AN ALTERNATIVE PROCEDURE FOR THE PERFORMANCE ASSESSMENT OF FRP-RETROFITTED RC BUILDINGS USING LUMPED PLASTICITY

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1 Fourth Asia-Pacific Conference on FRP in Structures (APFIS 2013) December 2013, Melbourne, Australia 2013 International Institute for FRP in Construction AN ALTERNATIVE PROCEDURE FOR THE PERFORMANCE ASSESSMENT OF FRP-RETROFITTED RC BUILDINGS USING LUMPED PLASTICITY P.J. Lim 1, S.S. Mahini 2, H.R. Ronagh 1 1 School of Civil Engineering, University of Queensland, Australia: s @uq.edu.au 2 Discipline of Civil and Environmental Engineering, University of New England, Australia ABSTRACT A reinforced concrete (RC) building designed prior to current codes for seismic design and guidelines for detailing RC beam-column joints needs to be evaluated against the new seismic requirements. Members found to be deficient need to be monitored and subsequently retrofitted. One solution for retrofitting a deficient RC joint so as to avoid brittle joint core failure in an earthquake is to increase its ductility by shifting potential plastic hinges away from the joint. Fibre reinforced polymers (FRPs) are increasingly used to perform such retrofitting. Non-linear static (pushover) analysis can be a fast and relatively accurate method for evaluating the overall seismic performance of a regularly shaped building. It can be performed on commonly available and easy-to-use lumped-plasticity frame analysis (LPFA) computer programs, such as SAP2000. However, such programs cannot directly determine the amount of retrofitting required for each joint and its enhancing effects, a task that only a spread-plasticity frame analysis (SPFA) program can do. Therefore, time-consuming finiteelement analyses (FEA) of the joints need to be performed first before transferring the properties over to the LPFA program for the pushover analysis. This paper will use a LPFA program to indirectly approximate the amount retrofitting required thus replacing the FEA step. The successful results show that this new approach can be easier and more time-efficient than current methods. KEYWORDS Reinforced concrete buildings, plastic hinge relocation, FRP retrofitting, pushover analysis, Finite element analysis, lumped-plasticity frame analysis programs, SAP2000 INTRODUCTION A reinforced concrete (RC) building designed based on older codes needs to be evaluated against the new seismic requirements particularly for detailing RC beam-column joints. Deficient members and joints should be upgraded in order to satisfy new requirements. Inadequate RC joints may suffer from brittle failure following earthquake actions. One solution for retrofitting a brittle RC joint which also increases the ductility of the frame is to shift potential plastic hinges away from the joint. Plastic hinges should be induced to develop sufficiently far away from the joint core to prevent cracks from entering the joint core (Paulay and Priestley 1992). For existing structures, retrofitting the joints by concrete jacketing, steel jacketing and bonding FRP onto the concrete surface have been tried with the latter presenting a simpler and more economical approach. Previous research into the FRP-retrofitting of RC joints with relocation of the plastic hinge into the beam span have had the FRP either bonded to the web (Ghobarah and Said 2001; Mahini and Ronagh 2011) or to the flange (Parvin and Granata 2000; Dalalbashi et al. 2012). The analysis of a building subjected to seismic loading requires consideration of its inelastic behaviour, hence the need for non-linear procedures such as static (pushover) or dynamic (time-history) analyses. Although time-history analyses are more accurate for assessing the behaviour of irregular buildings, pushover analyses can sufficiently evaluate most uniformly shaped buildings without requiring complex modelling, precise definitions of components, non-linear properties or detailed ground motion records (Eslami et al. 2013). Pushover analyses can also be quickly performed on commonly available and easy-to-use lumped-plasticity frame analysis (LPFA) computer programs. Two recent works (Niroomandi et al. 2010; Eslami et al. 2013) had evaluated the pushover performance of the same unretrofitted eight-storey, three-bay RC moment resisting frame (Figure 1) but they had arrived at very different performances (see Figure 2). The frame was designed with ACI (ACI Committee )

