Engineering Structures. Near surface mounted CFRP strips for the flexural strengthening of RC columns: Experimental and numerical research

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1 Engineering Strutures 30 (2008) Contents lists available at SieneDiret Engineering Strutures journal homepage: Near surfae mounted CFRP strips for the flexural strengthening of RC olumns: Experimental and numerial researh Joaquim A.O. Barros a,, Rajendra K. Varma a, José M. Sena-Cruz a, Alvaro F.M. Azevedo b a Department of Civil Engineering, University of Minho, Azurém, Guimarães, Portugal b Department of Civil Engineering, University of Porto, Rua Dr. Roberto Frias, Porto, Portugal a r t i l e i n f o a b s t r a t Artile history: Reeived 21 Marh 2007 Reeived in revised form 24 January 2008 Aepted 19 May 2008 Available online 27 June 2008 Keywords: Near surfae mounted reinforement Reinfored onrete olumns Strengthening Carbon fiber reinfored polymer strips Bending failure Epoxy adhesive In this work, a strengthening tehnique based on near surfae mounted (NSM) arbon fibre laminate strips bonded into slits opened on the onrete over is used to improve the flexural apaity of olumns subjeted to bending and ompression. This tehnique avoids the ourrene of the peeling phenomenon, is able to mobilize the full strengthening apaity of the strips, and provides higher protetion against fire and ats of vandalism. We desribe the adopted strengthening tehnique and report the experimental haraterization of the materials involved in the strengthening proess. The results obtained in two series of reinfored onrete olumns, subjeted to axial ompression and lateral yli loading, show that a signifiant inrease on the load arrying apaity an be ahieved by using the NSM tehnique. Cyli material onstitutive laws were implemented in a finite element program and the tests with reinfored onrete olumns strengthened with the NSM tehnique were numerially simulated under yli loading. These numerial simulations reprodue the experimental load displaement diagrams satisfatorily Elsevier Ltd. All rights reserved. 1. Introdution Until the last quarter of the twentieth entury seismi loading was not generally taken into aount in the design of reinfored onrete buildings or, when onsidered, the resulting reinforement detailing might not be satisfatory by the standards of the urrent strutural odes. For this reason, signifiant damage an our in old buildings, even with the ourrene of moderate seismi loads. In most ases, olumns represent the most vulnerable elements sine their failure leads to the ollapse of the struture. Sine the beginning of the nineties onventional materials used to strengthen reinfored onrete (RC) olumns are being replaed with arbon and glass fibre reinfored polymers (CFRP or GFRP). The advantages of these omposite materials are the strength/weight and stiffness/weight high ratios, as well as the high resistane to environmental ations, lightness, durability and ease of appliation [1 4]. In this work a strengthening tehnique, based on the installation of strips of arbon fibre reinfored polymer (CFRP) laminates into slits opened on the onrete over of the elements Corresponding author. Tel.: ; fax: addresses: barros@ivil.uminho.pt (J.A.O. Barros), rajendra@ivil.uminho.pt (R.K. Varma), jsena@ivil.uminho.pt (J.M. Sena-Cruz), alvaro@fe.up.pt (A.F.M. Azevedo). to strengthen, is used to inrease the flexural resistane of RC olumns failing in bending. These strips have a ross setion of mm 2 and are bonded to onrete by means of an epoxy adhesive. This tehnique is termed near surfae mounted (NSM) and its effetiveness in the flexural and shear strengthening of RC beams has been already assessed [5 10]. In reent years a signifiant amount of researh has been undertaken with the aim of aurately modelling the yli behaviour of RC olumns. An extensive review of available onstitutive models and appropriate FEM-based numerial strategies is published elsewhere [11]. The most ommon approahes regarding the modelling of RC olumns with finite elements involve a disretization with 3D solid elements or with Timoshenko beam elements. When 3D solid elements are used, some elements represent onrete and others simulate the reinforement. For the ase of Timoshenko beam elements eah ross setion is disretized into fibers, orresponding some to the onrete and the remaining to the reinforement [12]. Models based on 3D solid elements are more suitable to reprodue the behaviour of RC olumns subjeted to any type of loading suh as signifiant shear fores or torsion. Timoshenko beam based models are less demanding in terms of omputational resoures but are more appropriate to the simulation of olumns mainly subjeted to axial and flexural fores. In the present work, the effetiveness of the NSM tehnique in the flexural strengthening of RC olumns was appraised by means of two series of tests, with different steel reinforement ratios, subjeted to yli loading and onstant axial ompressive /$ see front matter 2008 Elsevier Ltd. All rights reserved. doi: /j.engstrut

2 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Notations The following symbols were used in the paper. Subsript s and denote steel and onrete respetively. C/T E /s E new E +/ so E pl E /+ re E s E /+ sh E st E /+ t f /s f t f f /+ f /+ new f /+ re f /+ su f /+ un f /+ sy n /+ R +/ so x sp x /+ x /+ r ε ε ε /+ so ε pl ε /+ re ε /+ sh ε /+ su ε t ε /+ un Compression /Tension Initial Young modulus of onrete/steel Tangent modulus at the new stress point Initial Young s modulus at reversal C/T branh Tangent modulus when the stress is released Tangent modulus at the returning point (ε /+ re, f /+ Tangent modulus of steel Tangent modulus at strain hardening (ε /+ sh ) Tangent modulus of steel Tangent modulus for onrete on C/T envelope Conrete/steel stress Peak onrete tension strength Peak onfined onrete strength re ) Conrete stress on the C/T envelope New stress at the unloading strain for C/T Stress at the returning strain (ε /+ re ) Ultimate (maximum) stress during C/T in steel Unloading stress from C/T onrete envelope urve Yield stress during C/T in steel n value for the C/T envelope urve Menegotto Pinto Eq. parameter Non-dimensional spalling strain Non-dimensional strain on the C/T envelope Non-dimensional ritial strain on C/T envelope urve. Conrete strain Conrete strain at peak onfined stress Point of origin of the C/T envelope urve Plasti strain Strain at the returning point to the C/T envelope urve Hardening strain during C/T in steel Strain at ultimate stress (f /+ su ) Strain at peak tension stress Unloading strain from C/T onrete envelope urve load. These tests were numerially simulated with the materially nonlinear algorithms of the FEMIX omputer ode [13]. In the ontext of this work, additional yli onstitutive material models were developed and implemented in the ode. The RC olumns are disretized with 3D Timoshenko beam elements and eah ross setion is treated as a set of quadrilateral sub domains (fibrous model, [12]). In the following setions the experimental and numerial researh are desribed and the main results are presented and disussed. 2. Experimental program The experimental program arried out in the ontext of the urrent work is omposed of eight speimens and twelve tests as shown in Table 1. Two series of olumns reinfored with longitudinal steel bars of 10 and 12 mm diameter, φ l, were used. The following denominations are adopted: NON series for non-strengthened olumns; PRE series for onrete olumns strengthened with CFRP strips; POS series for olumns of the NON Fig. 1. Test set-up (dimensions in mm). series whih were strengthened and then retested. The generi denomination of a series is Cnm_s, where n represents the diameter of the longitudinal bars, in mm, (10 or 12), m is equal to a or b (a and b are two tests in similar onditions for statistial purposes), and s is equal to NON, PRE or POS. 3. Test setup and testing proedures The test setup is shown in Fig. 1. Eah speimen is omposed of a olumn monolithially onneted to a footing, whih is fixed to a foundation blok by four steel bars. The yli horizontal load was applied by means of an atuator having a load apaity of 100 kn. The fore was measured using a tension/ompression load ell that an reah a maximum load of 250 kn with 0.05% auray. This load ell was attahed to the piston of the atuator (ell C1 in Fig. 1). To avoid eentri fores on the atuator, a 3D hinge was plaed between the olumn and the load ell that measures the horizontal fore. A vertial load of approximately 150 kn was applied to the olumn, whih orresponds to an axial load ratio of The vertial load was kept pratially onstant during the test by means of a 250 kn atuator. This atuator was supported by two bolted steel bars, whih were fixed to the foundation blok. The axial vertial fore was measured with a 500 kn load ell with 0.5% auray (ell C2 in Fig. 1). Linear variable displaement transduers (LVDT) were used to reord the horizontal displaements of the olumn, as well as an eventual vertial movement of the footing (see Fig. 2). The measuring stroke for eah LVDT is indiated in parentheses (±12.5 or ±25 mm). The loation of the strain-gauges (SG) whih were glued to the CFRP strips is also indiated in Fig. 2. The tests were arried out with losed-loop servo-ontrolled equipment. A displaement history was imposed to LVDT1, with

3 3414 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Table 1 Denominations for the speimens Longitudinal reinforement (1) Series NON a (2) PRE b (3) POS (4) 4φ10 C10a_NON C10a_PRE C10a_POS C10b_NON C10b_PRE C10b_POS 4φ12 C12a_NON C12a_PRE C12a_POS C12b_NON C12b_PRE C12b_POS a Non-strengthened. b Strengthened before testing. Columns of NON series after have been tested and strengthened. Table 2 Maximum fores obtained in the olumns of PRE series (strengthened before testing) Series PRE C10a_PRE C10b_PRE C12a_PRE C12b_PRE Age a (days) Average ompressive strength a (MPa) Tensile (kn) Compressive (kn) a Values at the age of the olumns at testing. Fig. 2. Loation of the displaement transduers (LVDT) and strain gauges (SG) (dimensions in mm). a full range of 50 mm and 0.05% auray, loated at the level of the horizontal atuator, see Fig. 1 and Fig. 2. From the analytial and numerial simulations it was verified that the steel yield initiation ourred for a lateral defletion of about 5 mm at the level of the horizontal atuator. Therefore, an inrement of 2.5 mm was seleted in the present experimental program. This inrement was the same for all the speimens, in order to allow for the omparison of stiffness and strength degradation for the same lateral defletions. The displaement history inluded eight full loading-unloading yles: ±2.5 mm, ±5.0 mm, ±7.5 mm, ±10.0 mm, ±12.5 mm, ±15.0 mm, ±17.5 mm and ±20.0 mm, with a displaement rate of 150 µm/s. 4. Material haraterization 4.1. Conrete A low strength onrete was used for all tests, in order to reprodue the type of onrete used in the sixties and seventies. The onrete was omposed of 250 kg/m 3 of normal Portland ement, kg/m 3 of gravel 5 15 mm, kg/m 3 of sand 0 5 mm, and l/m 3 of water. The uniaxial ompressive behaviour of the onrete of eah olumn series was assessed by performing ompression tests with two ylinders of 150 mm diameter and 300 mm height. These tests were performed at 28 days and at the time the olumns were tested. For eah series of olumns, two beams with dimensions of mm 3 were also ast for assessing the tensile strength in bending and the frature energy of the onrete [14]. The results obtained in the ompression tests indiated an average ompressive strength, at 28 days, of 16.7 MPa, with a standard deviation of 3.31 MPa. An average tensile strength of 2.62 MPa, with a standard deviation of 0.48 MPa, and an average frature energy of 0.08 N mm/mm 2 were registered from the three-point nothed beam bending tests, at 28 days. Tables 2 and 3 inlude the values of the onrete ompressive strength at the age of the olumn tests.

