MODELING OF CARBON FIBER REINFORCED POLYMER (CFRP) STRENGTHENED REINFORCED CONCRETE (RC) BEAMS: EFFECT OF BEAM SIZE AND CFRP THICKNESS

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 6, June 217, pp , Article ID: IJCIET_8_6_56 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed MODELING OF CARBON FIBER REINFORCED POLYMER (CFRP) STRENGTHENED REINFORCED CONCRETE (RC) BEAMS: EFFECT OF BEAM SIZE AND CFRP THICKNESS M. Jaiswal Assistant Professor, Department of Civil Engineering, NIT Raipur, India G.D. Ramtekkar Professor, Department of Civil Engineering, NIT Raipur, India ABSTRACT This paper is an attempt to simulate the CFRP strengthened RC beams using a software package ANSYS to attain the experimental results which were achieved by different researchers with same target parameters. The first parameter is to check the effect of beam size i.e. effective span which has been modified in such a way that the ratio of effective span to effective depth remains constant. The second parameter is the thickness of CFRP which has been observed with respect to the amount of strengthening. The experimental study carried by Maalej et al. [1] is taken as reference for the modeling parameters in this paper. Results obtained from all beams are compared with the respective models. Key words: Modeling of RC Structures, CFRP, Debonding, Flexure failure, FRP thickness Cite this Article: M. Jaiswal and G.D.Ramtekkar Modeling of Carbon Fiber Reinforced Polymer (CFRP) Strengthened Reinforced Concrete (RC) Beams: Effect of Beam Size and CFRP Thickness. International Journal of Civil Engineering and Technology, 8(6), 217, pp INTRODUCTION Application of fiber reinforced polymer (FRP) sheets to strengthen the existing reinforced concrete members has emerged as a better solution in recent times. Change in earthquake zones, corrosion in reinforcements, change in building type, loading conditions, and use of older versions of standard codes etc. may result to deficient design which leads to the deterioration of members. Strengthening of concrete with CFRP results in an increase in load 57 editor@iaeme.com

2 M. Jaiswal and G.D.Ramtekkar capacity as well as an increase in stiffness [2]. The material properties of the CFRP which shows good tensile strength, modulus of elasticity, and elastic strain are capable enough to enhance the capacity of RC beams. Different arrangements with respect to the direction of fibers, thickness of sheets, and number of layers are proposed by different researchers [3], [4].Non-linear finite element modeling has always been a difficult task to check the behavior of a given specimen. Finite element modeling software ANSYS is a sophisticated tool to simulate the non-linear behavior and shows a good agreement with the experimental results. Kachlakev et al. explained the modeling process of RC beams with FRP laminates [5]. Failure behavior of FRP strengthened RC beams has been explained by Gao et al. [6]. Six distinct failure modes i.e. compression failure before yielding of steel, compression failure after yielding of steel, rupture of FRP strips, shear failure, delimitation of FRP strips, and concrete cover separation have been discussed and explained with diagrams. The present study observes the failure pattern too with respect to the modeled specimen. 2. EXPERIMENTAL PROGRAM Maalej et al. [1] tested seventeen RC beams in four point loading conditions. These beams were categorized in three series A, B, and C. The basis of categorization is shown in Table 1. Each series of beams had two control beams in which no amount of CFRP is applied, two beams with single layer of CFRP, and remaining beams with two layers of CFRP. On the basis of experimental program, one additional category D has been created to check the efficiency of modeling. Beam size ratios have been taken as 1:2:3.2:1.5 for the series A,B,C, and D respectively. Series/ Beams Table 1 Categorization of beams. Effective Span (mm) Effective Depth (mm) No. of Layers of CFRP A1, A2 A A3, A A5, A6 2 B1, B2 B B3, B B5, B6 2 C1, C2 C C3, C C5 2 D1 D D D3 2 The percentage of reinforcement is taken constant in all series of the beams i.e. 1.71% in tension reinforcement, 1.14% in compression reinforcement, and.82% in shear reinforcement. 3. MODELING ANSYS offers different types of elements as per the requirements. In this paper concrete, steel bars, and CFRP are modeled by SOLID 65, LINK 18, and SOLID 185 elements respectively [7]. Each element has its specific properties editor@iaeme.com

