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Plastic hinge relocation in RC joints as an alternative method of retrofitting using FRP
Composite Structures 94 (2012) 2433–2439
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Plastic hinge relocation in RC joints as an alternative method of retrofitting using FRP A. Dalalbashi a, A. Eslami b, H.R. Ronagh b,⇑ a b
Graduate Student, Dept. of Civil Engineering, Yazd University, Yazd, Iran School of Civil Engineering, The University of Queensland, Brisbane, Australia
a r t i c l e
i n f o
Article history: Available online 19 February 2012 Keywords: FRP Beam–column joint Plastic hinge Retrofitting Nonlinear FE analysis
a b s t r a c t The efficiency of fiber reinforced polymers (FRPs) in enhancing the performance of deficient reinforced concrete (RC) joints has been investigated in recent years. Relocating plastic hinge from the column face toward the beam is an effective method of upgrading RC beam–column joints. This retrofitting approach might also prevent the formation of undesirable brittle joint failure. In this paper, the numerical results of analysing three FRP retrofitted RC joints are compared in order to investigate the effectiveness of FRP composites in improving the performance of the beam to column joints through the relocation of the plastic hinges away from the joint core. Different configurations of FRP application, including a novel retrofitting scheme at beam–column joints, are assessed and the efficiency of each composite architecture in relocating the plastic hinge is discussed. The results show that the newly proposed configuration is not only capable of relocating plastic hinges and improving the load carrying capacity of the joints but is also capable of preventing the typical interface failure. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Application of fibre reinforced polymers for strengthening/ restoring reinforced concrete structures has attracted a lot of attention from researchers and engineers alike in recent years. FRP has outstanding advantages over steel including light weight, high corrosion resistance, superior strength and ease of application. FRP laminates and sheets can be moulded to the concrete surface for structural repair/retrofitting purposes. Increasing the applied load, human errors and a lack of seismic detailing have been accounted as some of the main reasons of the strengthening. In addition, FRP composites in the form of bar, sheet, and/or laminate can be used in new construction. Seismic retrofitting/repairing of RC structural elements using advanced composite materials has been of great interest, especially in the last decade. Numerous studies have been carried out on the application of FRP in strengthening of RC members; such as, beams [1–3] and columns [4–8]. Researchers have also investigated related problems such as debonding failure and methods of overcoming brittle failures [9–11]. Beam–column joints are critical regions of RC structures designed for inelastic response to seismic forces. The overall ⇑ Corresponding author. Address: School of Civil Engineering, The University of Queensland, Brisbane, QLD 4072, Australia. Tel.: +61 7 3365 9117; fax: +61 7 3365 4599. E-mail address: [email protected] (H.R. Ronagh). 0263-8223/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2012.02.016
structural strength, stiffness and ductility, are highly dependent upon the performance of joint core and end critical regions of beams and columns in the vicinity of beam to column connections. The well-known design philosophy of strong-column weak-beam would only work properly if the joints of RC structures perform as intended without any brittle failure. The effectiveness of FRP composites to improve/restore the seismic capacity of beam– column connections has been confirmed in many studies [9,12– 17]. Recently, Attari et al. [18] carried out an experimental study to evaluate the effect of external strengthening of beam–column joints using different types of fiber reinforced composites. They concluded that a combination of carbon and glass fiber reinforced polymers could improve the shear strength and ductility of deficient beam–column joints. The web-bonded strengthening method for rehabilitation of deficient RC joints using composites has been investigated by Mahini and Ronagh [19,20]. Their experimental and analytical results confirmed the capability of this method in not only restoring, but also upgrading the strength of system. In particular, through the relocation of plastic hinges from the column face, they showed that this method can prevent joint core brittle failure mode. In another experimental investigation, Le-Trung et al. [21] carried out a comprehensive experimental study on the different configurations of FRP retrofit to strengthen RC joints. They concluded that the appropriate adding of composites can significantly enhance the lateral strength and ductility of non-seismically designed specimens. Despite the adequacy of numerical finite element modelling in predicting the behaviour
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of RC joints retrofitted using composite materials, only a few studies have been directed towards this. In a numerical study, Parvin and Granata [22] proposed a finite element model for the nonlinear analysis of FRP-strengthened RC joints. They observed that by using FRP composites, the moment capacity of the joints could be increased by up to 37% while a maximum 18% reduction in the rotation of the joints was noticed. In another study, Mostofinejad and Talaeitaba [23] developed a finite element modelling for nonlinear analysis of RC joints covered with FRP overlays. Their results showed that the numerical model could predict the experimental work with good accuracy. Based on the reviewed literature, all experimental and numerical studies on the use of FRP on RC beam–column joints were carried out on the non-seismically deficient specimens. Technically speaking, the main objective of the FRP retrofits in past studies were to improve the behaviour of RC joints suffering from structural deficiencies; nevertheless, many existing code-compliant RC buildings might be in need of retrofitting. Being located in the near-fault regions with their higher seismic demands as reported in some studies [24–29], represents another need for the retrofitting of modern engineered buildings detailed based on the recent seismic codes. It is also noted that most of the past studies available in the literature did not simulate real field conditions. Even in the exterior beam–column connections, the case in which both sides of the joint core were retrofitted in the earlier studies, only one side is accessible due to the existence of the transverse beam. According to Antonopoulos and Triantafillou [30], the effectiveness of an FRP retrofit in increasing the strength, stiffness, and energy dissipation is reduced significantly due to the presence of a transverse beam, a fact ignored in most of the mentioned studies. More investigations will need to be performed on the FRP retrofitting of RC joints simulating real field conditions and other limitations attributable to practicality of designs and real structures. Among the methods of retrofitting, increasing the level of steel reinforcing in the critical regions of beams near the joint region, has been suggested as an effective method in relocating the plastic hinge away from the joint core [31]. In addition to increasing the lateral load carrying capacity of the structure, this method can also prevent the undesirable failure mode of weak-column strongbeam. Installation of FRP sheets on the exterior surfaces of beams and columns provides an opportunity for strengthening RC joints through the relocation of plastic hinges towards the beams. However, an appropriate composite configuration needs to be proposed for this method to be effective. In this paper, the capability of FRP retrofits applied to the exterior surfaces of RC joints in a practical design for relocating plastic hinges away from the joint core is discussed. Through the calibration with experimental test, nonlinear finite element analyses of three feasible composite configurations were carried out and the capability and advantages of different retrofitting architectures were compared with each other. Due to the fact that many past studies [32,33] have highlighted the possibility of interface failure at the termination of FRP composites, in the current study a novel strengthening architecture is introduced to prevent such a stress concentration at the beam–column interface. The FRP architectures were designed considering the application of each scheme to actual structures.