4 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Table 3 Maximum fores obtained on the olumns of series NON (non-strengthened) and POS (strengthened after preliminary testing) Column C10a_ C10b_ C12a_ C12b_ Diameter of longitudinal bars (mm) Average ompressive strength a (MPa) Tensile NON (kn) (86) b (85) b (85) b (85) b POS (kn) (146) b (130) b (150) b (154) b Inrease (%) Compressive NON (kn) (86) b (85) b (85) b (85) b POS (kn) (146) b (130) b (150) b (154) b Inrease (%) a Values at the age of the olumns at testing of the series NON. b Values inside round parentheses represent the age of the olumns at testing, in days Epoxy mortar Fig. 3. Adopted flexural strengthening tehnique for RC olumns (dimensions in mm) Steel reinforement In the RC strutures built in the sixties and seventies smooth surfae steel bars were ommonly used. For this reason, this type of bars was also used in the reinforement of the tested olumns. To assess the behaviour of the steel bars, uniaxial tensile tests were arried out in a servo-ontrolled testing mahine, aording to the reommendations of the European standard EN [15]. The yield stress (f sy ), the ultimate stress (f su ), and the elastiity modulus (E s ) of φ6 bars are (as an average of the tests with three speimens): f sy = MPa, f su = MPa, and E s = MPa. The reinforement details for φ10 and φ12 bars are presented later (see Table 6). An epoxy mortar was used to fix the CFRP laminates to the olumn footing (see Fig. 3). The epoxy mortar was omposed of one part of epoxy and three parts of fine sand previously washed and dried (parts measured in weight). The uniaxial ompressive strength and the flexural tensile strength of the epoxy mortar were evaluated from tests in speimens with mm 3, at 48 h and at 28 days, following the European standard [16]. At 48 hours, a ompressive strength of MPa, with a standard deviation of 2.14 MPa, and a flexural tensile strength of MPa with a standard deviation of 0.57 MPa, were obtained. At 28 days, a ompressive strength of MPa, with a standard deviation of 0.47 MPa, and a flexural tensile strength of MPa, with a standard deviation of 1.70 MPa, were obtained. In order to evaluate the adhesive properties of the epoxy mortar relatively to a onrete surfae, the following proedure was undertaken: reutilization of the remains of previous bending tests with mm 3 beams, whih were used to evaluate the properties of the onrete used in the olumns; utilization of the epoxy mortar to glue both piees together; test of the resulting speimen under flexure load. In these tests it ould be observed that the frature neither propagated aross the epoxy mortar, nor aross its interfae with the onrete (see Fig. 4). Therefore, these tests indiated that the properties of the bonding between the developed epoxy mortar and onrete are very good CFRP laminate strips The CFRP strips, whih were provided in rolls, had a thikness of 1.45±0.005 mm and a width of 9.59±0.09 mm (average values of 15 measures). To evaluate the tensile strength and the elastiity Fig. 4. Nothed beam bending tests for the haraterization of the onrete-epoxy mortar bond performane: (a) test setup; (b) rak propagation.

5 3416 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Fig. 5. Tensile stress strain relationship for the epoxy adhesive speimens. modulus of the applied strips, uniaxial tensile tests were arried out in a servo-ontrolled test mahine (Instron, series 4208), aording to the reommendations of ISO [17]. Strains were registered by means of a lip-gauge with a measuring stroke of 50 mm, whereas fores were obtained from a 100 kn load ell with an auray less than 0.1%. The stress strain relationships obtained were linear up to failure, whih indiates a brittle behaviour. An elastiity modulus of MPa and a tensile strength of 1741 MPa resulted from the tests Epoxy adhesive The adhesive that was used to bond the CFRP strips to onrete was omposed of two parts of epoxy and one part of a hardening omponent (parts measured in weight). In order to assess the tensile behaviour of the epoxy adhesive, five speimens were tested with the same equipment and measurement devies that were used in the uniaxial tensile tests of the CFRP strips (see the previous Setion). The tests were arried out aording to the reommendations of ISO [18] and a load ell with 5 kn load apaity was used. Fig. 5 shows the uniaxial stress strain urves obtained in the tests. All the speimens exhibited similar uniaxial stress strain relationships with the exeption of the fourth. However, signifiant differenes are observed in terms of tensile strength probably due to spurious voids deteted in the frature surfaes of the tested speimens. In fat, in the frature surfae of speimen 4 the imperfetions were all miro-voids, while in the other speimens voids of a onsiderably larger size were observed. Aording to the reommendations of ISO [18], an elastiity modulus of 5090 ± 590 MPa was obtained. 5. Adopted strengthening tehnique Fig. 3 presents the strengthening tehnique adopted for the olumn elements. In a region mm high at the bottom of the olumn (herein designated as nonlinear hinged region ) the onrete over was removed. Afterwards, 5 mm wide and 15 mm deep slits were ut in the onrete over, in the faes that will be subjeted to the highest tensile stresses. In order to anhor the CFRP strips to the footing, 100 mm deep perforations were made in orrespondene with eah slit. Before the installation of the Fig. 6. Cyli fore defletion (at LVDT1) relationship for C10a olumn. strips, all the slits and holes were leaned using steel brushes and ompressed air. The CFRP strips were leaned with a solvent. The slits were then filled with the epoxy adhesive and the strips were installed into the slits. Finally, the nonlinear hinged region and the holes in the footing were filled with the epoxy mortar. A detailed desription of this strengthening tehnique an be found in [19]. 