Finite Element Analysis of CFRP Strengthened Concrete Beams

Transcription

1 Finite Element Analysis of CFRP Strengthened Concrete Beams R.Arunothayan 1, J.C.P.H.Gamage 1 and U.N.D.Perera 1 1 Department of Civil Engineering University of Moratuwa Moratuwa SRI LANKA arunothayan91@gmail.com Abstract: Introduction of Carbon Fiber Reinforced Polymer (CFRP) materials to the civil engineering constructions was an excellent solution for deteriorated infrastructures. Investigations on flexural behavior of CFRP strengthened concrete beams have been researched and well documented. However, the full capacity of CFRP/ concrete composites cannot be achieved due to premature failure of CFRP sheet at the concrete/epoxy or CFRP/epoxy interfaces. An introduction of anchorages to delay this premature failure has shown prominent results. A numerical model was developed to predict the flexural performance of CFRP strengthened concrete beams and also to quantify the effects of different parameters on flexural performance of the composite. The model predicted results showed a good agreement with experimental results. Provision of anchorages at 60 mm away from the ends of CFRP sheet is more effective. This paper presents background of CFRP/concrete composites, numerical modeling and the effects of parameters such as CFRP thickness, anchorages and their locations on flexural performance of the composite. Keywords: Concrete beam, CFRP, Finite Element Model, End anchorage 1. INTRODUCTION Introduction of Fibre Reinforced Polymers (FRP) to the construction industry is a superior solution in the development of modern methods for retrofitting degraded infrastructures. In the last few decades, many deficient structures were externally supported with FRP. It increases the life cycles and the load carrying capacities of strengthened members considerably. FRP composites have many advantages such as good corrosive resistance, light weight, high strength to weight ratio, easy installation, very low conductivity, flexibility in adapting to field conditions and chemical resistance (Triantafillou and Antonopoulos, 2000). This technology also enhances the fatigue behaviour and the durability of the strengthened structure. FRP materials can be classified into various forms such as carbon sheets, strips and glass laminates. Carbon fibres are light weight and more ductile than glass fibres. Carbon Fibre Reinforced Polymer (CFRP) is a thin plate that could be fixed to the beams in various dimensions and directions by binding a thermoset resin. Carbon fibres behave as a secondary reinforcement to the horizontal elements and provide additional protection (Chaallal et al, 1998). There are various failure modes for a CFRP strengthened section which have been observed by many past researches. The major classification of failure modes are; Pre mature failure mode where the concrete cover could be separated, interfacial de-bonding could occur, induced de-bonding due to pre-cracked properties could happen Classical failure modes such as rupture, compressive crushing and shear failure These failure modes are not discrete. They may occur as collectively and in various combinations. Shear failure of the CFRP strengthening systems when applied to concrete structures is usually typified by de-bonding of the CFRP sheet from the concrete substrate. This failure effect can be subdivided as concrete break-out from the CFRP plate at the flange (Ariyachandra and Gamage 2014), CFRP plate pull-off from the flange at the epoxy/frp surface (Bencardino et al 2006), CFRP plate pull-off from the flange at the concrete/epoxy surface (Balakrishnan et al 1988), FRP plate debonding from the RC beam web (Chaallal et al 1998) and de-bonding of the CFRP plate overlap at the beam soffit (Mofidi et al 2013). Introducing a proper anchorage system can minimize the above failure modes (ACI Committee 440, 2008) and it enables the tension reinforcement bars to yield and the CFRP laminate to reach a high proportion of its failure strain result in the higher load capacity with higher ductility of composite. The anchorage system enhances the strength and deformability 249