2. Experimental calibration It is common practice for the first step of every numerical study to be the verification of the analysis results through comparison with an experimental investigation. In this study, an experimental study carried out by Mahini and Ronagh [20] was selected in order to validate the finite element results and the analysis parameters. For this purpose, the specimen RSM2 was selected. In their study,
the scaled-down beam–column joints were retrofitted using web-bonded FRPs in order to relocate plastic hinges away from the joint core of deficient exterior beam–column sub-assemblage. Fig. 1 shows the details of CFRP strengthened beam–column joint tested in their study together with reinforcement details. The compressive strength of concrete was measured to be about 40.75 MPa. In addition, the yield steel strengths of longitudinal and transverse reinforcement in the beam–column joints were 500 MPa and 382 MPa, respectively. In this study, the commonly used Hognestad’s model [34] was used for the stress–strain curve of concrete in which the strain under uniaxial stress conditions corresponding to the concrete compressive strength was taken as 0.002. This value is recommended by Park and Paulay [35] and other researchers [36,37] for normal concrete. The ultimate concrete strain was assumed to be 0.0038. The simplified bilinear model with strain hardening was also used to simulate the behaviour of longitudinal steels. For shear reinforcements, an elastic-perfectly plastic model was used, according to test results [20]. ANSYS program [38] was employed to perform nonlinear FE analysis. All steel bars and stirrups were modelled using LINK8 truss element. In addition, SOLID65 element was employed to model concrete. This element, which is capable of modelling both cracking in tension and crushing in compression, has been especially designed for modelling concrete in ANSYS. FRP composites were modelled using an eight-node 3D solid element called SOLID45. This multi-layer element is defined by eight nodes. This element, which is normally used to represent bilinear anisotropic materials, was reported as the most suitable element in ANSYS for modelling the behaviour of FRP [20,22,23,39]. The above mentioned SOLID45 is also employed for the steel plates, which were added at the support locations of the column to provide a more even stress distribution over the support area. The behaviour of CFRP materials were modelled based on an anisotropic material called ANISO [20,23]. This model allows the introduction of the mechanical properties of FRPs in tension and compression in different directions. The mechanical properties of CFRP fibres used by Mahini and Ronagh [20] are given in Table 1. It is worth mentioning that these values satisfy the consistency equations necessary for an anisotropic material like ANISO in the nonlinear analysis, as described in ANSYS and stated by Kachlakev et al. [40]. The other assumptions for numerical modelling were the same as those implemented by Mahini and Ronagh [20]. In ANSYS, the five-parameter William–Wranke model in which both cracking and crushing failure modes are accounted for, has been suggested as a concrete failure criterion [38]. It should be mentioned that this model uses a smeared crack model. The 3-D failure surface for concrete calculated based on this model, is illustrated in Fig. 2. In addition, in order to define concrete materials in ANSYS, two shear transfer coefficients, bt and bc, need to be introduced for open cracks and closed cracks. Both coefficients have values between 0 and 1. The value used for bt in the past studies, however, varied between 0.05 and 0.3 [20,23,40]. According to the past study [20], the best estimate of the nonlinear behaviour of the tested joint is obtained if a shear transfer coefficient, bt, equal to 0.3 is taken for open cracks. Furthermore, The shear transfer coefficient, bc, of 0.7 was used for closed cracks, as recommended by ANSYS. Numerical analysis of the tested specimens was carried out according to aforementioned assumptions. In the nonlinear analysis, the load was applied step by step using the modified Newton– Raphson method to arrive at the solution. A displacement control method was used for loading in order to avoid convergence problems. Fig. 3 compares the beam tip load–displacement curves obtained from the nonlinear FE analysis in the current study with that extracted from the experiment [20]. Good agreement between the two curves proves reliability of the adopted FE analysis. This is
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220 mm 2N12
2N12
Section c-c
180
Tie R6.5
R6.5 @ 25mm 50 mm 2 R6.5
4 N12 R6.5 @ 150mm
Applied Load
Web bonded CFRP a
b
a
b
P1
1402 mm
4 N12
50
R6.5 @ 150mm R6.5 @ 30 mm 180
tf
tf
lf c
230
2N12
c
Tie R6.5 2N12
Section b-b
Section a-a Constant Axial Load ( P = 305 kN ) 2
1246 mm
Specimen
lf
(mm) No. of ply
tf
(mm)
CSM0
-
-
-
RSM1
350
1
0.165
RSM2
200
3
0.495
Fig. 1. The CFRP retrofitted beam–column joint (RSM2) tested by Mahini and Ronagh [20].
Table 1 Mechanical properties of CFRP fibres. Tensile strength ffr (MPa)
Ultimate tensile strain efr
Tensile modulus Ef (MPa)
Thickness tf (mm)
3900
0.0155
240,000
0.165
particularly so when this agreement is measured in terms of the ultimate strength.
objective. This moment-resisting building was detailed based on the intermediate seismic provisions of ACI 318-95 [42]. All numerical models were built to simulate this code-compliant joint as an un-retrofitted model. The joint was cut out from the inflection point to simulate the real performance of subassembly under seismic actions [20]. The dimensions and reinforcement details of the studied exterior beam–column connection are shown in Fig. 5. The compressive strength, fc0 and tensile strength, ft of concrete were 27.46 MPa and 3.67 MPa, respectively. Furthermore, the yield stress of steel bars was taken as 412 MPa. 3.1. Original joint
3. Numerical modelling of original and FRP retrofitted joint Following the validation of nonlinear FE parameters, the numerical analysis of a code-compliant RC joint retrofitted with composite sheets, was carried out to evaluate the capability of FRP retrofits in relocating plastic hinges away from the column faces. As illustrated in Fig. 4, the exterior beam–column joint at the first level of an 8-storey RC building designed by Maheri and Akbari [41], was selected as the case study in order to pursue this
Fig. 6 shows a FE illustration of the unreinforced joint considered for retrofitting in the current study. As is observed in this figure, the boundary conditions at the column supports are similar to the actual behaviour of the structure during seismic loads. The elements and parameters employed for nonlinear FE analysis was similar to the one applied in the verified model. The LINK8 and SOLID65 were used to model concrete material and steel reinforcement, respectively. Steel plates were also modelled at the column
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A
φ10 @ 200 mm
Constant Axial Load ( N=2685 kN )
P
A
φ10 @ 100 mm
φ10 @ 200 mm
B
φ10 @ 200 mm
2500 700
500
Fig. 2. Three dimensional failure surface calculated based on the William–Wranke criterion [38].
ρ ' s=0.009
60
ρ t=0.019
500
60
ρ s=0.012
Section B-B
700
φ10 @ 150 mm
3000
B
Section A-A
Fig. 5. Reinforcement details and geometry of the original joints (all dimensions in mm).
25
Load, P (kN)
20 15 10 Experiment [20]
5 0
Nonlinear FE analysis
0
10
20
30
40
50
60
70
Displacement, Δ (mm) Fig. 3. Comparison of load–displacement curves for specimen RSM2.
CL
8@3m
Fig. 6. FE model of original joint.
Selected joint 3@5m
Fig. 4. Exterior beam–column joint selected for FRP retrofitting.