6. Experimental results 6.1. Load arrying apaity The test series was arried out with the proedures desribed in Setion 3. Tables 2 and 3 ontain the extreme values obtained in the tests for the horizontal fore onsidering as positive a right to left fore in Fig. 1 (the age of the olumns at testing time is in parentheses). The maximum fore observed differs signifiantly, even between speimens of the same series. This disrepany is mainly due to the variability of the onrete properties and to some extent lak of preision in the loation of the steel reinforement. A signifiant inrease of the maximum load of the olumns of the PRE series (strengthened before testing) and POS series (strengthened after testing) was observed, relatively to the results obtained in the olumns of the NON series. As expeted, the strength inrease provided by the CFRP was higher in the olumns with lower longitudinal steel reinforement ratios (C10 series). The inrease of the load arrying apaity provided by the NSM strengthening tehnique was similar in the PRE series and in previously tested olumns (POS series) Fore displaement relationships Fig. 6 shows two typial relationships between the horizontal fore and the defletion at LVDT1. The envelopes of the relationships between fore and defletion at LVDT1 for all the tested olumns are shown in Figs. 7 to 9. It an be observed that, in olumns reinfored with φ10 and φ12 bars, the inrease of the load arrying apaity ourred before and after yielding of the steel longitudinal reinforement, respetively. Up to a defletion that approximately orresponds to the yield initiation of the steel

6 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Fig. 7. Fore displaement envelopes for all load yles of series C10_NON and C10_POS. Fig. 9. Fore displaement envelopes for all load yles of series PRE. Fig. 8. Fore displaement envelopes for all load yles of series C12_NON and C12_POS. longitudinal reinforement, the stiffness of the olumns of the POS series was, in general, lower than the stiffness of the olumns of PRE and NON series, sine, when tested, the olumns of the POS series were already signifiantly damaged. This effet is more evident in the olumns possessing more longitudinal reinforement, sine, due to the higher maximum load applied to these olumns, the onrete was signifiantly more damaged. In general, a pronouned pinhing effet ourred (narrowing of the hystereti diagrams), indiating that these olumns had redued apaity to dissipate energy. The relative high onrete ompressive axial stress (3.75 MPa) and the low onrete ompressive strength lass applied in the tested olumns have ontributed to this behaviour. Fig. 10. Total energy vs. aumulated horizontal displaement for C12b_POS olumn. In the strengthened olumns this pinhing effet was even more pronouned sine, due to the inrease of the flexural arrying apaity provided by the CFRP strips, the onrete axial ompressive stresses have inreased. From the horizontal fore vs. defletion at LVDT1 relationships reorded in the yli tests, the following diagrams an be obtained: dissipated energy vs. aumulated horizontal displaement, and maximum horizontal fore in eah series of load yles vs. horizontal displaement. Typial graphs for these relationships are depited in Figs. 10 and 11, whih orrespond to the C12b_POS olumn. Due to the fat that this strengthening tehnique does not provide signifiant onrete onfinement, the inrease on the dissipated energy was marginal. Table 4 inludes the values of the dissipated energy obtained in the yli tests.

7 3418 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Table 4 Dissipated energy Column referene Aumulated horizontal displaement (mm) Dissipated energy (kn mm) C10a_NON C10a_POS (72%) C10a_PRE C10b_NON C10b_POS (44%) C10b_PRE C12a_NON C12a_POS (26%) C12a_PRE C12b_NON C12b_POS (13%) C12b_PRE Values inside parentheses represent the dissipated energy inrement. Fig. 11. Variation of the peak load in the load yles for C12b_POS olumn Fore strain relationships In the majority of the strengthened olumns some CFRP strips have reahed tensile strain values lose to their ultimate strain ( =1%). As an example, Fig. 12 illustrates, for the olumn C10a_POS, the relationship between the horizontal fore applied to the olumn and the strain measured in the SG6 strain-gauge (see also Fig. 2). Due to the ontribution of the surrounding onrete, the maximum ompressive strain in the CFRP was about half the value reorded in tension. Relationships similar to those depited in Fig. 12 were obtained for the remaining olumns Crak patterns and failure modes In all the tested olumns a flexural failure mode ourred. Fig. 13 shows the rak patterns that ould be observed in the four lateral faes the olumns C10a_NON and C10a_POS, aording to the labels indiated in Fig. 2. These rak patterns are representative of the NON and POS series of olumns. The rak patterns of the PRE and POS series of olumns are similar (see also [19]). Fig. 13 shows that in the NON olumns the flexural failure rak formed at the olumn-footing interfae, while in the PRE and POS olumns a more diffuse rak pattern ourred. In these ases the flexural failure rak is loated above the repaired zone, i.e. approximately 150 mm above the olumn bottom surfae. This new loation of the failure surfae ontributed to the inrease of the flexural load arrying apaity of the strengthened olumns. Fig. 12. Relationship between the fore and the strain on the strain gauge SG6 (see Fig. 2) for the olumn C10a_POS. 7. Numerial simulation 7.1. Introdution A fibrous model with