2 using the weak-beam-strong-column philosophy and the design dead and live loads were kn/m and kn/m respectively. A peak ground acceleration of 0.30g was imposed on the frame and the earthquake weight of the system was based on dead load plus 20% of live load. Apart from the roof joints, all joints were then retrofitted with sufficient layers of equal length CFRP to relocate the plastic hinges away from the beam-column interface by an FRP length, l f, of 500 mm, equal to the beam overall depth. 500 mm would be adequate to prevent flexural cracks in the beam from entering the joint core. The first study (Niroomandi et al. 2010) had used web-bonded CFRP sheets similar to that by an earlier study (Mahini and Ronagh 2011) ( Figure 3) while the second (Eslami et al. 2013) had used top and bottom flange-bonded CFRP sheets to relocate the plastic hinge. The total thicknesses of CFRP used by the first study for various joints are shown in Figure 4 (each CFRP layer is mm thick) while the second study had used 5 layers of CFRP for beams in the top half of the building and 10 layers of CFRP for beams in the bottom half of the building. Both studies had used materials with the same mechanical properties thus allowing possible comparisons between the two. Figure 1. Concrete and reinforcement details of moment resisting frame (Niroomandi et al. 2010). Figure 2. Comparison of original frame pushover curves. Figure 3. Original (CSM0) and CFRP-retrofitted (RSM2) joint for verification (Mahini and Ronagh 2007) Figure 4. Joint configuration and CFRP thicknesses (Niroomandi et al. 2010) However, the determination of the number of layers of CFRP sufficient to relocate the plastic hinge at each joint and quantification of the effect of each retrofitting could not be directly achieved with an LPFA programs such as SAP2000 (CSI 2009) it could only be achieved with a spread-plasticity frame analysis (SPFA) programs.

3 As a result, each joint was first analysed with a FEA program, ANSYS (ANSYS 2009), and then an increasing number of CFRP sheets were retrofitted onto the joint until the plastic hinge was observed to have relocated to the cut-off point of the CFRP sheets. Both finite-element models (FEM) had been verified and found to have good agreement with the experimental results of the earlier study already mentioned (Mahini and Ronagh 2011). The moment-rotation curves for the joint before and after retrofitting were then plotted together and the difference at each common rotation was attributed to the enhancing effect of the CFRP. This enhancement was then transferred to their new plastic hinge locations in the retrofitted frame (i.e. 500 mm from the beam-column interface) for each retrofitted joint as additional rotational stiffnesses at the joints. In SAP2000, this was achieved through the use of LINK elements. The pushover analysis was then repeated to determine the frame s retrofitted performance. Additionally, to prevent the CFRP from debonding from the concrete surface, there was also a need to ensure that the strain in the CFRP falls within the limits specified for ε fd (Equation 1) by ACI 440.2R-08 (ACI Committee ), where ε fd is the debonding strain of externally bonded FRP reinforcement,, the specified compressive strength of concrete, n, the number of FRP layers, E f and t f the elastic modulus and thickness of the FRP respectively. Unfortunately, these FEA are costly in terms of tuning and model development time and they produce superfluous information not required for the current task. This study will demonstrate the use of the same LPFA program to indirectly approximate the amount of retrofitting required for the frame in the first study and the enhancements due to the retrofitting, thus replacing the FEA step and completing all analyses within a single LPFA program. ALTERNATIVE METHOD Equation 1 The proposed method involves using an LPFA program such as SAP2000 to determine the rotations at equal intervals along the beam for each of the joints in Figure 4 that are to be retrofitted, with the joint being subjected to the same loading and support configuration as in Figure 3. To do so, several plastic hinges will need to be assigned at those locations to be able to capture the instance when a hinge actually forms. The frame had been designed with the weak-beam-strong-column philosophy, so no hinges are expected in the columns and none need to be assigned there. When a graph of rotation versus distance from the column face is plotted, it should show a maximum rotation at the column face for the original unretrofitted joint due to the moment at that point being the maximum and the potential hinge being formed there. Retrofitting the joint with increasing number of layers of web-bonded CFRP, as per the regime used in the first study, would gradually decrease the rotation at the column face and increase it at where the CFRP layers terminate, i.e. at 500 mm from the column face. The plastic hinge has relocated when the rotation value at 500 mm exceeds that at the column face. Figure 5 shows the beam section in the joint being broken up into three parts comprising of: 1) the end-offset length, which is, in reality, within the column and it is of either 350 mm or 250 mm length for different storeys in the frame; 2) the to-be-retrofitted length, which is equal to 500 mm for all beams; and 3) the remaining unretrofitted length. Both the end-offset length and the to-be-retrofitted length will be assigned the appropriate frame section with different number of CFRP layers for their respective cases, while the unretrofitted length will be assigned the unretrofitted frame section throughout the analyses for each joint location. The properties of the materials can be found in the both studies and in Table 1. The moment-curvature relationships for all frame sections, retrofitted and unretrofitted are determined using the moment-curvature calculator within SAP2000 itself with the coordinates at yield and at ultimate strain of concrete recorded down. These values are then used to tabulate the hinge definitions for each frame section with the hinge length chosen as 50 mm. 50 mm will be the fixed distance between the hinges assigned to the beam. Plastic hinges with the correct hinge definitions are then assigned to the beam, with the 500 mm to-be-retrofitted length having 10 hinges and 10 hinge lengths and its first hinge starting at the column face. The unretrofitted length will only need two or three hinges to reveal if a maximum rotation value had occurred at 500 mm from the column face thus indicating plastic hinge relocation. The first hinge here will be placed at the location where the CFRP sheets terminate. After assigning the correct frame sections, hinges and hinge definition, the entire joint is subjected to the constant axial load on the column, as per Figure 3, and finally the load on the beam tip as a displacement-controlled pushover load, pushing the tip down by up to 100 mm to ensure failure. In post-processing, the correct rotations for all the hinges can be extracted and plotted against distances from column face.