support to eliminate stress concentration at the supports. A bilinear model with strain hardening was used in the nonlinear analysis
to consider the behaviour of steel reinforcement. The concrete nonlinear behaviour was simulated with the Hognestad model [34]. In order to consider the effect of axial forces on the nonlinear analysis, the column was subjected to a constant axial load equal to 0:2fc0 Ag where fc0 is the concrete compressive strength and Ag represents the gross area of the column cross section [43]. This load was applied in the form of surface pressure to the column. Reported experimental studies confirm that application of the column axial load increases the confinement effect of the beam– column joint area to a certain degree and results in increasing the shear strength of the joint [44]. As depicted in Fig. 5, a monotonically increasing static load was applied at the beam tip up to
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the failure. The load was applied in the form of displacement to prevent convergence problems and the reaction was calculated (see Fig. 6). 3.2. FRP retrofitted joints Similar to the verified model, the multi-layer SOLID45 element with ANISO material was used to model the behaviour of FRP. All other required parameters for modelling the composite material were identical to the verified model except for the thickness of laminates and wraps. Since the composite materials used were unidirectional, their properties were rotated for FRP wrapping in the numerical modelling. The retrofitting schemes included three different practical FRP configurations applied to the exterior surfaces of beam to column connections as illustrated in Fig. 7. All strengthening strategies were based on increasing the flexural strength of beam in the critical region near the joint core. The first case was the application of composite sheets at the beam to column connection in the form of an L shape, as shown in Fig. 7a. Past experimental and numerical studies [21,22] reported that wrapping of the beam and column can prevent the early delimitation of FRP laminate near the joint core resulting in a better performance for the retrofit. For this
200
(a)
500
Fibre Laminates
(b)
reason, two FRP wraps were applied at the beam and column ends. Moreover, some researchers suggested that a second wrap, as illustrated in Fig. 7a, could facilitate the transfer of tensile forces from the FRP laminate to the beam [45]. The thickness of composite sheets was selected to ensure the relocation of plastic hinges away from the column face. For the selected joint, this was achieved using at least six layers of CFRP sheets. Nonlinear FE analysis confirmed that this thickness is necessary in all retrofit configurations for the plastic hinge to be relocated. It should be noted that the thickness of composite sheets to cause this relocation depends on the beam and column geometry, reinforcement details, and composite properties. In another experimental study, Granata and Parvin [12] reported that the thickness of FRP wrap must be at least 35% greater than that of sheet thickness to prevent its rupture. Thus, in this study, nine layers of the abovementioned CFRP are utilised for each wrap. The width of all FRP wraps was taken as 75 mm to be practical. In the second design, FRP retrofit was applied at the top and bottom surfaces of the beam at the critical region near the joint core as observed in Fig. 7b. Since debonding is a significant drawback of FRP retrofit, in the third case, FRP sheets were placed inside the column for a length equal to the column concrete cover. In practice, this could be achieved by creating a groove inside the column cover and filling it after composite installation by injecting the epoxy resin. This method could provide a good bond between the FRP sheets and the concrete beam at the joint. Fig 7c shows the schematic illustration of this novel design. This configuration was decided as it was found that the second configuration is not capable of relocating the plastic hinge as discussed in the following. Debonding is a major problem associated with many FRP applications. Despite the wrapping and grooving in the configurations above, in order to prevent undesired debonding failure at the end sections, a failure controlled by FRP debonding may occur away from the end section where the externally bonded FRP laminates terminates. In order to eliminate such intermediate crack-induced debonding failure mode, the maximum strain in the FRP laminates was limited to the threshold value suggested by ACI 440.2-08 [46]. According to this code, the strain level at which debonding may occur, efd, is given by:
efd 500
Fibre Laminates
(c)
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sffiffiffiffiffiffiffiffiffiffiffi fc0 ¼ 0:41 6 0:9efu nEf t f
ð1Þ
where fc0 is the compressive strength of concrete; Ef is the elastic modulus of composite materials, tf is the thickness of FRP laminates; n is the number of FRP layers; and efu is the ultimate tensile strain of FRP. It should be mentioned that the model of FRP debonding adopted by Eq. (1) is a modified form of the one proposed by Teng et al. [47]. A comprehensive review on the state-of-the-art of bond strength of FRP laminate to concrete has been provided by Sayed-Ahmed et al. [48]. 4. FE analysis results and discussion
50
500
Fibre Laminates
Fig. 7. FRP configuration and loading conditions of the selected joint (all dimensions in mm): (a) first design; (b) second design; and (c) third design.
In addition to increase the joint strength, relocation of the plastic hinges away from the column face is considered as the main aim of the proposed retrofitting undertaken in this study. It was found that this can be achieved in the first and third case with at least six layers of CFRP. However, the result of the second design was substantially different from others. While all retrofitting configurations resulted in strength enhancement, FRP composites did not affect the formation of the plastic hinge in the second case. Fig. 8 compares the strain distribution in the tensile longitudinal reinforcements of the beam at the last step of loading for the three retrofitting schemes. Taking into consideration the strain values
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0.014 0.012
Strain (mm/mm)
Table 2 Nonlinear analysis results.
Original joint First retrofitting design Second retrofitting design Third retrofitting design
0.010 0.008 0.006
No. of laminate layers
No. of wrap layers
Maximum load (kN)
Increase (%)
Ductility index
Decrease (%)
Original First Second Third
– 6 6 6
– 9 – 9
268.8 328.4 309.4 340.1
– 22 15 27
2.2 1.8 1.5 1.9
– 18 32 14
0.004 0.002 0.000
0
500
1000
1500
2000
2500
Distance from the column face (mm) Fig. 8. Comparison of strain variation in the longitudinal tensile steels of beam at the last step of loading before and after FRP retrofitting.
along the beam top bars, the capability of the first and third cases in relocating plastic hinges were confirmed. It is worth mentioning that even with increasing the thickness of FRP sheets up to five times in the second retrofitting configuration; plastic hinge was formed near the joint core, indicating the inability of the retrofitting scheme in relocating plastic hinge. This is particularly due to the termination of composite laminates at the beam–column interface. The load–displacement curves of beam tip for the three retrofitting models obtained from nonlinear FE analysis are compared in Fig. 9. While the initial stiffness of all joints were identical, this showed a notable increase for the retrofitted joints after cracking resulting in the remarkable increases in the ultimate strength. The maximum strength and its magnitude of increase for strengthened and original joints are given in Table 2. In addition to the strength, ductility is also an important parameter in seismic performance of structures. The ductility factor is defined as the ratio of ultimate displacement to the displacement at first yield of tensile reinforcements. The amount of ductility depends to a great extent on the retrofitting configuration. A retrofitting architecture might aim to improve strength, ductility or both of these in a structural component which results in the overall enhancement of the structural behaviour. Ductility enhancement could be obtained through the retrofitting techniques aim to provide confinement. However, ductility enhancement could not be expected with the types of FRP architectures in this study as they aimed to increase the strength. As shown in Table 2, the results
400 350 300
Load, P (kN)
Design no.
5. Conclusion This paper reports the results of a numerical investigation on FRP strengthening of RC structures. Three practical retrofitting architectures were proposed in order not only to increase the load carrying capacity, but also relocate the plastic hinges away from the column faces. However, the latter was not observed using the second retrofitting technique due to the interface failure. The first and third design indicated the capability of externally bonded FRP laminates in relocating the plastic hinge away from the column faces in order to increase the load carrying capacity and eliminating the undesirable weak-column strong-beam mechanism. This could also prevent the brittle joint shear failure. All strengthening configurations showed a significant increase in the ultimate strength of the joint. The highest value (almost 27%) was observed in the third design where the interface failure was prevented through the insertion of FRP laminates in the concrete cover of column. Nonlinear FE outcomes confirmed the reliability of the adopted FE model in predicting the seismic behaviour and load carrying capacity of RC structures, especially for retrofitting purposes. While the results are reliable and justifiable, more studies have to be conducted on the FRP retrofitting of code-compliant RC joint in order to quantify the increase in both strength and/or ductility and to formulate a design approach. References
250 200 150 Original joint
100
First retrofitting design Second retrofitting design
50 0
of FE analysis also confirmed the objective of this type of retrofitting. This conclusion has also been addressed by other researchers [18,23]. Design of the third retrofitting configuration was based on the elimination of interface failure as mentioned above and reported by other researchers [32,33]. Other conditions in the third case were exactly similar to the second scheme. The nonlinear analysis outcomes in the three retrofitting cases showed that the third case offers some advantages, particularly in the strength enhancement and ductility, compared to the others. Considering the high proportion of labour cost in the strengthening of structures, implementation of the third architecture would be more acceptable in real practice. It is noted that others have found it to be advantageous due to the excellent bond between FRP and concrete [18] created as a result of grooving.
Third retrofitting design
0
5
10
15
20
25
30
35
40
45
Displacement, Δ (mm) Fig. 9. Distribution of load vs. displacement of the beam tip for original and FRPretrofitted joint.