yli onstitutive laws for onrete and steel bars was implemented in the FEMIX omputer program [20], whih is based on the finite element method. The fibrous model was inorporated in the three-dimensional Timoshenko beam finite element [12]. With this finite element and the FEMIX framework, three-dimensional reinfored onrete frames with yli loading and nonlinear material behaviour an be analysed. This model was used in the numerial simulation of the behaviour of RC olumns strengthened with the NSM tehnique and submitted to axial and yli lateral loads (see the previous Setions). The simulated olumns were disretized with isoparametri Timoshenko beam elements with three nodes eah. The ross setion of eah element is disretized with 4- noded quadrilateral elements representing eah a longitudinal fibre (see Fig. 14). The geometry of the ross setion of eah fibre an vary along the beam element. The material model may vary from fibre to fibre thus allowing for the onsideration of non onstant onrete properties in the ross setion (e.g., unonfined and onfined onrete). A 2 2 Gauss Legendre rule is adopted to

8 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Fig. 13. Crak pattern on olumn C10a_NON (a) and C10a_POS (b) Note: thik line means higher rak opening; shaded zone represents onrete too damaged. Fig. 14. Fibrous model onept. evaluate the integrals related to eah 4-noded finite element used in the disretization of the ross setion. In the integrals that are required to evaluate the stiffness matrix and the internal fores of the Timoshenko beam element a Gauss Legendre rule with two points is used. A linear stress strain relationship was assumed for the CFRP strips, in agreement with the results obtained in the experimental tests. The formulation that was adopted for the simulation of the yli behaviour of the onrete and steel materials is briefly desribed in the following setions. A more detailed desription an be found elsewhere [21,22] Constitutive laws Conrete yli model Chang and Mander [21] developed a yli model for unonfined and onfined onrete based on the expression that was originally proposed by Tsai [23] to simulate the monotoni onrete ompressive behaviour. Chang and Mander assumed that onrete subjeted to a monotoni tensile stress an also be simulated with the Tsai equation by seleting appropriate values for the parameters. In the present work the aforementioned models are adopted, with minor adjustments, to simulate the onrete behaviour under monotoni and yli loading. These adjustments essentially involve the alulation proedure of parameter r in Eq. (3) (see Appendix A). The new proedure is based on experimental results that suggest the alulation of the parameter r with Eq. (4) Steel yli model The original formulation of the Menegotto and Pinto model is adopted in the present work [24]. A brief desription of this model is inluded in Appendix B. Some adjustments are neessary, being the main modifiation restrited to Eq. (22). 8. Model appraisal The tested RC olumns were numerially simulated with the FEMIX omputer ode [20]. All the tested olumns were disretized with six isoparametri Timoshenko beam elements with three nodes eah. Aording to the developed approah, at the ross setion level eah fibre is disretized with a quadrilateral finite element. These fibres are represented by 4-noded finite elements with a 2 2 Gauss Legendre integration rule, thus simulating the onrete ore, onrete over, steel bars and CFRP strips. The onrete part of the ross setion was disretized with sixteen

9 3420 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Table 5 Data used in the numerial analysis to simulate the onrete behaviour Column f (N/mm 2 ) ε x r E a (N/mm 2 ) ε t x + r f t b (N/mm 2 ) C10b_NON e e C10b_PRE e e C12b_NON e e C12b_PRE e e a Young s Modulus. b Uniaxial tensile strength, aording to CEB FIP Model Code [26]. Table 6 Data used in the numerial analysis to simulate the behaviour of the steel bars Column E s (N/mm 2 ) f sy (N/mm 2 ) ε sh f sh (N/mm 2 ) ε su f su (N/mm 2 ) E sh (N/mm 2 ) C C Fig. 16. Numerial and experimental results of the C12b_PRE olumn. Fig. 15. Numerial and experimental results of the (a) C10b_NON and (b) C10b_PRE olumns. quadrilateral elements. Eah longitudinal bar and eah CFRP strip was simulated with an additional quadrilateral element. A linear stress strain relationship was assumed for the CFRP strips, in agreement with the results obtained in the experimental tests [19]. Tables 5 and 6 inlude the values that were adopted for the parameters that define the onrete and steel onstitutive models (the definition of the parameters inluded in these tables an be found in Appendies A and B). These values were obtained from tests that were arried out with onrete and steel speimens, as desribed in Setion 4. Fig. 15 shows the omparison between the experimental and numerial envelope urves for the NON and PRE tested olumns with φ10 steel bars. It an be onluded that the implemented numerial model reprodues the main phenomena observed in the experimental tests. The POS olumns require a two-phase strutural analysis: without and with strengthening. Sine the omputer ode annot simulate a struture with more than one phase, the POS olumns were not numerially analyzed. Fig. 16 inludes, for the C12b_PRE olumn, the numerial and experimental horizontal fore-defletion relationships. Regardless of orretly prediting the envelope response, in the numerial model larger energy dissipation ourred when ompared with the experimental test. This is due to the fat that, in the present version of the program, it was assumed that onrete behaves

