FINITE ELEMENT SIMULATION ANALYSIS ON STRENGTHENING OF REINFORCED CONCRETE COLUMNS WITH DIFFERENT KINDS OF FRP SHEETS

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1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 26 Paper No. 98 FINITE ELEMENT SIMULATION ANALYSIS ON STRENGTHENING OF REINFORCED CONCRETE COLUMNS WITH DIFFERENT KINDS OF FRP SHEETS Da-chang Zhang 1 and Zhi-shen Wu 2 ABSTRACT The purpose of this paper is to develop choosing standards of FRP sheets, best methods of seismic strengthening and the corresponding theory of strengthening for reinforced concrete columns. Therefore, two-dimensional nonlinear finite element numerical simulations on seismic strengthening of RC columns with 4-type of axial force ratio are carried out, in which the types and the amount (i.e. FRPs stiffness) of FRP sheets are chosen as parameters and the stress-strain curve of confined concrete from FRP and hoops is considered through adopting modified Kent-Park model. Numerical investigation on loading characteristics of RC columns and its retrofitting effectiveness of seismic performance with different types and amount of FRP sheets are performed. Simultaneously, the effects of axial force ratio on the load-deformation relationships of RC columns are discussed. What s more, the failure modes of RC columns are discussed based on the loading characteristics. Lastly, the theory on seismic strengthening of RC column with FRP sheets is provided. Keywords: FRPs, RC column, seismic performance, strengthening, two-dimensional finite element analysis (2D-FEA), load-deformation behavior INTRODUCTION Fiber Reinforced Polymers (FRPs) has been increasingly used to strengthen or rehabilitate the deteriorated, damaged and substandard infrastructures, because FRPs possess many beneficial characteristics such as high strength- and stiffness-to weight ratio, high corrosion resistance, electromagnetic neutrality, inherent tailorability. These high-performance materials can be externally bonded to the surface of concrete structures to be strengthened via a thin layer of adhesive and thus enhance the corresponding service performance. Such kind of bonding technique is very easy to handle by hand without additional equipment and has been accepted as an innovative and promising method for the maintenance, rehabilitation and upgrading of the existing infrastructure. FRPs usually consist of glass, aramid and carbon fibers. Recently, new fiber reinforcing materials like PBO (Zylon ) and ultra-high-strength polyethylene (dyneema ) fibers possess high strength and energy dissipation capacity [1]. Being different from metal material such as steel, FRPs stay elastic until failure and fail in a noticeably brittle manner (as shown in Fig.1). The comparisons of FRPs capacities with steel are shown in Fig.1. However, FRP-strengthened concrete structures can not merely fail in brittle pattern, and it has more complex mechanics behavior than FRPs and reinforced concrete. 1 Associate Professor, College of Civil Engineering, Nanjing University of Technology, Nanjing 219, China, dczhang@njut.edu.cn 2 Professor, Faculty of Engineering, Ibaraki University, Hitachi , Japan, zswu@mx.ibaraki.ac.jp