[1] Shahawy MA, Arockiasamy M, Beitelman T, Sowrirajan R. Reinforced concrete rectangular beams strengthened with CFRP laminates. Compos Part B: Eng 1996;27:225–33. [2] Saadatmanesh H. Extending service life of concrete and masonry structures with fiber composites. Construct Build Mater 1997;11:327–35. [3] Rabinovitch O, Frostig Y. Experiments and analytical comparison of RC beams strengthened with CFRP composites. Compos Part B: Eng 2003;34:663–77. [4] Saadatmanesh H, Ehsani MR, Jin L. Repair of earthquake-damaged RC columns with FRP wraps. ACI Struct J 1997;94:206–15. [5] Chaallal O, Shahawy M. Performance of fiber-reinforced polymer-wrapped reinforced concrete column under combined axial-flexural loading. ACI Struct J 2000;97:659–68. [6] Harajli MH, Rteil AA. Effect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismic performance of gravity load-designed columns. ACI Struct J 2004;101:47–56.
A. Dalalbashi et al. / Composite Structures 94 (2012) 2433–2439 [7] Toutanji H, Han M, Gilbert J, Matthys S. Behavior of large-scale rectangular columns confined with FRP composites. J Compos Construct 2010;14:62–71. [8] De Luca A, Nardone F, Matta F, Nanni A, Lignola GP, Prota A. Structural evaluation of full-scale FRP-confined reinforced concrete columns. J Compos Construct 2011;15:112–23. [9] Antonopoulos CP, Triantafillou TC. Analysis of FRP-strengthened RC beam– column joints. J Compos Construct 2002;6:41–51. [10] Mosallam AS, Banerjee S. Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates. Compos Part B: Eng 2007;38:781–93. [11] Mostofinejad D, Mahmoudabadi E. Grooving as alternative method of surface preparation to postpone debonding of FRP laminates in concrete beams. J Compos Construct 2010;14:804–11. [12] Granata PJ, Parvin A. An experimental study on Kevlar strengthening of beam– column connections. Compos Struct 2001;53:163–71. [13] El-Amoury T, Ghobarah A. Seismic rehabilitation of beam–column joint using GFRP sheets. Eng Struct 2002;24:1397–407. [14] Ghobarah A, Said A. Shear strengthening of beam–column joints. Eng Struct 2002;24:881–8. [15] Said AM, Nehdi ML. Use of FRP for RC frames in seismic zones: Part I. Evaluation of FRP beam–column joint rehabilitation techniques. Appl Compos Mater 2004;11:205–26. [16] Ghobarah A, El-Amoury T. Seismic rehabilitation of deficient exterior concrete frame joints. J Compos Construct 2005;9:408–16. [17] Mukherjee A, Joshi M. FRPC reinforced concrete beam–column joints under cyclic excitation. Compos Struct 2005;70:185–99. [18] Attari N, Amziane S, Chemrouk M. Efficiency of beam–column joint strengthened by FRP laminates. Adv Compos Mater 2010;19:171–83. [19] Mahini SS, Ronagh HR. Strength and ductility of FRP web-bonded RC beams for the assessment of retrofitted beam–column joints. Compos Struct 2010;92:1325–32. [20] Mahini SS, Ronagh HR. Web-bonded FRPs for relocation of plastic hinges away from the column face in exterior RC joints. Compos Struct 2011;93:2460–72. [21] Le-Trung K, Lee K, Lee J, Lee DH, Woo S. Experimental study of RC beam– column joints strengthened using CFRP composites. Compos Part B: Eng 2010;41:76–85. [22] Parvin A, Granata P. Investigation on the effects of fiber composites at concrete joints. Compos Part B: Eng 2000;31:499–509. [23] Mostofinejad D, Talaeitaba SB. Finite element modeling of RC connections strengthened with FRP laminates. Iran J Sci Technol, T B: Eng 2006;30:21–30. [24] Alavi B, Krawinkler H. Strengthening of moment-resisting frame structures against near-fault ground motion effects. Earthq Eng Struct Dyn 2004;33:707–22. [25] Alavi B, Krawinkler H. Behavior of moment-resisting frame structures subjected to near-fault ground motions. Earthq Eng Struct Dyn 2004;33:687–706. [26] Liao WI, Loh C-H, Wan S. Earthquake responses of RC moment frames subjected to near-fault ground motions. Struct Des Tall Build 2001;10:219–29. [27] Anderson JC, Bertero VV, Bertero RD. Performance improvement of long period building structures subjected to severe pulse-type ground
[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
[40]
[41] [42]
[43] [44]
[45] [46]
[47] [48]
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motions. Berkeley: Pacific Earthquake Engineering Research Center, University of California; 1999. Elsheikh A, Ghobarah A. Response of RC structures to near-fault records. Emirates J Eng Res 2004;9:45–51. Kalkan E, Kunnath SK. Effects of fling step and forward directivity on seismic response of buildings. Earthq Spectra 2006;22:367–90. Antonopoulos CP, Triantafillou TC. Experimental investigation of FRPstrengthened RC beam–column joints. J Compos Construct 2003;7:39–49. Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry buildings. New York: Wiley; 1992. Prota A, Nanni A, Manfredi G, Cosenza E. Capacity assessment of RC subassemblages upgraded with CFRP. J Reinf Plast Compos 2003;22:1287–304. Balsamo A, Colombo A, Manfredi G, Negro P, Prota A. Seismic behavior of a fullscale RC frame repaired using CFRP laminates. Eng Struct 2005;27:769–80. Hognestad E, Hanson NW, McHenry D. Concrete stress distribution in ultimate strength design. Am Conc Inst J 1955;27:455–79. Park R, Paulay T. Reinforced concrete structures. New York: Wiley; 1975. Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete. J Struct Eng 1988;114:1804–26. Lam L, Teng JG. Design-oriented stress–strain model for FRP-confined concrete. Construct Build Mater 2003;17:471–89. ANSYS Manual. 12.1 ed. Canonsburg, PA 15317, USA: ANSYS, Inc.; 2009. Niroomandi A, Maheri A, Maheri MR, Mahini SS. Seismic performance of ordinary RC frames retrofitted at joints by FRP sheets. Eng Struct 2010;32:2326–36. Kachlakev D, Miller T, Yim S, Chansawat K, Potisuk T. Finite element modeling of reinforced concrete structures strengthened with FRP laminates. SPR 316: Oregon Department of Transportation Research Group and Federal Highway Administration; 2001. Maheri MR, Akbari R. Seismic behaviour factor, R, for steel X-braced and kneebraced RC buildings. Eng Struct 2003;25:1505–13. ACI Committee 318. Building code requirements for structural concrete (ACI 318-95) and commentary (ACI 318R-95). Farmington Hills, Mich.: American Concrete Institute; 1995. Ghobarah A, Said A. Seismic rehabilitation of beam–column joints using FRP laminates. J Earthq Eng 2001;5:113–29. Quintero-Febres CG, Wight JK. Experimental study of reinforced concrete interior wide beam–column connections subjected to lateral loading. ACI Struct J 2001;98:572–82. Ritchie PA, Thomas DA, Lu L-W, Connelly GM. External reinforcement of concrete beams using fiber reinforced plastics. ACI Struct J 1991;88:490. ACI Committee 440. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R-08). Farmington Hills, Mich.: American Concrete Institute; 2008. Teng JG, Smith ST, Yao J, Chen JF. Intermediate crack-induced debonding in RC beams and slabs. Construct Build Mater 2003;17:447–62. Sayed-Ahmed EY, Bakay R, Shrive NG. Bond strength of FRP laminates to concrete: state-of-the-art review. Electron J Struct Eng 2009;9:45–61.