2 properties of the CFRP plated beam, as reflected by the global performance factor (Bencardino et al 2006). In this research, CFRP strengthened concrete beam was modelled using a commercially available finite element software. Preliminary testing done by Ariyachandra and Gamage (2014) was used for the validation purpose. This paper presents the overview of test programme, development of numerical model and predictions. 2. METHODOLOGY 2.1. Finite Element Modelling The finite element method (FEM) is the dominant discretization technique in structural mechanics. The basic concept in the physical interpretation of the FEM is the subdivision of the mathematical model into disjoint (non-overlapping) components of simple geometry. Commercially available finite element software, ANSYS 15.0 was used to develop the FE models for this study. Concrete was modelled using Solid65 element (ANSYS Inc, 2009). Reinforcement is modelled with Link180 and CFRP/Epoxy combined shell section is modelled with Shell181 (ANSYS Inc, 2009). Target and contact elements are developed for contact mechanisms. Concrete is meshed as hexahedral sweeping where certain incremental dimension spacing is maintained. Concrete has a mesh size of 20 mm x 20 mm. CFRP shell is meshed as 10 mm x 10 mm elements as shown in Figure 1. CFRP sheet Concrete Figure 1 Bottom view of a beam model 2.2. Material properties Grade 30 concrete was used for both modelling and experiments. In order to simulate the concrete behaviour accurately as possible, ANSYS requires several parameters to be entered. The modulus of elasticity of concrete (EX) which can be calculated by the gradient of the stress-strain curve developed, Poisson ratio (PRXY) which has been taken as 0.2, Shear transfer coefficients, Uniaxial cracking stress and Uniaxial crushing stress. Shear transfer coefficients represent the condition at the crack face while it is opened (loaded) and closed (reversed). Values range from 0 to 1 where 0 stands for a smooth crack, when shear transfer is completely lost, while 1.0 stands for a rough crack with no loss of shear transfer. Uniaxial cracking stress defines the modulus of rupture of the concrete (Sayed et al, 2014). The stress strain behaviour of the concrete is developed such that the initial portion is linear lasting up to about 30% 40% of the ultimate load and then the curve is non-linear, with large strains being registered for small increments of stress. The summary of the values considered in the analysis is listed in Table 1. Table 1 Properties of Concrete Elastic modulus MPa Density 2500 kg/m 3 Poisson ratio 0.2 Open Shear Transfer Coefficient 0.4 Closed Shear Transfer Coefficient 0.6 Uniaxial Cracking Stress

3 The Elastic modulus of reinforcement is 200,000 N/mm 2 and Poisson ratio is 0.3. Tensile strength of the main bars is 250 N/mm 2. Strain hardening of the steel is not incorporated since it is not critical. Carbon Fibre is an orthotropic material predominantly characterized by its properties in the axial direction. Primer and Saturant of Epoxy may differ in properties (ACI Committee 440, 2008). Table 2 and 3 shows the properties of CFRP and epoxy, respectively. Table 2 Properties of CFRP [Ariyachandra and Gamage, 2014] Density 2100 kg/m3 Elastic Modulus (axial) 640 GPa Elastic Modulus (lateral) 45 GPa Tensile elongation 0.4% Table 3 Properties of Epoxy Resin [Ariyachandra and Gamage, 2014] Thickness Elastic Modulus Yield Stress 1mm 3724 MPa 138 MPa 2.3. Geometry and boundary conditions The length of reinforced concrete beam is 750 mm and the cross section was 150 mm x 100 mm (depth x width). Reinforcements of 6 mm diameter steel bars were used as main tensile bars and 4 mm galvanized iron bars were used for shear links to accommodate in the small cross section. Nominal cover of 25 mm was provided. Shear links were spaced at 50 mm centres and the attributes to idealize pin support conditions were provided at 75 mm from the both ends as shown in Figure 2. One support is fixed in the vertical direction only (roller) and the other support is fixed in the vertical and axial direction (pinned). CFRP and epoxy is created together as shell sections (ANSYS Inc, 2009) Contact pair is created between epoxy adhesive and concrete surfaces. Penalty method is used for analysis. Normal penalty stiffness and tangent penalty stiffness are maintained at 6. Penetration tolerance is 0.1. The behaviour of the contact surface is defined as bonded at initial contact. Figure 2 Reinforcement details and FE mesh and attributes of Numerical Model Three models were developed as similar as in test programme. Initially, non-strengthened reinforced concrete beam was modelled. This was considered as the control specimen. Figure 3 shows the side view and the bottom view of the model of the control specimen. Figure 3 Numerical model for non-strengthened reinforced concrete beam (Model B1); Side View and Bottom view 251