3 Modeling of Carbon Fiber Reinforced Polymer (Cfrp) Strengthened Reinforced Concrete (Rc)Beams: Effect of Beam Size and Cfrp Thickness SOLID 65 is an eight nodded solid element with three translation degrees of freedom at each node i.e. x, y, and z directions. It is capable of cracking in three orthogonal directions, plastic deformations, crushing, and creep. There are pre-defined input parameters which enables the user to observe different responses. Crack initiation and propagation is defined in terms of shear transfer coefficient β. The value of β varies from (smooth crack, complete loss of shear transfer) to 1 (rough crack, no loss of shear transfer). In this study to achieve proper convergence shear transfer coefficient β, has been considered from.2 to.4 [8]. Uniaxial tensile stress and uniaxial crushing stress are also the input parameter with respect to the available experimental values. The behavior of concrete in uniaxial compression is expressed by equations (1), (2), and (3) given by Desayi et al. [9] and Gere et al. [1]. The stress strain curve of concrete is converted into a multilinear plotas shown in the figure 1 below. (1) 2 (2) (3) Where; f = stress at strain ε ε= strain at the ultimate compressive strength f c Figure 1 Simplified stress-strain curve for uniaxial compression in concrete. [1] The strain for point 1(up to elastic) is assumed at stress value of.3f c and following points are calculated by using equations 1, 2, and 3. Perfectly plastic state is assumed after point 5 in the figure 1. LINK 18 is a two nodded line element with three translation degree of freedom at each node i. e. x, y, and z directions. This element is capable of plastic deformations. SOLID 185 is a layered solid element with 8 nodes. Each node is having three translational degrees of freedom in x, y, and z directions. The element has plasticity, hyper elasticity, stress stiffening, creep, large deflection, and large strain capabilities. The layers in the element can have anisotropic properties and the orientation of the materials can be defined 59 editor@iaeme.com

4 M. Jaiswal and G.D.Ramtekkar by the direction of shell i. e. perpendicular or z direction of the shell. User can modify the number of layers too in the element as per the requirement. 4. MATERIAL PROPERTIES Steel reinforcements properties for series A, B, C, and D are taken as per the experimental program as shown in the Table 2. Modulus of elasticity, Poisson s ratio, and Yield stress are required in FEM analysis. The behavior of steel bars is assumed as elastic perfectly plastic. Series/ Bars, Diameter (mm) Table 2 Properties of Steel Bars. Young s Modulus (E c), GPa Poisson s Ratio Yield Stress (f y), MPa Yield Strain (ε y), % Longitudinal, A Stirrups, Longitudinal, B Stirrups, Longitudinal, C Stirrups, Longitudinal, D Stirrups, The behavior of concrete is assumed as multilinear elastic. The stresses at different strains are calculated by using equations 1, 2, and 3. Table 3 shows the properties of concrete used in modeling. Table 3 Properties of Concrete Series A 27 Modulus of Elasticity Series B 27 (Ec), GPa Series C 25 Series D 27 Poisson s Ratio.2 Ultimate uniaxial compressive strength (f c), MPa 5 Ultimate uniaxial tensile strength (f r), MPa 3.24 Open Shear Transfer Coefficient.2 Closed Shear Transfer Coefficient.4 Stress (MPa) Strain (mm/mm).. Multilinear uniaxial stress-strain values as per equation 1, 2, and The material properties of CFRP depends upon the orientation of fibers, accordingly one can state the behavior as isotropic, orthotropic, or anisotropic. In current study CFRP is assumed as orthotropic. The carbon fibers are embedded in epoxy resin matrix in such a way that elastic modulus is highest in x direction and same in y and z directions. The Poisson s 51 editor@iaeme.com

5 Modeling of Carbon Fiber Reinforced Polymer (Cfrp) Strengthened Reinforced Concrete (Rc)Beams: Effect of Beam Size and Cfrp Thickness ratio is also different for different planes. Table 4 shows the orthotropic properties of the CFRP material which is used in the modeling. Table 4 Properties of CFRP Modulus of Elasticity (MPa) Poisson s Ratio Shear Modulus (MPa) E x 235 ν xy.22 G xy 126 Tensile Strength (MPa) Ultimate Strain (mm/mm) E y 1824 ν zx.22 G zx E z 1824 ν yz.3 G yz GEOMETRY AND LOADING The longitudinal and transverse profile of series A, B, C, and D beams are shown in the figure 2 and figure 3 respectively and the specification of individual series is defined in Table 5. The transverse reinforcement is avoided at the centre portion of the beam to observe flexural failure. To minimize the computational time, reduction in the number of elements is a preferable method in finite element analysis. This can be achieved by taking the symmetrical planes in the given geometry. All series beams are symmetric at the centre so half beams are modeled. Figure 4 shows the geometry of Series A beam with a symmetric plane at the centre. P/2 P/2 L/3 L/3 L/3 h D1 CFRP D3 D2 Figure 2 Longitudinal profile of Series A, B, C, and D beams. e D1 D2 D3 b CFRP Figure 3 Transverse profile of Series A, B, C, and D beams editor@iaeme.com