4 To-beretrofitted End-offset Unretrofitted Applied load P 10 hinges 2/3 hinges Constant Axial Load Figure 5. Modelling of joint and hinges in SAP2000 Figure 6. (From SAP2000) Rotation of RC member vs distance from beam-column interface for Joint 13. (Negative rotation merely indicates downward curvature.) Table 1. Material properties of joints in frame (in MPa except for Poisson s ratios) Concrete Elastic Modulus E = 24,630 Compressive f c = Tensile f t = Poisson s ratio ν = 0.2 Reinforcement Elastic Modulus E = 200,000 Yield f y = 412 Ultimate f u = Poisson s ratio ν = 0.2 Uniaxial CFRP (fibres in x-direction) Elastic Modulus E x = 240,000 E y =18,581 E x = 18,581 Tensile σ x = 3900 σ y = 53.7 σ z = 53.7 Compressive σ x = 80 σ y = 80 σ z = 80 Shear Modulus G xy = 12,576 G xz = 12,576 G yz = 7,147 Poisson s ratio ν xy = 0.2 ν xz = 0.2 ν yz = 0.3 For Joint 13 in Figure 4, the rotation versus distance from the column face relationships is shown in Figure 6. The relationship for the unretrofitted joint is represented by the J13 line and that for the section with 5 layers of CFRP is represented by the J13 FRP5 line and so on. As can be seen, only 5 layers of CFRP are required to relocate the plastic hinge to 500 mm from the column face. This approach to determining plastic hinge relocation is in principle similar to that used by the two studies (Niroomandi et al. 2010; Eslami et al. 2013) that had used FEMs developed in ANSYS to compare the strain variations in the beam tensile reinforcement in the original joint and the joint retrofitted with 10 layers of CFRP as shown in Figure 7. However, Figure 7 lacks the strain variations for the joint for 5, 6 and 8 layers of CFRP. As a result, FEM of the joint needs to be done here to determine the minimum number of layers required to relocate the plastic hinge so as to verify the results in Figure 6. Any FEM should be verified against available analytical models or experimental data for the model to be reliable. An ANSYS model of the retrofitted joint in Figure 3, RSM2, taken from an earlier study (Mahini and Ronagh 2011), is created and then calibrated against experimental data from the same study. In the model, concrete was represented by eight-node solid elements called SOLID65 elements, steel reinforcement by twonode truss elements called LINK8 elements and the CFRP was modelled as an anisotropic material with eightnode 3D solid elements called SOLID45 elements. The concrete was modelled as a smeared crack model with the five parameter William-Wranke failure criterion (ANSYS 2009) that accounts for both cracking and crushing failures. Shear transfer coefficients for open and closed cracks were taken as 0.3 and 0.7 respectively. Failure of the model is considered to have occurred when either the concrete reaches a strain of or when the steel reinforcement reaches a strain of 0.1. The reader can refer to both studies for more details of the verification model, if required. The force-deformation relationship of the model was plotted, verified against experimental data and found to agree well. The same approach was then used to model Joint 13 of Figure 4 with different number of layers of CFRP retrofitting and the results are shown in Figure 8. Using the rule that the plastic hinge is relocated when the strain in the beam longitudinal tensile reinforcement at/near the column face falls below that at where the CFRP sheets terminate, i.e. at 500 mm, Figure 8 shows that 6 layers of CFRP were required to relocate the plastic