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Plastic hinge relocation in RC joints as an alternative method of retrofitting using FRP A. Dalalbashi a, A. Eslami b, H.R. Ronagh b,⇑ a b
Graduate Student, Dept. of Civil Engineering, Yazd University, Yazd, Iran School of Civil Engineering, The University of Queensland, Brisbane, Australia
a r t i c l e
i n f o
Article history: Available online 19 February 2012 Keywords: FRP Beam–column joint Plastic hinge Retrofitting Nonlinear FE analysis
a b s t r a c t The efficiency of fiber reinforced polymers (FRPs) in enhancing the performance of deficient reinforced concrete (RC) joints has been investigated in recent years. Relocating plastic hinge from the column face toward the beam is an effective method of upgrading RC beam–column joints. This retrofitting approach might also prevent the formation of undesirable brittle joint failure. In this paper, the numerical results of analysing three FRP retrofitted RC joints are compared in order to investigate the effectiveness of FRP composites in improving the performance of the beam to column joints through the relocation of the plastic hinges away from the joint core. Different configurations of FRP application, including a novel retrofitting scheme at beam–column joints, are assessed and the efficiency of each composite architecture in relocating the plastic hinge is discussed. The results show that the newly proposed configuration is not only capable of relocating plastic hinges and improving the load carrying capacity of the joints but is also capable of preventing the typical interface failure. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Application of fibre reinforced polymers for strengthening/ restoring reinforced concrete structures has attracted a lot of attention from researchers and engineers alike in recent years. FRP has outstanding advantages over steel including light weight, high corrosion resistance, superior strength and ease of application. FRP laminates and sheets can be moulded to the concrete surface for structural repair/retrofitting purposes. Increasing the applied load, human errors and a lack of seismic detailing have been accounted as some of the main reasons of the strengthening. In addition, FRP composites in the form of bar, sheet, and/or laminate can be used in new construction. Seismic retrofitting/repairing of RC structural elements using advanced composite materials has been of great interest, especially in the last decade. Numerous studies have been carried out on the application of FRP in strengthening of RC members; such as, beams [1–3] and columns [4–8]. Researchers have also investigated related problems such as debonding failure and methods of overcoming brittle failures [9–11]. Beam–column joints are critical regions of RC structures designed for inelastic response to seismic forces. The overall ⇑ Corresponding author. Address: School of Civil Engineering, The University of Queensland, Brisbane, QLD 4072, Australia. Tel.: +61 7 3365 9117; fax: +61 7 3365 4599. E-mail address: [email protected] (H.R. Ronagh). 0263-8223/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2012.02.016
structural strength, stiffness and ductility, are highly dependent upon the performance of joint core and end critical regions of beams and columns in the vicinity of beam to column connections. The well-known design philosophy of strong-column weak-beam would only work properly if the joints of RC structures perform as intended without any brittle failure. The effectiveness of FRP composites to improve/restore the seismic capacity of beam– column connections has been confirmed in many studies [9,12– 17]. Recently, Attari et al. [18] carried out an experimental study to evaluate the effect of external strengthening of beam–column joints using different types of fiber reinforced composites. They concluded that a combination of carbon and glass fiber reinforced polymers could improve the shear strength and ductility of deficient beam–column joints. The web-bonded strengthening method for rehabilitation of deficient RC joints using composites has been investigated by Mahini and Ronagh [19,20]. Their experimental and analytical results confirmed the capability of this method in not only restoring, but also upgrading the strength of system. In particular, through the relocation of plastic hinges from the column face, they showed that this method can prevent joint core brittle failure mode. In another experimental investigation, Le-Trung et al. [21] carried out a comprehensive experimental study on the different configurations of FRP retrofit to strengthen RC joints. They concluded that the appropriate adding of composites can significantly enhance the lateral strength and ductility of non-seismically designed specimens. Despite the adequacy of numerical finite element modelling in predicting the behaviour
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of RC joints retrofitted using composite materials, only a few studies have been directed towards this. In a numerical study, Parvin and Granata [22] proposed a finite element model for the nonlinear analysis of FRP-strengthened RC joints. They observed that by using FRP composites, the moment capacity of the joints could be increased by up to 37% while a maximum 18% reduction in the rotation of the joints was noticed. In another study, Mostofinejad and Talaeitaba [23] developed a finite element modelling for nonlinear analysis of RC joints covered with FRP overlays. Their results showed that the numerical model could predict the experimental work with good accuracy. Based on the reviewed literature, all experimental and numerical studies on the use of FRP on RC beam–column joints were carried out on the non-seismically deficient specimens. Technically speaking, the main objective of the FRP retrofits in past studies were to improve the behaviour of RC joints suffering from structural deficiencies; nevertheless, many existing code-compliant RC buildings might be in need of retrofitting. Being located in the near-fault regions with their higher seismic demands as reported in some studies [24–29], represents another need for the retrofitting of modern engineered buildings detailed based on the recent seismic codes. It is also noted that most of the past studies available in the literature did not simulate real field conditions. Even in the exterior beam–column connections, the case in which both sides of the joint core were retrofitted in the earlier studies, only one side is accessible due to the existence of the transverse beam. According to Antonopoulos and Triantafillou [30], the effectiveness of an FRP retrofit in increasing the strength, stiffness, and energy dissipation is reduced significantly due to the presence of a transverse beam, a fact ignored in most of the mentioned studies. More investigations will need to be performed on the FRP retrofitting of RC joints simulating real field conditions and other limitations attributable to practicality of designs and real structures. Among the methods of retrofitting, increasing the level of steel reinforcing in the critical regions of beams near the joint region, has been suggested as an effective method in relocating the plastic hinge away from the joint core [31]. In addition to increasing the lateral load carrying capacity of the structure, this method can also prevent the undesirable failure mode of weak-column strongbeam. Installation of FRP sheets on the exterior surfaces of beams and columns provides an opportunity for strengthening RC joints through the relocation of plastic hinges towards the beams. However, an appropriate composite configuration needs to be proposed for this method to be effective. In this paper, the capability of FRP retrofits applied to the exterior surfaces of RC joints in a practical design for relocating plastic hinges away from the joint core is discussed. Through the calibration with experimental test, nonlinear finite element analyses of three feasible composite configurations were carried out and the capability and advantages of different retrofitting architectures were compared with each other. Due to the fact that many past studies [32,33] have highlighted the possibility of interface failure at the termination of FRP composites, in the current study a novel strengthening architecture is introduced to prevent such a stress concentration at the beam–column interface. The FRP architectures were designed considering the application of each scheme to actual structures.
