Upgrading ductility of RC beam-column connection with high performance FRP laminates

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1 Upgrading ductility of RC beam-column connection with high performance FRP laminates M, Z, Kabir, H. R. Ashrafi & M. N, Varzaneh Dept. of Civil Engineering, Amirkabir University of Technology, Tehran, Iran Abstract Strengthening and retrofitting of the reinforced concrete beams, which have been designed and built in the past, is one of the most important issues in structural engineering. In this study, reversal loading represents seismic excitation. The criterion for upgrading a RC joint against such loading is increasing its strength and ductility. Using composite fabrics does such enhancement. In this direction, FEM is adopted to analyze the problem, The non-linearity of concrete material, such as tension cracks and compression crush, are included. The steel bars behavior is considered as bilinear elasto-plastic, and Tsai-Wu criterion is used to control FRP failure. 8-Node solid element, 3-D link element, and layer shell element are used for modeling of concrete, steel rebar and FRP laminate, respectively, Both of the as-is and the retrofitted comer joints are subjected to quasi-static cyclic loading, and their performance is investigated and compared with each other, in terms of peak lateral load capacity, ductility, moment-rotation diagram, crack patterns and cracks width. The stacking sequence of FRP laminates is (45,- 45),, and it is made fi-omglass/epoxy materials. The results are presented in terms of load-deflection curves and hysteretic energy loops. The load-deflection curves, for both as-is and strengthened bearncolumn connections, are studied in details, and the influence of using the composite fabrics on continuity of joints, smearing the cracks and limiting their sizes, are considered. The behavior of retrofitted joints is significantly improved in terms of moment bearing capacity, ductility, axial load, and drift.

2 4fj4 DamageandFractureMechanicsVII 1 Introduction Retrofitting and strengthening of the existing structures, and improving their behavior are the important problems, which nowadays are studied by some of the engineers who research in the structural fields. For structural repairing and retrofitting the existing structures, different materials and methods are applied. Some of the study cases are: old buildings; buildings which have technical problems; existing building which are to be used for ti,mctions different from those which have been designed for; buildings which have been damaged by different factors, such as earthquake, explosion, etc.; and building which their behavior needs to improve. A recent experimental work by Pantelides et al [1] is involved with the comparison between retrofitted beam-column joint with FRP fabric. Thdy showed the upgrade of joint strength and fracture mechanism during applied load. There are numerous methods for retrofitting of structures, such as using steel plates which are attached to the structural members, confining the joint or a part of the beam or the column by inserting it in a concrete box, and using composite laminates. Parvin and Granata [2] measured the moment capacity of beam column connection by enhancing FRP overlays. In this paper, the ductility behavior of a concrete connection, retrofitted by polymer fibers, is studied, and then, the results for retrofitted connection are compared with the results for non-retrofitted one. The maximum resisted load in the connection at the time of failure, the stresses in the tensile steel bars, the deformation of the connection for the loading capacity, which is recommended in the code, and the energy, which has been absorbed at the time of failure, are from the cases which are controlled in the retrofitted and non-retrofitted connections. The current analysis is performed, by assuming non-linear behavior, and considering cracking of concrete in tension, crushing of concrete in compression, elasto-plastic behavior of steel, and Tsai- Wu failure criterion for composite, In this direction, the response of RC cantilever been is examined. 2 Geometry of the joint The studied connection is one of the usual ones in concrete structures (especially in those with shear wall), The dimension of the beam is d=300 mm & b=400 mm, and the column is d=400 mm & b=400 mm, The magnitude of bending reinforcement is equal to the least permissible one in the code, and is considered equal to p=o.02 in the column. The beam in the connection is 2000 mm long, and is considered as a cantilever, The loading on it is applied in term of tip reversal displacement, The column length is taken as 3000 mm, which is 1500 mm, at each side of the joint. The length of FRP fabric is 1000 mm at each face of beam-column joint. It is also assumed that the both ends of the column, up and down, are rigid; this is the assumption in equivalent frame, in the contra