6 M. Jaiswal and G.D.Ramtekkar Table 5 Specification of Series A, B, and C Beams Properties Series A Series B Series C Series D L 15 mm 3 mm 48 mm 24 g 75 mm 15 mm 24 mm 12 h 25 mm 5 mm 8 mm 4 D1 2 # 1 φ 2 # 2 φ 2 # 32 φ 2 # 16 φ D2 3 # 1 φ 3 # 2 φ 3 # 32 φ 3 # 16 φ D3 6 6 mm c/c mm c/c mm c/c 1 12 mm c/c b 115 mm 23 mm 368 mm 184 mm d 146 mm 292 mm mm 234 mm e 15 mm 3 mm 51.2 mm 24 mm A plate is provided at the support and loading location to distribute the load evenly. In this case load is applied through the centre nodes of the plate. There are 11 nodes in Series A beams and applied load on each load will be (P/2)/11, where P is the total load on beam. Mesh density is determined by checking the convergence criteria. This will help user to fix the size of the element or number of elements in a model. For Series A beams, element size has been taken as 15 mm. This size is achieved by checking the convergence criteria. A plot (Figure 4) is drawn between deflection and size of element to check the optimum element size. Element size of other beams are calculated by similar method. To apply step loading, ANSYS divides the total load into steps and each step is divided into sub steps. The behavior of structure is seen after each loading step and if convergence problem does not arise than load increases to the next step. ANSYS uses Newton-Raphson method to update the equilibrium stiffness after each iteration. Selection of load steps is a critical decision as one may select number of load steps too large then it may lead to more computational time and selecting less number of load steps may lead to convergence problem and user may not get the desired solution. Convergence Plot Deflection (mm) Element Size (mm) Figure 4 Convergence plot for Series A Beam Figure 5 Geometry of Series A Beam 6. RESULTS AND DISCUSSION Application of CFRP gives a notable amount of strength enhancement in the RC beams and the beams A, B, C, and D have shown the same. Figure 6 shows a typical crack formation in ANSYS. Crack formation takes place when the longitudinal stress (x direction) exceeds the ultimate uniaxial tensile stress of concrete. The vertical lines represent the flexural cracks in editor@iaeme.com

7 Modeling of Carbon Fiber Reinforced Polymer (Cfrp) Strengthened Reinforced Concrete (Rc)Beams: Effect of Beam Size and Cfrp Thickness the beams, circle represents the crushing failure and the diagonal lines are representing the combined failure due to flexure and shear. (a) (b) Figure 6 Initiation of first crack (a), flexural crack (b), and ultimate crack(c) at support and mid span of control beam of Series A. Series B, C, and D beams were modeled in full scale i.e. no plane of symmetry was applied in the model. Following plots show the comparison between experimental and simulated load-deflection curves. It can be observed from the Figure 7 and Figure 8 that loaddeflection curves are following the similar pattern for series A and series B beams respectively. The difference of load values in experimental and FEM method were found as % for A1, A2 beams, 7.24 % for A3, A4 beams, and 4.53 % for A5, A6 beams. The difference of load values in experimental and FEM method were found as 9.37% for B1, B2 beams, 4.45 % for B3, B4 beams, and 4.1 % for B5, B6 beams. Similar results have been found in series C beams. The load value changes significantly when the thickness of CFRP increases from zero layer to one layer and from one layer to two layers. Midspan deflection changes drastically when one layer of CFRP was applied but there is less change in midspan deflection value when second layer of CFRP was applied. This observation itself confirms the stress sharing capacity of the CFRP sheet when it takes the stress carried by the concrete at the location where CFRP and concrete bond was developed. The maximum stress capacity of the CFRP sheet in longitudinal direction is more than the stress developed at the concrete so CFRP sheet failure did not take place. (c) editor@iaeme.com

8 M. Jaiswal and G.D.Ramtekkar A1, A2 A3, A4 A5, A6 1 8 Load (kn) Midspan Displacement (mm) a) (b) Figure 7 Load-Deflection curve of Series A beams: (a) FEM, (b) Experimental [1]. B5, B6 B3, B4 B1, B2 a) Load (kn) Midspan Displacement (mm) Figure 8 Load-Deflection curve of Series B beams: (a) FEM, (b) Experimental [1]. In case of series D beams, load-midspan deflection curve is similar to the pattern observed in other series of beams. Percentage enhancement in load values while implementing CFRP sheets are also close to the expected values. Load-Midspan deflection plot for series D beams is shown in Figure 9. 2 D1 D2 D3 Load (kn) Midspan Deflection (mm) Figure 9 Load-Deflection curve of Series D beams editor@iaeme.com

