, visualization and processing.

Materials
Details of the beams tested in the experimental procedure is illustrated in

Experimental Results and Discussion
The results obtained from the experimental tests are summarized in Table 5 (reference beams) and Table 6 (strengthened beams with CFRP wraps).
Based on the experimental results of the "T" beams strengthened to shear using CFRP composites, the following observations can be drawn: the smaller strengthened ratio has been obtained for VTC5 (CFRP sheet without anchorage, see Figure 5-a) and the largest ratio has been obtained for beams with anchorage mechanism (see Figure 2), VTC2 (110.3%) and VTC4 (89.6%) -in these beams the failure mode found was rupture of CFRP; the stirrup strains were larger in VTC5 and VTC1, as shown in Figure 6-a -in these beams the observed rupture was the shear mode; the behavior of the beams strengthened without anchorage was more fragile in comparison to the reference beams (RTC1 and RTC2, see Similar results regarding load capacity and ductility can be obtained using an anchorage system more viable economically, replacing the CFRP bar by a rebar of conventional steel CA-50, and using a cement based instead of a polymeric based grout.Figure 7 presents the strain evolutions in the CFRP wraps for the beam VTC3.Observe that the strains in CFRP wraps intercept-ing the critical shear crack are slightly higher than the strains in the wraps out of the crack nucleation zone.In Figure 7 one can observe that the CFRP strip with the strain gage sg-2 was the one intercepting the critical crack, debonding from the substract earlier than the remaining strips.These results served as a comparative basis for computational simulations performed by the authors (Gamino; Sousa; Bittencourt [18]).

Comparison of Predictions and Experimental Results
The comparison of the theoretical results using the analytical models described in this paper and the experimental results are shown in Table 7 and 8.These results are illustrated in Figure 8.
Some safeguards are required at this point: the properties of the CFRP strips used in the calculation were obtained from characterization tests (average values); the experimental values of "V f " were obtained from the shear increase quota of the CFRP beams; Khalifa et [9], Chen; Teng [10] [12] models are applicable only to beams strengthened to in "U" or in two sides; the computed values of "V " for beams VTC2 and VTC4 were performed under assumption that the strengthening wraps the whole section in order to simulate the anchorage system in the junction slab/web adopted in this work.From the comparison between experimental and analytical results the following observations can be drawn: a) for the beam VC 01 strengthened with CFRP fabric the V f value found with the Nollet; Chaallal; Perraton [11] model is closer to the experimental result; b) for the beams strengthened with CFRP with anchorage mechanism (VTC2 and VTC4), the theoretical values predicted by ACI-R/C Structures Strengthened With CFRP -Part II: Analysis of Shear Models 440 [7] is closer to the experimental V f than those predicted by fib-14 [8]; c) for the beam VTC5 strengthened with laminate glued externally the values of "V f " computed according to Chen; Teng [10] e Khalifa et al. [9] were higher than the experimental value due to the higher fiber area; in other words, these models seem not applicable to structures strengthened with externally glued laminates since they increase too much the "V f " values, tendency that should be investigated with a larger number of tests; in this beam the values obtained from fib-14 [8] and ACI-440 [7] were below the experimental value, and the value obtained from Nollet; Chaallal; Perraton [11] has shown more appropriated; Khalifa et al. [9] and Täljsten [12] models are not applicable to beams strengthened with laminates.d) the predictions of fib-14 [8] have shown more conservative, followed by Khalifa et al. [9] model;

Conclusions
Based on the results from the experimental investigations, the fol-lowing conclusions can be drawn: n The technique of strengthening to shear with carbon fiber reinforced polymer revealed to be very effective, especially when anchorage system of the CFRP wraps was used.For these cases the shear capacity has been substantially improved without significant changes of ductility in comparison with the original beams, not strengthened with CFRP.n Predictions of ACI-440 [7] is suggested instead of fib-14 [8], which has shown too conservative when compared to the experimental values.n Although conservative in most analyses, the analytical models, including those from international recommendations and design codes, were not capable of properly simulating the behavior of all beams tested in the experimental program.

Acknowledgments
The authors wish to express their gratitude and sincere appreciation to Fapesp -Research Support Foundation of São Paulo angle of FRP; f s = FRP strip spacing; f d = depth to center of gravity of FRP; Figure 5-b); on the other hand, for the beams R/C Structures Strengthened With CFRP -Part II: Analysis of Shear Models strengthened with anchorage the observed behavior was more ductile in comparison to the reference beams.