2 Especially, FRP-strengthened concrete structures need better ductility for prevent earthquake force after seismic strengthening is performed with FRPs. According to engineering experience, the seismic performance of RC structures can be improved in some degree, but the retrofitting effectiveness greatly depending on the kind and layers of FRPs. Therefore, it is very necessary to investigate the failure mechanics, deformation capacity of FRPstrengthened concrete structures with different kinds and layers of FRPs, and provided theories for FRPs seismic strengthening Tensile strength N/mm 2 High strength carbon High elastic carbon Glass fibre D fibre PBO fibre Steel 5 Tensile strain ε In this paper, two-dimensional nonlinear finite Fig.1 Mechanic behaviors of different types of FRPs element numerical simulations on seismic strengthening of RC columns for 1 cases with 4-type of axial force ratio as are carried out, in which the types and the amount (i.e. reinforcing stiffness) of FRP sheets are chosen as parameters and the stress-strain curve of confined concrete from FRP and hoops is considered through adopting modified Kent-Park model. Numerical investigation on loading characteristics of RC columns and its retrofitting effectiveness of seismic performance with different types and amount of FRP sheets are performed. What s more, the failure modes of strengthened RC columns are discussed based on the loading characteristics and deformation pattern. THE OBJECTS AND MODELS OF 2D-FEA Reinforce Concrete Columns Selected or Analysis The RC columns tested by Yoshimura of Tokyo Metropolitan University are selected as analysis objects [2, 3]. The details of these are shown in Fig.2, whose axial force ratio is respectively In test, the four columns failed in shear failure, in which the hoop steels yielded and main bars didn t. In this research, all the columns are assumed strengthened by FRPs in different types and amount, and the investigations of seismic performance for these columns are simulated with 2D-FEA. Constant axial force Longitudinal Steel: 12Φ19 Steel hoop: 2-Φ1@1 Rollers Lateral load y x Rollers Fig.2 Dimensions and reinforcements of RC columns Fig.3 Mesh and boundaries

3 2D-FEA Model of Columns Plane stress element, bar element and grid element are adopted to simulate concrete, bars and hoops, respectively. The mesh configurations and boundary conditions are shown in Fig.3. Loading method of analysis is similar to the test, in which the axial force is firstly applied and kept constant in y- direction, and then lateral load is added with displacement control in x-direction until failure. Material Models Applied in 2D-FEA Concrete In general, continuum model of concrete for cracking, softening and failure is adopted to simulate nonlinear-elastic characteristics for concrete. In previous researches, smeared crack model starts from the notion of a continuum with strain, representing either the width of an individual localized crack, or an average crack strain in case of distribution cracking in reinforced concrete [4]. It has been proved to be effective to decompose the strain into a part that belongs to the crack and a part that belongs to the material at either side of the cracks. An advantage of the continuum model is that cracking, elastic softening behavior and failure can be described in hypoelasticity model. Darwin, Pecknold s equivalent uniaxial strain model is generally applied in strength theory [5, 6], and the equivalent uniaxial strain is calculated from the incremental constitutive relationships before using the uniaxial stress-strain relationship of concrete. Simultaneously, cracking, failure criteria of concrete under biaxial or multi-directional stress states are applied based on equivalent uniaxial strain. The total equivalent uniaxial strain is determined by integrating as Eq.1 over the load path. dσ i ε iu = (1) Ei Failure criteria of concrete under multidirectional stresses state is to describe the differences from uniaxial stress state, in which the failure models and factual strength of concrete can be determined such as compression-compression, tension-compression and tension-tension stresses states. In general, failure criteria are widely used in strength theory under multidirectional stresses state to determine cracking, factual strength and failure of concrete. In this paper, Darwin model 1) is adopted as concrete failure condition under biaxial stresses state, which based on the Kupfer s failure criteria [7, 8]. This model can consider the increase of factual compressive strength under biaxial compressions state and reduction of factual compressive strength under one-axial compression and one-axial tension state. Factual concrete strength will be increased in some degree, because the core concrete is confined by lateral hoop and FRPs. The capacity of RC structure can be evaluated correctly, unless the confinement effect for concrete can be considered in a rational way. Based on the previous researches, modified Kent-Park model [9] can simulate the confinement effect from lateral steels, especially for maximum strength and the descending branch after maximum strength. In this paper, modified Kent- Park model is applied to evaluate the confinement effect on concrete from hoop steels and FRPs. f c = Kf c [ 1 Z m ( ε.2k) ] ε m =. 2K ρ s f yh where K = 1+,.5 Zm =, f c fc 3 h + ρs.2k 145 fc 1 4 sh fc is compressive strength of concrete, f yh is yielding strength of steel, ρ s is steel volume ratio, h and s h are respectively width of core zone concrete in lateral load direction and the space of hoops. Steel and FRP Sheets Models for 2D-FEA 2-node truss element is used to model the main bars. The stress-strain relationship is approximated by