4 Then, a CFRP sheet was attached to the bottom surface of the beam, starting from 75 mm towards the mid span from the support. This represents the basic arrangement of CFRP strengthened concrete beam. The model developed to predict the behaviour of CFRP strengthened non anchored concrete beam is shown in Figure 4. Concrete beam Supports CFRP sheet Figure 4 Numerical model for CFRP strengthened non-anchored beam (Model B2); Side View and Bottom view The main problem of a CFRP retrofitted beam is the premature failure due to delamination of CFRP sheets at the ends. An introduction of polymer anchorages at ends may delay this phenomena result in higher load carrying capacity. The model B3 represents the CFRP strengthened concrete beams with polymer anchorages at ends (Figure 5). Supports End anchors CFRP sheet Figure 5 Numerical model for CFRP strengthened end anchored beam (Model B3); Side View and Bottom view 3. TEST PROGRAMME Concrete beams with dimensions, 100 mm x 150 mm x 750 mm were cast. The specimens were immersed in water for 28 days. The surfaces of specimens to be strengthened were sand blasted and cleaned. The substrates were improved using a thin layer of primer in accordance with CFRP manufacturer's guidelines. The primed surfaces were kept to cure for an hour. Then, the CFRP sheets were bonded as shown in Figures 4 and 5 using the wet layup method. Two part epoxy adhesive was selected for this purpose. The strengthened specimens were kept to cure at least 7 days before conducting destructive testing. In order to review the flexural performance of the beams, three-point bending test was conducted. The deflection at mid span was monitored with respect to applied loading. The load related to initiation of 0.3 mm wide crack was considered as the ultimate failure load of beams. 4. MODEL RESULTS AND VALIDATION Three models were developed with three different conditions. The summary of these models is listed in Table 4. B1 represents the control beam which implies the behaviour of a non-strengthened reinforced concrete beam. B2 is the strengthened concrete beam without end anchorages and B3 incorporates the additional end anchorages. Model CFRP Thickness Table 4 Details of Beam Models CFRP dimensions - bottom face CFRP dimensions - end anchors Remarks B Control Beam B mm 450 mm x 100 mm - Strengthened beam B mm 450 mm x 100 mm 100 mm x 50 mm Strengthened beam with end anchors 252

5 Transient load was applied in 25 N load steps. Newton-Raphson iterative process solver was used for analysis. Von Misses stress-strain relationship was selected. CPU Processor with 2.2 GHz capacity was used for modelling. The model was run for approximately three hours. Analytical and experimental results were compared and the variation of deflection at mid span was monitored and plotted in Figure 6. It has been shown that both predicted and test results have a similar load - deflection behaviour. Strengthened beams have revealed more ductile behaviour than the non- strengthened beam. Finally, the graph interprets that the model predicted results differ for about 9% from the experimental results. Also, the variation of predicted and experimental failure loads is lesser than 2% (Table 5, Figure 6). This indicates that the experimental results have a good agreement with the predictions. However, there are minor variations as the practical workmanship characteristics and the on-site behaviour of the concrete are difficult to be regularized under a framework of guidelines. Figure 6 Load vs. Deflection curves for beam models B1, B2 & B3 Beam No. Failure load (Experimental) (kn) Table 5 Comparison of Experimental and Numerical Results Failure load (Numerical) (kn) % Difference in Failure load Mid span Deflection at Failure (Experimental) (mm) Mid Deflection at Failure (Numerical) (mm) % Difference in Deflection B B B PARAMETRIC STUDY 5.1. Effects of different anchorage systems Parametric analyses were carried out for different arrangements of CFRP anchors. The main objective was to determine the effects of flexural enhancement with the position of anchorages. B4 incorporates 253

6 additional pair of vertical strips of CFRP at both ends. A distance of 10 mm is maintained between the strips that are identical (Figure 7). A similar approach was adopted in B5 with three vertical CFRP strips (Figure 8). Figure 7 Numerical model for CFRP strengthened end anchored beam with two vertical strips (Model B4); Side View and Bottom view Figure 8 Numerical model for CFRP strengthened end anchored beam with three vertical strips (Model B5); Side View and Bottom view Failure loads of B4 and B5 are compared against B3 and the percentage increments in the failure loads are listed in Table 6. It can be observed that, when additional vertical layers are installed, there is an increment in the failure loads as well as a decrement in mid span deflection. With two anchorage layers from each end, the failure load is increased by 6% whereas when the anchorage layers are increased to three, the failure load is increased by 11%. Percentage reduction in deflection is not much considerable and it is about 3-4 %. Table 6 Predicted performance of CFRP strengthened beams with different end anchorages Beam No. Failure Load (kn) Percentage Increment in Failure Load with respect to B3 Mid span Deflection (mm) Percentage Reduction in Deflection with respect to B3 B B % % B % % Analyses were also carried out for CFRP end anchorages with the same area installed at various locations. The purpose of the analysis is to establish the most efficient position for the application of CFRP end anchorages. In the model B6 (Figure 9), the pair of end anchorages is moved towards the middle by 60 mm from the initial location. In the model B7 (Figure 10), it moves towards the middle by 120 mm from the initial location. Figure 9 Numerical model for CFRP strengthened end anchored beam (Model B6); Side View and Bottom view 254