2. Experimental calibration It is common practice for the first step of every numerical study to be the verification of the analysis results through comparison with an experimental investigation. In this study, an experimental study carried out by Mahini and Ronagh [20] was selected in order to validate the finite element results and the analysis parameters. For this purpose, the specimen RSM2 was selected. In their study,
the scaled-down beam–column joints were retrofitted using web-bonded FRPs in order to relocate plastic hinges away from the joint core of deficient exterior beam–column sub-assemblage. Fig. 1 shows the details of CFRP strengthened beam–column joint tested in their study together with reinforcement details. The compressive strength of concrete was measured to be about 40.75 MPa. In addition, the yield steel strengths of longitudinal and transverse reinforcement in the beam–column joints were 500 MPa and 382 MPa, respectively. In this study, the commonly used Hognestad’s model [34] was used for the stress–strain curve of concrete in which the strain under uniaxial stress conditions corresponding to the concrete compressive strength was taken as 0.002. This value is recommended by Park and Paulay [35] and other researchers [36,37] for normal concrete. The ultimate concrete strain was assumed to be 0.0038. The simplified bilinear model with strain hardening was also used to simulate the behaviour of longitudinal steels. For shear reinforcements, an elastic-perfectly plastic model was used, according to test results [20]. ANSYS program [38] was employed to perform nonlinear FE analysis. All steel bars and stirrups were modelled using LINK8 truss element. In addition, SOLID65 element was employed to model concrete. This element, which is capable of modelling both cracking in tension and crushing in compression, has been especially designed for modelling concrete in ANSYS. FRP composites were modelled using an eight-node 3D solid element called SOLID45. This multi-layer element is defined by eight nodes. This element, which is normally used to represent bilinear anisotropic materials, was reported as the most suitable element in ANSYS for modelling the behaviour of FRP [20,22,23,39]. The above mentioned SOLID45 is also employed for the steel plates, which were added at the support locations of the column to provide a more even stress distribution over the support area. The behaviour of CFRP materials were modelled based on an anisotropic material called ANISO [20,23]. This model allows the introduction of the mechanical properties of FRPs in tension and compression in different directions. The mechanical properties of CFRP fibres used by Mahini and Ronagh [20] are given in Table 1. It is worth mentioning that these values satisfy the consistency equations necessary for an anisotropic material like ANISO in the nonlinear analysis, as described in ANSYS and stated by Kachlakev et al. [40]. The other assumptions for numerical modelling were the same as those implemented by Mahini and Ronagh [20]. In ANSYS, the five-parameter William–Wranke model in which both cracking and crushing failure modes are accounted for, has been suggested as a concrete failure criterion [38]. It should be mentioned that this model uses a smeared crack model. The 3-D failure surface for concrete calculated based on this model, is illustrated in Fig. 2. In addition, in order to define concrete materials in ANSYS, two shear transfer coefficients, bt and bc, need to be introduced for open cracks and closed cracks. Both coefficients have values between 0 and 1. The value used for bt in the past studies, however, varied between 0.05 and 0.3 [20,23,40]. According to the past study [20], the best estimate of the nonlinear behaviour of the tested joint is obtained if a shear transfer coefficient, bt, equal to 0.3 is taken for open cracks. Furthermore, The shear transfer coefficient, bc, of 0.7 was used for closed cracks, as recommended by ANSYS. Numerical analysis of the tested specimens was carried out according to aforementioned assumptions. In the nonlinear analysis, the load was applied step by step using the modified Newton– Raphson method to arrive at the solution. A displacement control method was used for loading in order to avoid convergence problems. Fig. 3 compares the beam tip load–displacement curves obtained from the nonlinear FE analysis in the current study with that extracted from the experiment [20]. Good agreement between the two curves proves reliability of the adopted FE analysis. This is
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220 mm 2N12
2N12
Section c-c
180
Tie R6.5
R6.5 @ 25mm 50 mm 2 R6.5
4 N12 R6.5 @ 150mm
Applied Load
Web bonded CFRP a
b
a
b
P1
1402 mm
4 N12
50
R6.5 @ 150mm R6.5 @ 30 mm 180
tf
tf
lf c
230
2N12
c
Tie R6.5 2N12
Section b-b
Section a-a Constant Axial Load ( P = 305 kN ) 2
1246 mm
Specimen
lf
(mm) No. of ply
tf
(mm)
CSM0
-
-
-
RSM1
350
1
0.165
RSM2
200
3
0.495
Fig. 1. The CFRP retrofitted beam–column joint (RSM2) tested by Mahini and Ronagh [20].
Table 1 Mechanical properties of CFRP fibres. Tensile strength ffr (MPa)
Ultimate tensile strain efr
Tensile modulus Ef (MPa)
Thickness tf (mm)
3900
0.0155
240,000
0.165
particularly so when this agreement is measured in terms of the ultimate strength.
objective. This moment-resisting building was detailed based on the intermediate seismic provisions of ACI 318-95 [42]. All numerical models were built to simulate this code-compliant joint as an un-retrofitted model. The joint was cut out from the inflection point to simulate the real performance of subassembly under seismic actions [20]. The dimensions and reinforcement details of the studied exterior beam–column connection are shown in Fig. 5. The compressive strength, fc0 and tensile strength, ft of concrete were 27.46 MPa and 3.67 MPa, respectively. Furthermore, the yield stress of steel bars was taken as 412 MPa. 3.1. Original joint
3. Numerical modelling of original and FRP retrofitted joint Following the validation of nonlinear FE parameters, the numerical analysis of a code-compliant RC joint retrofitted with composite sheets, was carried out to evaluate the capability of FRP retrofits in relocating plastic hinges away from the column faces. As illustrated in Fig. 4, the exterior beam–column joint at the first level of an 8-storey RC building designed by Maheri and Akbari [41], was selected as the case study in order to pursue this
Fig. 6 shows a FE illustration of the unreinforced joint considered for retrofitting in the current study. As is observed in this figure, the boundary conditions at the column supports are similar to the actual behaviour of the structure during seismic loads. The elements and parameters employed for nonlinear FE analysis was similar to the one applied in the verified model. The LINK8 and SOLID65 were used to model concrete material and steel reinforcement, respectively. Steel plates were also modelled at the column
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A
φ10 @ 200 mm
Constant Axial Load ( N=2685 kN )
P
A
φ10 @ 100 mm
φ10 @ 200 mm
B
φ10 @ 200 mm
2500 700
500
Fig. 2. Three dimensional failure surface calculated based on the William–Wranke criterion [38].
ρ ' s=0.009
60
ρ t=0.019
500
60
ρ s=0.012
Section B-B
700
φ10 @ 150 mm
3000
B
Section A-A
Fig. 5. Reinforcement details and geometry of the original joints (all dimensions in mm).
25
Load, P (kN)
20 15 10 Experiment [20]
5 0
Nonlinear FE analysis
0
10
20
30
40
50
60
70
Displacement, Δ (mm) Fig. 3. Comparison of load–displacement curves for specimen RSM2.
CL
8@3m
Fig. 6. FE model of original joint.
Selected joint 3@5m
Fig. 4. Exterior beam–column joint selected for FRP retrofitting.