4 bilinear shown in Fig.4. The second module is E 2 =E 1 /1, where E 1 is the elastic modulus of steel. The grid element is used to model hoops. According to previous studies, generally, the contribution of the adhesive for FRP-concrete is very small as compared with that of FRP and so can be ignored. Of course, its bond function between FRPs and concrete is very essential, especially for bending members. Here, the interfacial behavior fy for shear strengthening FRPs is assumed perfect E 21 =E 21 /1 ff bonding. FRP sheets are anisotropic and cannot resist compression and bending but only tensile E 1 stress along its longitudinal direction. In this paper, the mechanical property of FRPs is assumed perfect elastic until rupture shown in Fig.4. (a) Steel model (b) FRP sheet Fig.4 Models of steel and FRP sheets Strengthening FRPs These members were strengthened with different types of FRPs. CF1 (NC) is high strength carbon fibers, and CF7 (GC) is high modulus carbon fibers. The effect of the FRPs stiffness on the behavior of RC beams subjected to shear forces is thus investigated. The stiffness of FRPs laminates is defined as the product t of elastic modulus E f and fiber thickness t [1]. The FRPs reinforcing details of all cases are shown in table 1. The limited growth of CF1(2)[NC], CF7[GC], GF, DF, PF sheets are 1.48%,.35%, 2.5%, 2.64%, 1.675%, respectively. The strength will lose completely when rupture happens. In order to investigate the seismic strengthening performance, the FRPs stiffness t is selected as constant C, namely t = C. 5-kind of C=,, 2553, 516, 7659 are selected, its equivalent layers of high strength carbon fibers are.25,.5, 1., 2., 3., respectively. FRP CF1 (2) [NC] CF7 [GC] Tensile strength /N/mm GF 15 DF 185 PF 4 Table 1 Stiffness parameters of FRP for seismic strengthening Elastic modulus /N/mm 2 Thickness of a layer /mm t /N/mm Total thickness /mm Equivalent layers Note: CF1(2)[NC], CF7[GC], GF, DF, PF are respectively high strength carbon fibers, high modulus carbon fibers, glass fibers, PBO fibers and dyneema fibers.

5 ANALYSIS RESULTS In order to validate the validity of numerous simulating, firstly, the load-deformation relationships of RC columns before being strengthened are simulated and compared with the test results. Above material models are applied in 2D-FEA, the comparisons of the relationships of story shear forcedeformation obtained from analyses and tests are shown in figures 5~9. It can be seen that the 2D- FEA can simulate the load-deformation relationships for RC columns with different axial force ratios. And then the load-deformation relationships of columns strengthened with different FRPs are simulated as above and shown in figures 5~9. As shown in figure 5, the maximum strengths of columns NY, N2Y, N4Y, N6Y are respectively increased comparing with 47kN, 415kN, 437kN, 441kN of RC columns. Moreover, the increasing rates of maximum strengths are larger than 1% except for high modulus carbon fibers. The decreasing rates of post-peak capacities of columns are smaller than before strengthened. Especially for NY, N6Y strengthened with Dyneema fibers didn t decreased obviously. However, the differences of strengths and ductility of columns are not so large, because the FRPs stiffness is small. As shown in figure 6, the maximum strengths of columns after being strengthened are increased in a large degree except for high modulus carbon fibers CF7. The differences of capacities and deformation using different FRPs are obvious. The post-peak capacities show downtrend because of local rupture of FRPs, but the decreasing rates are smaller and slower than these of FRPs stiffness. According to the load-deformation relationships, it can be seen that seismic performance of column strengthened with DF is the best As shown in figure 7, the maximum strengths of columns NY, N2Y, N4Y, N6Y strengthened with FRPs except high modulus CF7 have larger increase than RC columns. The differences of loaddeformation have more obvious than FRPs stiffness. Besides, the column of small axial force ratio has large story deformation corresponding to maximum strength than others. The order of story deformation of columns strengthened by FRPs is NY, N2Y, N4Y, N6Y. The capacities of columns NY, N6Y strengthened by DF didn t show downtrend, but these of columns N2Y, N4Y have downtrends after the story deformation respectively rise to 22.3mm, 22.mm, and DF locally happens rupture. 516 As shown in figure 8, the maximum and its corresponding deformation become larger with the increase of FRPs reinforcing stiffness. The axial force ratio has effect on the story deformation, namely, the column subjected to small axial force has larger story deformation corresponding to maximum capacity. Comparing with above three kind of FRPs stiffness, the capacities didn t shown downtrend during the whole loading process, but there were sudden downtrends for columns reinforced by PF and NC due to local rupture of FRPs As shown in figure 9, the maximum and its corresponding deformation increase with the increase of