3 DamageandFractureMechanicsVII 465 flexure point. The steel bars in the beam and column are distributed uniformly in the four corners of them. The steel bars are mounted such that the continuity of connection could be satisfied. Figure 1shows schematically the joint details. V, *Q Q..,. Figure 1: Geometric characteristics of the RC connection, 3 Modeling of materials The materials, used in this connection, are concrete, steel, and composite laminates. The failure criterion is considered for each material, and is assumed that they behave non-linear. The characteristics of the concrete have been inserted in the table 1, The introduced concrete is capable to cracking in tension and crushing in compression. The failure criterion of the concrete due to multi-axial stresses is: F/fC S>O (1) In which, F is a fimction of the principal stresses, i.e. OXP, cryp, crzp,and S is the failure surface which is determined by the principal stresses and the strength terms of the concrete, The coefficients, which appear in the failure criterion of the concrete, are introduced to the program as constant, and are used in the nonlinear analysis, Table 1 also shows the characteristics of the steel used in the joint. The elasto- plastic behavior of these steel bars is sketched in Figure 2. Figure 3, represents the hysteretic stress-strain relationship of the steel, when subjected to interactive reversal loading. The failure criterion of the steel is at its strain to 0.25.

4 466 DamageandFractureMechanicsVII (7A E=6. 9e6 N/m > Figure 2: The stress-strain of steel AII, used in the Connection. Figure 3: The hysteretic stress-strain relation of steel. A composite laminate, with four layers and total thickness of 1.5 mm (each mm) is used. The applied stacking sequences are (45,-45),. The laminates are made fkom Glass/Epoxy. The strength characteristics of the composite are inserted in table 1, The applied failure criterion is Tsai-Wu. The length of composite laminate is 1,0 m and the beam and column faces are worn by.5 m of this laminate. Figure 1 shows the location of laminate, 4 Finite element solution Four types of element are chosen as: Solid element (3-D reinforced concrete solid element), Link element (3-D spar element), Pipe element (Elastic straight pipe element) and Shell element (Structural shell element), for concrete, steel rebar, dummy element and composite layer, respectively. Pipe is a virtual element that joins node between solid & shell elements in order to produce compatible connecting.

5 DamageandFractureMechanicsVII 467 The analyses are performed at the non-linearity stage. Each step of loading (or unloading) is divided in to 50 to 1000 sub-steps, due to convergence requirements. The Newton-Rophson solution, is applied fully, with the Frontal Method, and all possibilities of the program are employed for convergence. To apply loading procedure, the tip displacement of the cantilever is measured for each step and its equivalent tip force (support reaction); moment and joint rotation are calculated. Thus, for avoid of numerical difficulties, the displacement control is chosen. Two separated loading patterns are performed. In the fust loading, the tip displacement of the cantilever is increased until failure occurs. For second loading pattern, both of the as-is and the retrofitted corner joints are subjected to quasi-static cyclic load. At each cycle, the magnitude of displacement is increased. The loading process is presented in Figure 4, Table 1. General characteristics of the materials Concrete EC=2.6e4N/mmz V=.17 f.=30 N/mmz EU=.003 f,=3 N/mmz Steel E,=2.0e5 N/mmz V=.3 fy=320n/mmz ZU=.25 E,=6.9 N/mm* IComposite E1=4.0e4 N/mmz E2=1.0e3 N/mmz V12=.3 t=0,375 mm G=4.0e3 N/mmz Figure 4: Cyclic loading for hysteretic analysis 5 Limitation and assumptions To overcome in converging of the nonlinear problem, the following assumptions are made:

6 468 DamageandFractureMechanicsVII 5.1 The cross section of the beam element and column element remains plane. For considering this assumption, we should constrain the displacement of all beam or column section nodes (even middle nodes of the beam/column section), The reason of this is that when the crack reached to these nodes, because of high horizontal (or vertical) displacements, the problem does not converge, 5,2 We use SOLID and LINK elements for concrete and steel rebars respectively. It is assumed that the cracks transfer all the shear. 6 Numerical results 6.1 Load-deflection behavior for tip load cantilever beam Figure 5 reveals the importance of FRP laminates effect on increasing of energy absorption, The energy absorbed by retrofitted joint is about 140 percent of as-is one, ~ g :,p + x- -~ w u u. 3a As-Is Retrofitted o S eu 70 SO 93 Tip Displacement (mm) Figure 5: Force-Displacement comparison between as-is and retrofitted connection It is also observed that for finite deformation, the FRP laminates do not increase the load capacity of joints at the limit of service load. But for large displacement, when concrete is crushed and steel is yield, the FRP helps the joints and postpones the failure collapse for higher level of applied tip load. The reason of this event is backed to the nature of GFRP laminates, which have low elasticity modulus and high ultimate load.

7 DamageandFractureMechanicsVII 469 The distribution of crack s pattern for strengthen and un-strengthen of beamcolumn connection at the failure stage, are depicted in Figures 6 & 7, respectively. The transverse cracks at the connection area for retrofitted joint is less than non-retrofitted ones. In another words, FRP helps the joint to be more survived by shifting the transverse cracks to another points,.... /,,! I 1,..,,.,, I, /, I I + H Figure 6: Pattern of developed cracks, while failure occurs in the unretrofitted connection Figure 7: Pattern of developed cracks, while failure occurs in the retrofitted connection

8 470 DamageandFractureMechanicsVII The circle shows the cracks in the crack surface. Lateral views of these circles are as lines. 6.2 Hysteresis loop of joint The applied tip load versus vertical drift curve for the non-retrofitted and retrofitted joints are shown in figures 8a,b. The elongated hysteresis loops show a more ductile behavior in terms of number of cycles and load bearing capacity than the model without FRP composite. For retrofitted connection, the loops are longer and thinner for each cycle of loading, This means that for the same absorbed strain energy; limited deformation and less failure are as a result of strengthening with GFRP. The fust yielding occurred in a longitudinal beam bar at tip Ioadtof 24.4 kn and its corresponding tip displacement of 9 mm. The joint ultimately failed at a tip displacement of 85 mm. A summary and comparison of the strength and ductility results are presented in Table 2. The GFRP composite retrofit increased the strength of joint by 910/0, Table 2: Summary of comparison of the strength and ductility for retrofitted and as-is joint As-is FRP retrofit Ratio 1 PeakLoad 26.79kN 51.19kN 1.91 Tip Displacementat 85mm 95mm 1.12 Instantof Failure Ductility Also note that the elastic stiffhess of the joint does not appreciably increase from as-is to the FRP retrofitted joint. However, the retrofitted joint has a system displacement ductility 44 -%greater than the as-is one, (.?5.20.,5.,. TIP DI Pla..m. t( IIO ~! Figure 8a: Tip force-displacement hysteretic curve for un-retrofitted connection

9 DamageandFractureMechanicsVII Figure 8b: Tip force-displacement hysteretic curve for retrofitted comection Also, the envelope cure for maximum load at each cycle is depicted in figure 9 for both as-is and enhanced connection. M As-ls M Retrofltied Loop Number Figure 9: Envelope curve for maximum load of each cycle

10 472 DamageandFractureMechanicsVII The important influence of strengthening by FRP fabric on continuity of the connection is presented in figure 10 by plotting moment at the face of column versus rotation of joint. It can be seen that atler yielding of steel bars, the FRP wrap limits deformation of joint. Y 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 Rotation (Rad.) 7 Conclusions Figure 10: Moment-rotation at the column face The following conclusion remarks can be made: The GFRP composite can substantially improve the seismic performance of exterior WC building joints without adequate reinforcement, The importance of FRP influence is after yielding of steel bars. Using minimum reinforcement designated by ACI standard code satisfies this condition. The GFRP composite wrap can increase the strength, ductility and drift performance of the joint. References [1] [2] [3] Pantelides, C. P,, Clyde, C., D Reaveley, L., Rehabilitation of WC building joints with FRP composites, Proc, Of 12th WCEE, P , Parvin A, and Granata P.,Numerical study of structural joints reinforced with composite fabrics ACI design code, 1995