9 Modeling of Carbon Fiber Reinforced Polymer (Cfrp) Strengthened Reinforced Concrete (Rc)Beams: Effect of Beam Size and Cfrp Thickness The Figure 1 shows the effect of number of CFRP layers on interfacial stresses for all the cases. It can be said that the number of layers have similar influence on each beams. Debonding takes place when one layer of CFRP is applied which can be avoided by increasing the number of layers. Similarly if we compare the beam size with the shear stress it was found that it did not have significant influence. Beams were plotted in two groups, Group 1 with single layer of CFRP and Group 2 with Double layers of CFRP. Figure 11 shows the shear stress versus beam depth plot and it can be observed that change in depth does not have noticeable impact. 4 Stress (MPa) Number of CFRP Layers A B C D Figure 1 Flexural stresses for all cases. 2.5 Shear Stress (MPa) Beam Depth (mm) Group 2 ANSYS Group 1 ANSYS Group 1 Experimental Group 2 Experimental Figure 11 Shear Stress vs Beam Depth. 7. CONCLUSION The similarity between experimental and simulated results shows the effectiveness of ANSYS in modeling of FRP strengthened RC members. Use of CFRP in strengthening of deficient designed RC members has significant influence. The tensile strength capabilities of CFRP can be utilized in strengthening of beams, columns, beam-column joints and other members of a RC structure. The effect of beam size by taking beams of different cross sections and number of layers of external FRP system is discussed in the paper and it has been found that interfacial stresses are increased while increasing the beam size and number of layers. The ultimate FRP strain is decreased when number of layers were increased editor@iaeme.com

10 M. Jaiswal and G.D.Ramtekkar REFERENCES [1] Maalej, M., & Leong, K. S. (25). Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRP-strengthened beams. Composites Science and Technology, 65(7), [2] Issa, C. A., & AbouJouadeh, A. (24). Carbon fiber reinforced polymer strengthening of reinforced concrete beams: Experimental study. Journal of architectural engineering, 1(4), [3] Brena, S. F., & Macri, B. M. (24). Effect of carbon-fiber-reinforced polymer laminate configuration on the behavior of strengthened reinforced concrete beams. Journal of composites for construction, 8(3), [4] Alagusundaramoorthy, P., Harik, I. E., & Choo, C. C. (23). Flexural behavior of R/C beams strengthened with carbon fiber reinforced polymer sheets or fabric. Journal of composites for Construction, 7(4), [5] Damian, K., Thomas, M., Solomon, Y., Kasidit, C., & Tanarat, P. (21). Finite element modeling of reinforced concrete structures strengthened with FRP laminates. Report for Oregon Department of Transportation, Salem. [6] Gao, B., Leung, C. K., & Kim, J. K. (27). Failure diagrams of FRP strengthened RC beams. Composite structures, 77(4), [7] ANSYS, U. S. M. (1998). Structural analysis guide. ANSYS Inc. [8] Kachlakev, D., Miller, T., Yim, S., Chansawat, K., & Potisuk, T. (21). Finite element modeling of concrete structures strengthened with FRP laminates. Final report, SPR, 316. [9] Desayi, P., & Krishnan, S. (1964, March). Equation for the stress-strain curve of concrete. In Journal Proceedings (Vol. 61, No. 3, pp ). [1] Gere, J. M., & Timoshenko, S. P. (1997). Mechanics of materials, PWS-KENT Publishing Company, ISBN, 534(92174), 4. [11] R. Sasipriya, E. Ezhilarasi, A. Thangadurai and P. Magudeaswaran, An Experimental Study on Flexural Behaviour of Damaged Reinforced HPC Beams Strengthened with CFRP Wrapping. International Journal of Civil Engineering and Technology, 8(3), 217, pp [12] Asst. Prof. Abdul Ridah Saleh Al-Fatlawi and Ahmed Hadi Hassan, CFRP Strengthening of Circular Concrete Slab with and without Openings, International Journal of Civil Engineering and Technology, 7(1), 216, pp [13] Abdul Ridah Saleh Al-Fatlawi and Dhoha Saad Hanoon, Stress Analysis of CFRP Strengthened Slabs Subjected to Temperature Change. International Journal of Civil Engineering and Technology, 8(1), 217, pp [14] Bangash, M. Y. H. (1989). Concrete and concrete structures: Numerical modelling and applications