7 Figure 10 Numerical model for CFRP strengthened end anchored beam (Model B7); Side View and Bottom view When the location of the anchorage is changed, the capacity of the beam is also increases. In B6, where the CFRP anchorages are placed 60 mm apart from the initial location, the failure load increases about 2% than in B3. In B7, where CFRP anchorages are placed further 60 mm away from its location at B6, the failure load increases about 5% than in B3. Further shifting of location did not provide any strength gain with respect to the model B3. Table 7 Predicted performance of CFRP strengthened beams with different positions of anchorages Percentage Increment in Failure Beam No. Failure Load (kn) Mid Span Deflection (mm) Load with respect to B3 B B % B % 6. CONCLUSIONS This study was focused on numerical modeling of CFRP strengthened reinforced concrete beams. The main focus was to enhance the performance by introducing polymer anchorages. The model predicted results are in good agreement with experimental results. The following conclusions shall be drawn from the study: Failure loads of reinforced concrete beams can be increased in a significant manner by installing CFRP laminates at the bottom face of the beam. Results show that the failure load of a CFRP strengthened, end anchored RC beam is about 3 times greater than that of a normal RC beam. The flexural capacity can be further enhanced by providing end anchorages to the beam. It has been encountered for about 10 % increment in failure load with provision of anchorages at the ends. It has also been observed that deflection is not affected in a large scale (about 4%) and this might be for the reason of short spans of the beams considered. The application of end anchorages with different positions does not strongly reflect on the increment in failure loads. The contribution of end anchorages to failure load is less than 12% from all the data analyzed. Further research studies should focus on this phenomena where long beams shall be modeled and tested. The reasons for the possible discrepancies between the experimental and analytical results could be due to the poor workmanship, changes in temperature in concrete, workability mixtures, etc. REFERENCES American Concrete Institute Committee 440 (Busel, J.P. Chair), July 2008, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R- 08), Farmington Hills, MI 48331, USA 255

8 ANSYS Inc, November 2009, Structural Analysis Guide, Canonsburg, PA., ANSYS Inc, November 2009, Contact Technology Guide, Canonsburg, Ariyachandra, M.R.E.F., Gamage, J.C.P.H., 2014, A review on fracture-mechanics based models on debonding nature of CFRP/Concrete composites, 5th International Conference on Sustainable Built Environment (ICSBE2014), Kandy, Sri Lanka, 2014, pp Bencardino, F., Spadea, G. and Swamy, R.N., 2007, The Problem of Shear in RC Beams Strengthened with CFRP Laminates, Construction and Building Materials 21(11), Balakrishnan, S., Elwi, A. E., and Murray, D. W., 1998, Effect of modelling on NLFE analysis of concrete structures, Journal of Structural Engineering 114(7), Chaallal, O., Nollet, M.J. and Perraton, D., 1998, Shear Strengthening of RC Beams by Externally Bonded Side CFRP Strips. Journal of Composites for Construction 2(2), Mofidi, A., Chaallal, O. and Shao, Y., 2013, Analytical Design Model for Reinforced Concrete Beams Strengthened in Shear Using L-Shaped CFRP Plates, Journal of Composites for Construction18(1), Triantafillou, T.C. and Antonopoulos, C.P., 2000, Design of Concrete Flexural Members Strengthened in Shear with FRP. Journal of Composites for Construction 4(4), Sayed, A.M., Wang, X. and Wu, Z., 2014, Finite element modeling of the shear capacity of RC beams strengthened with FRP sheets by considering different failure modes, Construction and Building Materials 59,