5 hinge. According to the results from the LPFA procedure (Figure 6), five layers of CFRP were found to be required. The closeness of the results indicates that this LPFA procedure can be used as a fast alternative for analysis of FRP-retrofitted joints. Figure 7. (From ANSYS) Strain variations in Joint 13 beam tensile reinforcement before and after 10 layers of FRP retrofitting vs distance/ length from the column face (Niroomandi et al. 2010). Figure 8. (From ANSYS) Strain variations in Joint 13 beam longitudinal tensile reinforcement for different number of layers of CFRP. Furthermore, a plot of the strain contours on the CFRP elements for Specimen J13 FRP6 (Figure 9) showed a maximum tensile strain of mm/mm at the column face which was more than the ACI 440.2R-08 recommended value of mm/mm for 6 layers of CFRP. This issue was resolved when 8 layers of CFRP was used as shown in Figure 10, in which the maximum tensile strain reached mm/mm which was below the limit of mm/mm for 8 layers of CFRP. 10 layers of CFRP was recommended by the first study and the difference is perhaps due to modelling differences or due to the number of layers being rounded off to the nearest 5 layers by the first study. If FEA were not to be used in the LPFA approach suggested in this paper, it is suggested that the number of layers required to relocate the plastic hinge, as determined earlier, should be factored up by 25% or more to satisfy the code requirements. Figure 9. (From ANSYS) Total strain variations in Joint 13 s CFRP elements when concrete ultimate strain is reached. (Largest tensile strain is mm/mm at column face [red].) Figure 10. (From ANSYS) Total strain variations in Joint 13 s CFRP elements when concrete ultimate strain is reached. (Largest tensile strain is mm/mm at column face [red].) VERIFICATION OF THE ALTERNATIVE METHOD Pushover analyses were performed on the original and the retrofitted frames. The result for shown in Figure 2. Close agreement of this result with that of the second study verifies the proposed alternative procedure. For the retrofitted frame, it was first analysed using the former procedure of the two studies (i.e. with a combination of ANSYS and SAP2000 analyses). The thicknesses of CFRP used in the FEM followed that in Figure 4. The same retrofitted frame was then re-analysed with lumped plasticity using SAP2000 only. The

6 length and thickness of CFRP were modelled directly by breaking up retrofitted beams into three parts to incorporate the CFRP retrofitting at their ends (Figure 5). Figure 11 shows the base shear vs roof displacement diagram of the two procedures. Closeness of the results proves that this new alternative procedure is reliable. Figure 11. Comparison of retrofitted frame pushover curves done with ANSYS and with SAP2000. CONCLUSIONS This study has attempted to replace the time-consuming finite-element analysis of FRP-retrofitted RC joints procedure that precedes the pushover analysis of FRP-retrofitted frames, with a simpler and faster lumpedplasticity frame analysis procedure. In this approach, the difference in rotation values along the length of the beam was used to indicate when the plastic hinge has successfully relocated to the cut-off point of CFRP sheets. The results were found to be very close to that found with the former procedure. However, the strain in the CFRP at the column face turned out to be the deciding factor and it is suggested that the number of layers required to relocate the plastic hinge should be factored up by 25% or more to satisfy the code requirements. REFERENCES ACI Committee 318 (1995). Building Code Requirements for Structural Concrete (ACI ) and Commentary. Detroit, Michigan, American Concrete Institute. ACI Committee 440 (2008). ACI 440.2R-08 : Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. Farmington Hills, MI, American Concrete Institute. ANSYS (2009). ANSYS v12.1 Manual. Canonsburg, PA, ANSYS Inc. CSI (2009). SAP2000 v14.1 Manual. Berkeley, CA, Computers and Structures Inc. Dalalbashi, A., Eslami, A. and Ronagh, H. R. (2012). "Plastic hinge relocation in RC joints as an alternative method of retrofitting using FRP." Composite Structures 94(8): Eslami, A., Dalalbashi, A. and Ronagh, H. R. (2013). "On the effect of plastic hinge relocation in RC buildings using CFRP." Composites Part B: Engineering 52(0):

7 Ghobarah, A. and Said, A. (2001). "Seismic Rehabilitation of Beam-Column Joints using FRP Laminates." Journal of Earthquake Engineering 5(1): Mahini, S. S. and Ronagh, H. R. (2007). "A new method for improving ductility in existing RC ordinary moment resisting frames using FRPs." Asian Journal of Civil Engineering (Building and Housing) 8(6): Mahini, S. S. and Ronagh, H. R. (2011). "Web-bonded FRPs for Relocation of Plastic Hinges Away from the Column Face in Exterior RC Joints." Composite Structures 93(10): Niroomandi, A., Maheri, A., Maheri, M. R. and Mahini, S. S. (2010). "Seismic Performance of Ordinary RC Frames Retrofitted at Joints by FRP Sheets." Engineering Structures 32(8): Parvin, A. and Granata, P. (2000). "Investigation on the Effects of Fiber Composites at Concrete Joints." Composites Part B: Engineering 31(6-7): Paulay, T. and Priestley, J. N. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings, Wiley.