6 FRPs reinforcing stiffness. The post-peak capacities of columns NY, N2Y, N4Y strengthened with DF, GF, PF, NC didn t shown downtrend, and N6Y strengthened with NC, PF has a downtrend in capacity, when the story deformation got to 22.6mm, 18.2mm. 6 NY (.25-Layer) for NC for GC for DF for PF NY (.5-Layer) 15 for NC for GC for DF for PF N2Y (.25-Layer) for NC for GC for DF for PF N2Y (.5-Layer) for NC for GC for DF for PF N4Y (.25-Layer) for NC for GC for DF for PF N4Y (.5-Layer) 15 for NC for GC for DF for PF N6Y (.25-Layer) for NC for GC for DF for PF Deflection Deformation X-Direction / 3 N6Y (.5-Layer) 15 for NC for GC for DF for PF Fig.5 Load-deformation relationships of Fig.6 Load-deformation relationships of

7 8 NY (1-Layer) 8 NY (2-Layer) for NC for GC for DF for PF for NC for GC for DF for PF N2Y (1-Layer) 1 N2Y (2-Layer) for NC for GC for DF for PF for NC 2 for GC for DF for PF N4Y (1-Layer) 1 N4Y (2-Layer) for NC for GC for DF for PF for NC 2 for GC for DF for PF N6Y (1-Layer) 1 N6Y (2-Layer) for NC for GC for DF for PF for NC for GC for DF for PF Fig.7 Load-deformation relationships of 2553 Fig.8 Load-deformation relationships of 516

8 8 1 NY (3-Layer) N2Y (3-Layer) for NC for GC for DF for PF for NC for GC for DF for PF N4Y (3-Layer) 12 1 N6Y (3-Layer) for NC for GC for DF for PF for NC for GC for DF for PF Fig.9 Load-deformation relationships of CONCLUSIONS 7659 Based on above investigations on seismic strengthening performance with 2D-FEA, the following conclusions can be drawn. (1) Using FRPs sheets to reinforce RC Columns with different axial force ratio, the shear strength and deformation capacity of RC columns can be improved in some degree, namely, the seismic performances were increased. However, the effectiveness of high modulus carbon fibers with small growth was not better than others, comparatively. (2) The story deformations of strengthened columns were nearly same and the downtrend after maximum strength consistent, when the reinforcing FRPs stiffness was small. With the increase of FRPs stiffness, the effect on load-deformation relationships became larger and larger. (3) Based on load-deformation relationships retrofit with FRPs, it can be seen that the story deformation getting to maximum strength was larger when the FRPs with large growth is adopted. (4) The axial force ratio had an effect on the load-deformation relationships. With the increase of axial force ratio, the maximum strengths retrofitted with FRPs increased a litter, but the corresponding deformations became smaller. (5) The orders of improving seismic performance for 5 types FRPs were DF, GF, PF, NC and GC. REFERENCES Niu H D, Wu Z S. Numerical investigation on strengthening behavior of concrete structures strengthened with hybrid fiber sheets [A]. Japan: Tokyo. Journal of Applied Mechanics [C]. 23,

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