10 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Fig. 17. Shemati representation of the onrete yli onstitutive model. linear-elastially in shear, whih is an inaurate approah, and the inelasti bukling of the steel bars was not integrated in the steel yli onstitutive model. The inapability of the numerial model to simulate the pronouned pinhing effet observed in the experimental tests resides on the fat that the model, in the present version, an not model the debonding between reinforement and surrounding onrete, whih results in a redution of the energy dissipation apaity of the RC olumn. To aurately simulate this effet, a bond-slip model needs to be implemented to model the bond behaviour between reinforement and onrete. 9. Conlusions A strengthening tehnique based on bonding CFRP laminate strips into slits opened on the onrete over was applied to RC olumns subjeted to axial ompression and lateral yli loading. Sine the amount of CFRP strengthening was the same for all olumns, those with a smaller onventional steel reinforement (4φ10) had a larger load arrying apaity inrease (92%) than those with 4φ12, whih had only a apaity inrease of 34%. With the proposed strengthening tehnique premature debonding ould be avoided, whih allowed for the possibility of a full exploitation of the CFRP resistane as was indiated by the attainment of high strain values. This fat lead to the failure of some CFRP strips in the base of the olumns. The obtained experimental results indiate that the proposed strengthening tehnique is very promising for inreasing the load arrying apaity of onrete olumns failing in bending. However, as was expeted, the energy absorption apaity of the tested RC olumns was not improved by this tehnique, sine it does not provide signifiant onrete onfinement. With the aim of simulating the behaviour of reinfored onrete olumns strengthened with the tehnique proposed in this work, a fibrous model with yli onstitutive laws for onrete and steel bars was implemented in a omputational ode based on finite element tehniques. This omputational model an simulate the yli behaviour in ompression and in tension of unonfined and onfined onrete. The numerial model has reprodued, with good agreement, the behaviour observed in the experiments, being a useful tool for the analysis of this type of strutures. Aknowledgments The study reported in this paper is inluded in the researh program CUTINSHEAR Performane assessment of an innovative strutural FRP strengthening tehnique using an integrated system based on optial fiber sensors supported by FCT, POCTI/ECM/59033/2004. The seond author aknowledges the support provided by the grant in the ambit of this researh projet. Appendix A. Chang and Mander model Fig. 17 represents the envelope urves and yli rules of the model. The supersript + or indiates that the parameter orresponds to a tensile or ompressive state, respetively. The non-dimensional stress strain relationship of the envelope urve for the ase of the ompressive behaviour an be written in the following manner: for 0 < x < x r f = f y(x ) E t = E z(x ) for x r x x sp f = f [y(x ) + r n z(x r )(x x )] r E = r E z(x ) r for x > x sp f = E t = 0 (1a) (1b) (1) where, f is the onrete ompressive strength (for onfined onrete f = f ; for unonfined onrete f = f ), E is the onrete initial Young s Modulus (CEB-FIP 1993, [26]), y(x ) = n x (2) D(x ) [ 1 (x ) r] z(x ) = (3) [D(x )] 2 r = f , with f in MPa (4)

11 3422 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Table 7 Controlling parameters used in transition urves for the onrete yli onstitutive model Parameters Rule number ε a ε un ε + un ε un ε + un ε pl ε + pl ε r ε r ε r ε r ε r f a f un f + un f new f + new 0 0 f r f r 0 f r f r E a E E E new E + new E pl E + pl E E 0 E E ε b ε pl ε + pl ε re ε + re ε + un ε un ε b ε a ε un ε b ε a f b 0 0 f re f + re f + new f new f b f a f new 0 f a E b E pl E + pl E re E + re E + new E new E t,9 (ε b ) E t,10 (ε a ) E new 0 E t,13 (ε a ) Table 8 Parameters used in transition urves for the onrete yli onstitutive model Parameter ( ) (+) Parameter ( ) (+) E ± f un E ε se E f + un E εt ε E un ε ε+ un εo ε ± ε un εt ε 0.22ε + un un ε ( ) E ± pl 0.1E exp 2 ε un E ε ε+ un εo 1.1 f ± 0.09f ε un un 0.15f + ε un +1 f ± new E ± new f ± re f = un f ( ε un ε εt f un f f + un f + ε ± pl ε f un un f new ε un ε pl f ) ; f + = un f + ( ) ε re ε ( ε + un εo εt ). f + new ε + un ε + pl f + ( ) ε re εo + ( D(x ) = 1 + n r ) x + (x ) r r 1 r 1 for r 1 = 1 + [n 1 + ln (x )] x for r = 1. (5) In the above equations x, x r and n x = ε ε, are defined by x r = ε r ε, n = E ε f. (6) In (6) ε is the strain that orresponds to the onrete ompressive strength (for onfined onrete ε = ε ; for unonfined onrete ε = ε, where ε and ε are the strains that orrespond to f and f, respetively). The parameter ε r represents the ritial ompressive strain, after whih a linear stress strain relationship is assumed for the onrete in ompression (see Fig. 17). The non-dimensional spalling strain, x sp, determined aording to Eq. (7), orresponds to the maximum ompressive strain, after whih, due to onrete spalling, it is assumed that the onrete residual strength is exhausted. x sp = x r y(x r ) n z(x r). (7) Eqs. (1a) and (1b) define the rule 1, while Eq. (1) defines the rule 5. As already mentioned, the shape of the tension envelope urve is the same as that of the ompression envelope urve [21], hene similar Eqs. an be used to define the rule 2 (Eqs. (8a) and (8b)) and rule 6 Eq. (8) of the onrete tension envelope urve, as follows: for x + < x + r f + = f t y(x + ) E + t = E z(x + ) for x + r x+ x tu f + = f t [y(x + ) + r n+ z(x+ r )(x+ x + )] r E + = r E z(x + ) r for x + > x tu f + = E + t = 0 εt (8a) (8b) (8) E se ε + un f + un E + se ε ± re ε + un ε ε + + un ε+ ( ) ( ) ε re ε re εo + E ± re where x + = ε ε o