support to eliminate stress concentration at the supports. A bilinear model with strain hardening was used in the nonlinear analysis
to consider the behaviour of steel reinforcement. The concrete nonlinear behaviour was simulated with the Hognestad model [34]. In order to consider the effect of axial forces on the nonlinear analysis, the column was subjected to a constant axial load equal to 0:2fc0 Ag where fc0 is the concrete compressive strength and Ag represents the gross area of the column cross section [43]. This load was applied in the form of surface pressure to the column. Reported experimental studies confirm that application of the column axial load increases the confinement effect of the beam– column joint area to a certain degree and results in increasing the shear strength of the joint [44]. As depicted in Fig. 5, a monotonically increasing static load was applied at the beam tip up to
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the failure. The load was applied in the form of displacement to prevent convergence problems and the reaction was calculated (see Fig. 6). 3.2. FRP retrofitted joints Similar to the verified model, the multi-layer SOLID45 element with ANISO material was used to model the behaviour of FRP. All other required parameters for modelling the composite material were identical to the verified model except for the thickness of laminates and wraps. Since the composite materials used were unidirectional, their properties were rotated for FRP wrapping in the numerical modelling. The retrofitting schemes included three different practical FRP configurations applied to the exterior surfaces of beam to column connections as illustrated in Fig. 7. All strengthening strategies were based on increasing the flexural strength of beam in the critical region near the joint core. The first case was the application of composite sheets at the beam to column connection in the form of an L shape, as shown in Fig. 7a. Past experimental and numerical studies [21,22] reported that wrapping of the beam and column can prevent the early delimitation of FRP laminate near the joint core resulting in a better performance for the retrofit. For this
200
(a)
500
Fibre Laminates
(b)
reason, two FRP wraps were applied at the beam and column ends. Moreover, some researchers suggested that a second wrap, as illustrated in Fig. 7a, could facilitate the transfer of tensile forces from the FRP laminate to the beam [45]. The thickness of composite sheets was selected to ensure the relocation of plastic hinges away from the column face. For the selected joint, this was achieved using at least six layers of CFRP sheets. Nonlinear FE analysis confirmed that this thickness is necessary in all retrofit configurations for the plastic hinge to be relocated. It should be noted that the thickness of composite sheets to cause this relocation depends on the beam and column geometry, reinforcement details, and composite properties. In another experimental study, Granata and Parvin [12] reported that the thickness of FRP wrap must be at least 35% greater than that of sheet thickness to prevent its rupture. Thus, in this study, nine layers of the abovementioned CFRP are utilised for each wrap. The width of all FRP wraps was taken as 75 mm to be practical. In the second design, FRP retrofit was applied at the top and bottom surfaces of the beam at the critical region near the joint core as observed in Fig. 7b. Since debonding is a significant drawback of FRP retrofit, in the third case, FRP sheets were placed inside the column for a length equal to the column concrete cover. In practice, this could be achieved by creating a groove inside the column cover and filling it after composite installation by injecting the epoxy resin. This method could provide a good bond between the FRP sheets and the concrete beam at the joint. Fig 7c shows the schematic illustration of this novel design. This configuration was decided as it was found that the second configuration is not capable of relocating the plastic hinge as discussed in the following. Debonding is a major problem associated with many FRP applications. Despite the wrapping and grooving in the configurations above, in order to prevent undesired debonding failure at the end sections, a failure controlled by FRP debonding may occur away from the end section where the externally bonded FRP laminates terminates. In order to eliminate such intermediate crack-induced debonding failure mode, the maximum strain in the FRP laminates was limited to the threshold value suggested by ACI 440.2-08 [46]. According to this code, the strain level at which debonding may occur, efd, is given by:
efd 500
Fibre Laminates
(c)
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sffiffiffiffiffiffiffiffiffiffiffi fc0 ¼ 0:41 6 0:9efu nEf t f
ð1Þ
where fc0 is the compressive strength of concrete; Ef is the elastic modulus of composite materials, tf is the thickness of FRP laminates; n is the number of FRP layers; and efu is the ultimate tensile strain of FRP. It should be mentioned that the model of FRP debonding adopted by Eq. (1) is a modified form of the one proposed by Teng et al. [47]. A comprehensive review on the state-of-the-art of bond strength of FRP laminate to concrete has been provided by Sayed-Ahmed et al. [48]. 4. FE analysis results and discussion
50
500
Fibre Laminates
Fig. 7. FRP configuration and loading conditions of the selected joint (all dimensions in mm): (a) first design; (b) second design; and (c) third design.
In addition to increase the joint strength, relocation of the plastic hinges away from the column face is considered as the main aim of the proposed retrofitting undertaken in this study. It was found that this can be achieved in the first and third case with at least six layers of CFRP. However, the result of the second design was substantially different from others. While all retrofitting configurations resulted in strength enhancement, FRP composites did not affect the formation of the plastic hinge in the second case. Fig. 8 compares the strain distribution in the tensile longitudinal reinforcements of the beam at the last step of loading for the three retrofitting schemes. Taking into consideration the strain values
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0.014 0.012
Strain (mm/mm)
Table 2 Nonlinear analysis results.
Original joint First retrofitting design Second retrofitting design Third retrofitting design
0.010 0.008 0.006
No. of laminate layers
No. of wrap layers
Maximum load (kN)
Increase (%)
Ductility index
Decrease (%)
Original First Second Third
– 6 6 6
– 9 – 9
268.8 328.4 309.4 340.1
– 22 15 27
2.2 1.8 1.5 1.9
– 18 32 14
0.004 0.002 0.000
0
500
1000
1500
2000
2500
Distance from the column face (mm) Fig. 8. Comparison of strain variation in the longitudinal tensile steels of beam at the last step of loading before and after FRP retrofitting.
along the beam top bars, the capability of the first and third cases in relocating plastic hinges were confirmed. It is worth mentioning that even with increasing the thickness of FRP sheets up to five times in the second retrofitting configuration; plastic hinge was formed near the joint core, indicating the inability of the retrofitting scheme in relocating plastic hinge. This is particularly due to the termination of composite laminates at the beam–column interface. The load–displacement curves of beam tip for the three retrofitting models obtained from nonlinear FE analysis are compared in Fig. 9. While the initial stiffness of all joints were identical, this showed a notable increase for the retrofitted joints after cracking resulting in the remarkable increases in the ultimate strength. The maximum strength and its magnitude of increase for strengthened and original joints are given in Table 2. In addition to the strength, ductility is also an important parameter in seismic performance of structures. The ductility factor is defined as the ratio of ultimate displacement to the displacement at first yield of tensile reinforcements. The amount of ductility depends to a great extent on the retrofitting configuration. A retrofitting architecture might aim to improve strength, ductility or both of these in a structural component which results in the overall enhancement of the structural behaviour. Ductility enhancement could be obtained through the retrofitting techniques aim to provide confinement. However, ductility enhancement could not be expected with the types of FRP architectures in this study as they aimed to increase the strength. As shown in Table 2, the results
400 350 300
Load, P (kN)
Design no.
5. Conclusion This paper reports the results of a numerical investigation on FRP strengthening of RC structures. Three practical retrofitting architectures were proposed in order not only to increase the load carrying capacity, but also relocate the plastic hinges away from the column faces. However, the latter was not observed using the second retrofitting technique due to the interface failure. The first and third design indicated the capability of externally bonded FRP laminates in relocating the plastic hinge away from the column faces in order to increase the load carrying capacity and eliminating the undesirable weak-column strong-beam mechanism. This could also prevent the brittle joint shear failure. All strengthening configurations showed a significant increase in the ultimate strength of the joint. The highest value (almost 27%) was observed in the third design where the interface failure was prevented through the insertion of FRP laminates in the concrete cover of column. Nonlinear FE outcomes confirmed the reliability of the adopted FE model in predicting the seismic behaviour and load carrying capacity of RC structures, especially for retrofitting purposes. While the results are reliable and justifiable, more studies have to be conducted on the FRP retrofitting of code-compliant RC joint in order to quantify the increase in both strength and/or ductility and to formulate a design approach. References
250 200 150 Original joint
100
First retrofitting design Second retrofitting design
50 0
of FE analysis also confirmed the objective of this type of retrofitting. This conclusion has also been addressed by other researchers [18,23]. Design of the third retrofitting configuration was based on the elimination of interface failure as mentioned above and reported by other researchers [32,33]. Other conditions in the third case were exactly similar to the second scheme. The nonlinear analysis outcomes in the three retrofitting cases showed that the third case offers some advantages, particularly in the strength enhancement and ductility, compared to the others. Considering the high proportion of labour cost in the strengthening of structures, implementation of the third architecture would be more acceptable in real practice. It is noted that others have found it to be advantageous due to the excellent bond between FRP and concrete [18] created as a result of grooving.
Third retrofitting design
0
5
10
15
20
25
30
35
40
45
Displacement, Δ (mm) Fig. 9. Distribution of load vs. displacement of the beam tip for original and FRPretrofitted joint.