ε, n+ = E ε t t f t x tu = x + y(x+ ) r r n + z(x + r) E ε and with f t being the onrete tensile strength and ε t its orresponding strain. All other rules orresponding to unloading and reloading branhes are represented by a transition urve, whih starts from an already known starting point (a subsript a is used to designate this point: ε a ; f a ) and slope (E a ) that needs to be evaluated, and ends at a target point (a subsript b is used to designate this point: ε b ; f b ), whose oordinates, as well as the slope at this point (E b ) need to be alulated. The transition urve is represented by f = f a + (ε ε a ) ( E a + A ε ε a R ) (10) where R = E b E se E se E a and A = E se E a ε b ε a R. (11) The rules are summarized in Table 7. The parameters used in this table are alulated using the expressions inluded in Table 8. In Table 7 ε r and f r are the strain and the stress omponents of the last reversal point. The parameter E t,k (ε i ) in Table 7 represents the tangent Young s Modulus at strain ε i for the kth rule (i represents the a or b point). In Table 8 f ± (ε i ) and E ± (ε i ) represent the stress and the tangent elastiity modulus at strain ε i, evaluated with the equations that define the envelope urves. If, during the unloading proess modelled with rule 3, a reversal ours (see Fig. 17), the values that define the target point of the funtion that establishes the rule 7 are obtained from linear interpolation, using values alulated with the expressions of Table 8 orresponding to rule 7, as desribed elsewhere [21]. Similarly, when a reversal in rule 4 takes plae, a linear interpolation is used to obtain the values of the parameters that define the rule 8. A reversal in rule 9 is modelled with rule 11, while a reversal in rule 10 is simulated with rule 12 (see Fig. 17). In order to define the rules 11 and 12, the points a and b are E + εt (9)

12 J.A.O. Barros et al. / Engineering Strutures 30 (2008) parameter ε so (Fig. 18), whih is dependent on the experiened plasti exursion into the envelope urve, an be reloated and saled in order to simulate strength degradation [21]. The stress and the tangent elastiity modulus of the envelope urve are alulated with the expressions defined by Eqs. (17a) and (17b). In the following equations the tensile envelope urve (rule 1) is desribed by onsidering the (+) version of the parameters, while the ompressive envelope urve (rule 2) by onsidering the ( ) version. f s = E s ε ss [ ( ) ] sign ( ε s1) + 1 (f ± 2 su f ± ) sy E 1 + s ε ss f ± sy ( 1 ε ± ε su ss p±) ε ± su ε ± (17a) sh Fig. 18. Shemati representation of the parameters for the steel yli onstitutive model. assumed to be loated in the branhes orresponding to rule 9 and 10, respetively (in ase of rule 12, a is now the target point). The following equation is used to obtain the strain at the target point ε a ε pl ε + un ε pl = ε ε un b ε un ε +. (12) pl A reversal in rule 13 is simulated with rule 14, whih has the b target point lying on the absissa, whose strain value, ε b, an be alulated from the following equation ε b = ε a f a E se. (13) The shift in the tension envelope urve, whose definition is based on the strain parameter ε o (see Fig. 17), is alulated as desribed in the following steps: (a) Calulate the ompressive and tensile non-dimensional strain dutility parameters x = ε un u ε and x + = ε + ε un o u ε. (14) t (Note: in the first iteration ε o = 0; in the first reversal ε + un = 0). (b) If x + < u x u then x + u = x u, ε o = 0, ε + un = x+ u ε t (15) and the orresponding stress, f + un, is obtained from the tensile envelope urve at ε + un. The shift is finally alulated from 2f + un ε o = ε + ε pl o x + ε u t, where, ε o = E + se + E. (16) pl The utilization of the yli onrete model that was desribed above only requires the following parameters: E, f, f t, ε, ε t, ε + r, ε r. Appendix B. Menegotto and Pinto model Ten rules define the yli model assumed for steel bars, being five assoiated with the ompressive state and the remaining with the tensile state. The tensile and ompressive envelope urves depend on the monotoni stress strain (f s ε s ) relations defined by rules 1 and 2, respetively (see Figs. 18 and 19). The strain E st = where [ ( 1 + E s E s ε ss f ± sy f ± su f s f ± su f ± sy ε ss = ε s ε ± so ; ε s1 = ε ss ε + sh ; ) ] sign ( ε s1) + 1 sign ( ε s2 )E ± sh 2 p ± 1 p ± p± = E ± ε ± su ε± sh sh f ± su f ± sy ε s2 = ε + su ε ss for the ase of the tensile envelope ε s1 = ε ε sh ss; ε s2 = ε ss ε su for the ase of the ompressive envelope. (17b) (18) (19a) (19b) All the rules simulating the unloading and reloading branhes (see Fig. 19) are based on the model proposed by Menegotto and Pinto [24]. The following equations define these branhes ( f s = f sa + E sa (ε s ε sa ) Q + 1 Q A E st = E s se E s se QE sa ε 1 + E s ε sa R s sa f h f sa ) (20a) (20b) where ε sa and f sa are the strain and stress omponents of the a initial point, E sa is the tangent elastiity modulus at this point, and A = [1 1 = + E ε s ε sa sa f h f sa Q = E s se E sa 1 f h = f sa + E sa (1 R s ) 1 Rs ] 1 R s Rs (ε sb ε sa ). (21) An iterative proedure is required to obtain the strain and stress omponents that define the unloading and reloading branhes. The parameters that define these rules are summarized in Table 9, where ε sr and f sr are the strain and the stress omponents of the last reversal point, and ε s max and ε s min are the maximum exursions into the tensile envelope branh and into the ompressive envelope branh, respetively. Table 10 shows how to alulate the parameters required by the rules indiated in Table 9. In a raked reinfored onrete element the stress in the steel reinforement attains a higher value in the viinity of the raks