[1] Shahawy MA, Arockiasamy M, Beitelman T, Sowrirajan R. Reinforced concrete rectangular beams strengthened with CFRP laminates. Compos Part B: Eng 1996;27:225–33. [2] Saadatmanesh H. Extending service life of concrete and masonry structures with fiber composites. Construct Build Mater 1997;11:327–35. [3] Rabinovitch O, Frostig Y. Experiments and analytical comparison of RC beams strengthened with CFRP composites. Compos Part B: Eng 2003;34:663–77. [4] Saadatmanesh H, Ehsani MR, Jin L. Repair of earthquake-damaged RC columns with FRP wraps. ACI Struct J 1997;94:206–15. [5] Chaallal O, Shahawy M. Performance of fiber-reinforced polymer-wrapped reinforced concrete column under combined axial-flexural loading. ACI Struct J 2000;97:659–68. [6] Harajli MH, Rteil AA. Effect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismic performance of gravity load-designed columns. ACI Struct J 2004;101:47–56.
A. Dalalbashi et al. / Composite Structures 94 (2012) 2433–2439 [7] Toutanji H, Han M, Gilbert J, Matthys S. Behavior of large-scale rectangular columns confined with FRP composites. J Compos Construct 2010;14:62–71. [8] De Luca A, Nardone F, Matta F, Nanni A, Lignola GP, Prota A. Structural evaluation of full-scale FRP-confined reinforced concrete columns. J Compos Construct 2011;15:112–23. [9] Antonopoulos CP, Triantafillou TC. Analysis of FRP-strengthened RC beam– column joints. J Compos Construct 2002;6:41–51. [10] Mosallam AS, Banerjee S. Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates. Compos Part B: Eng 2007;38:781–93. [11] Mostofinejad D, Mahmoudabadi E. Grooving as alternative method of surface preparation to postpone debonding of FRP laminates in concrete beams. J Compos Construct 2010;14:804–11. [12] Granata PJ, Parvin A. An experimental study on Kevlar strengthening of beam– column connections. Compos Struct 2001;53:163–71. [13] El-Amoury T, Ghobarah A. Seismic rehabilitation of beam–column joint using GFRP sheets. Eng Struct 2002;24:1397–407. [14] Ghobarah A, Said A. Shear strengthening of beam–column joints. Eng Struct 2002;24:881–8. [15] Said AM, Nehdi ML. Use of FRP for RC frames in seismic zones: Part I. Evaluation of FRP beam–column joint rehabilitation techniques. Appl Compos Mater 2004;11:205–26. [16] Ghobarah A, El-Amoury T. Seismic rehabilitation of deficient exterior concrete frame joints. J Compos Construct 2005;9:408–16. [17] Mukherjee A, Joshi M. FRPC reinforced concrete beam–column joints under cyclic excitation. Compos Struct 2005;70:185–99. [18] Attari N, Amziane S, Chemrouk M. Efficiency of beam–column joint strengthened by FRP laminates. Adv Compos Mater 2010;19:171–83. [19] Mahini SS, Ronagh HR. Strength and ductility of FRP web-bonded RC beams for the assessment of retrofitted beam–column joints. Compos Struct 2010;92:1325–32. [20] Mahini SS, Ronagh HR. Web-bonded FRPs for relocation of plastic hinges away from the column face in exterior RC joints. Compos Struct 2011;93:2460–72. [21] Le-Trung K, Lee K, Lee J, Lee DH, Woo S. Experimental study of RC beam– column joints strengthened using CFRP composites. Compos Part B: Eng 2010;41:76–85. [22] Parvin A, Granata P. Investigation on the effects of fiber composites at concrete joints. Compos Part B: Eng 2000;31:499–509. [23] Mostofinejad D, Talaeitaba SB. Finite element modeling of RC connections strengthened with FRP laminates. Iran J Sci Technol, T B: Eng 2006;30:21–30. [24] Alavi B, Krawinkler H. Strengthening of moment-resisting frame structures against near-fault ground motion effects. Earthq Eng Struct Dyn 2004;33:707–22. [25] Alavi B, Krawinkler H. Behavior of moment-resisting frame structures subjected to near-fault ground motions. Earthq Eng Struct Dyn 2004;33:687–706. [26] Liao WI, Loh C-H, Wan S. Earthquake responses of RC moment frames subjected to near-fault ground motions. Struct Des Tall Build 2001;10:219–29. [27] Anderson JC, Bertero VV, Bertero RD. Performance improvement of long period building structures subjected to severe pulse-type ground
[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
[40]
[41] [42]
[43] [44]
[45] [46]
[47] [48]
2439
motions. Berkeley: Pacific Earthquake Engineering Research Center, University of California; 1999. Elsheikh A, Ghobarah A. Response of RC structures to near-fault records. Emirates J Eng Res 2004;9:45–51. Kalkan E, Kunnath SK. Effects of fling step and forward directivity on seismic response of buildings. Earthq Spectra 2006;22:367–90. Antonopoulos CP, Triantafillou TC. Experimental investigation of FRPstrengthened RC beam–column joints. J Compos Construct 2003;7:39–49. Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry buildings. New York: Wiley; 1992. Prota A, Nanni A, Manfredi G, Cosenza E. Capacity assessment of RC subassemblages upgraded with CFRP. J Reinf Plast Compos 2003;22:1287–304. Balsamo A, Colombo A, Manfredi G, Negro P, Prota A. Seismic behavior of a fullscale RC frame repaired using CFRP laminates. Eng Struct 2005;27:769–80. Hognestad E, Hanson NW, McHenry D. Concrete stress distribution in ultimate strength design. Am Conc Inst J 1955;27:455–79. Park R, Paulay T. Reinforced concrete structures. New York: Wiley; 1975. Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete. J Struct Eng 1988;114:1804–26. Lam L, Teng JG. Design-oriented stress–strain model for FRP-confined concrete. Construct Build Mater 2003;17:471–89. ANSYS Manual. 12.1 ed. Canonsburg, PA 15317, USA: ANSYS, Inc.; 2009. Niroomandi A, Maheri A, Maheri MR, Mahini SS. Seismic performance of ordinary RC frames retrofitted at joints by FRP sheets. Eng Struct 2010;32:2326–36. Kachlakev D, Miller T, Yim S, Chansawat K, Potisuk T. Finite element modeling of reinforced concrete structures strengthened with FRP laminates. SPR 316: Oregon Department of Transportation Research Group and Federal Highway Administration; 2001. Maheri MR, Akbari R. Seismic behaviour factor, R, for steel X-braced and kneebraced RC buildings. Eng Struct 2003;25:1505–13. ACI Committee 318. Building code requirements for structural concrete (ACI 318-95) and commentary (ACI 318R-95). Farmington Hills, Mich.: American Concrete Institute; 1995. Ghobarah A, Said A. Seismic rehabilitation of beam–column joints using FRP laminates. J Earthq Eng 2001;5:113–29. Quintero-Febres CG, Wight JK. Experimental study of reinforced concrete interior wide beam–column connections subjected to lateral loading. ACI Struct J 2001;98:572–82. Ritchie PA, Thomas DA, Lu L-W, Connelly GM. External reinforcement of concrete beams using fiber reinforced plastics. ACI Struct J 1991;88:490. ACI Committee 440. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R-08). Farmington Hills, Mich.: American Concrete Institute; 2008. Teng JG, Smith ST, Yao J, Chen JF. Intermediate crack-induced debonding in RC beams and slabs. Construct Build Mater 2003;17:447–62. Sayed-Ahmed EY, Bakay R, Shrive NG. Bond strength of FRP laminates to concrete: state-of-the-art review. Electron J Struct Eng 2009;9:45–61.