13 3424 J.A.O. Barros et al. / Engineering Strutures 30 (2008) Fig. 19. Shemati representation of the yli steel onstitutive model. Table 9 Controlling parameters used in Menegotto Pinto model [24] Parameter Rule number ε sai ε sr ε sr ε sr ε sr ε sr ε sr ε sr ε sr f sai f sr f sr f sr f sr f sr f sr f sr f sr E sai E so E + so E + so E so E so E + so E + so E so ε sbi ε s min +ε so ε s max +ε + so ε s max + ε + + ε so sa3 ε sa5 f + sy ε s min + ε + ε 1.2Es so sa4 ε sa6 f sy ε sa5 ε sa6 ε sa7 ε sa8 1.2Es f sbi f s (ε sb3 ) f s (ε sb4 ) f s (ε sb5 ) f s (ε sb6 ) f sa5 f sa6 f sa7 f sa8 E sbi E s (ε sb3 ) E s (ε sb4 ) E s (ε sb5 ) E s (ε sb6 ) E sa,5 (ε sa5 ) E sa,6 (ε sa6 ) E sa,7 (ε sa7 ) E sa,8 (ε sa8 ) Table 10 Parameters required for Menegotto Pinto model [24] Parameter (+) ( ) Parameter (+) ( ) ε ± so ε + sa k + rev ε+ sb (1 k ) rev ε sa (1 k+ ) + rev ε sb k+ rev ε ± sa ε + + so ε+ f + y ( sh Es ε + + ε fs max so s max ε + ε so s min f s min exp ε ± sb Es E ± so (1 ε sa )E s (1 3 ε sa )E s R ± s 20 ε sa = ε sbi ε sai 2. Es k ± rev ) ε s min 5000(εsy) ( ) 2 1 fsy 3 Es (1 20 ε sa ) 16 ε + so ε f y ( sh Es exp ( fsy Es ) εs max 5000(ε sy) + 2 ) 1 3 (1 10 ε sa ) than in the intat zones. Therefore, when a steel onstitutive model is based on the average stress, this stress is smaller than the one that in reality ours in the raked zone. For this reason, steel yield initiation at raked zones is not orretly simulated if average stress values are adopted to haraterize the stress field in a steel bar involved by raked onrete. To overome this defiieny an improvement has been implemented in the present onstitutive model by means of a tehnique proposed by Stevens [25], whih is based on a redution of the tensile envelope urve (see Fig. 18), aording to the following reommendation f s = 75 f t C b, with f t in MPa φ s { 1 for steel bars of high adherene C b = τ b 5f t in the remaining ases, with τ b = 13.5 Mpa (22) where φ s is the bar diameter in millimetres. The utilization of the yli steel model that was desribed above only requires the following parameters: E s, f sy, ε sh, f sh, E sh, ε su and f su. Referenes [1] FIB. Externally bonded FRP reinforement for RC strutures. Bulletin 14. Lausanne p [2] ACI. Guide for the design and onstrution of externally bonded FRP systems for strengthening onrete strutures. Amerian onrete institute (Committee 440); p [3] Oehlers DJ, Seraino R, Smith S. Design guideline for RC strutures retrofitted with FRP and metal plates: Beams and slabs, SAI global limited standards pages [in press] doehle01.html. [4] CNR-DT 200. Instrutions for design, exeution and ontrol of strengthening intervention with FRP. Consiglio Nazionale delle Riherhe p [5] Blashko M, Zilh K. Rehabilitation of onrete strutures with CFRP strips glued into slits. In: Proeedings of 12th int. onf. on omposite materials p. 7. [6] Carolin A. Carbon fibre reinfored polymers for strengthening of strutural elements. Ph.D. thesis. Division of Strutural Engineering. Luleå University of Tehnology p [7] El-Haha R, Rizkalla SH. Near-surfae-mounted fiber-reinfored polymer reinforements for flexural strengthening of onrete strutures. ACI Strut J 2004;101(5): [8] Barros JAO, Fortes AS. Flexural strengthening of onrete beams with CFRP laminates bonded into slits. J Cem Conr Compos 2005;27(4): [9] Barros JAO, Dias SJE. Near surfae mounted CFRP laminates for shear strengthening of onrete beams. J Cem Conr Compos 2006;28(3): [10] De Lorenzis L, Rizzo A. Behaviour and apaity of RC beams strengthened in shear with NSM FRP reinforement. In: Proeedings of the 2nd international FIB ongress Paper ID [11] CEB. RC elements under yli loading: State of the art report. Thomas Telford (ed.). Comite Euro-International du Beton; [12] Guedes JPSCM. Seismi behaviour of reinfored onrete bridges. Modelling, numerial analysis and experimental assessment. Ph.D. thesis. Joint Researh Centre ISPRA

14 J.A.O. Barros et al. / Engineering Strutures 30 (2008) [13] Sena-Cruz JM. Strengthening of onrete strutures with near-surfae mounted CFRP laminate strips. Ph.D. thesis. Department of Civil Engineering, University of Minho; Publiations/2004/PhD2004_001_JSenaCruz.pdf [14] RILEM TC 50-FMC. Determination of frature energy of mortar and onrete by means of three-point bend tests on nothed beams. Mater Strut 1985; 18(106): [15] EN Metalli materials. Tensile testing. Part 1: Method of test (at ambient temperature); p. 35. [16] EN Methods of testing ement. Part 1: Determination of strength [17] ISO Plastis Determination of tensile properties Part 5: Test onditions for unidiretional fibre-reinfored plasti omposites. Geneva (Switzerland): International Organization for Standardization (ISO); p. 9. [18] ISO Plastis Determination of tensile properties Part 2: Test onditions for moulding and extrusion plastis. Geneva (Switzerland): International Organization for Standardization (ISO); p. 5. [19] Ferreira DRSM. Pilares de Betão Armado Reforçados om Laminados de Fibras de Carbono (Reinfored onrete olumns strengthened with CFRP laminates). M.S. thesis. Department of Civil Engineering, University of Minho; _DFerreira.pdf [in Portuguese]. [20] Sena-Cruz JM, Barros JAO, Azevedo AFM, Ventura Gouveia A. Numerial simulation of the nonlinear behavior of RC beams strengthened with NSM CFRP strips. CMNE/CILAMCE Paper n o 485 published in CD FEUP pp /CP2007_001_CMNE2007.pdf [21] Chang GA, Mander JB. Seismi energy based fatigue damage analysis of bridge olumns: Part I-Evaluation of seismi apaity. Report No. NCEER [22] Varma RK, Barros JAO, Sena-Cruz JM. Fibrous model for the simulation of the yli behaviour of 3D reinfored onrete frames. Report No. 07-DEC/E-04. Department of Civil Engineering. University of Minho; p. 90. [23] Tsai WT. Uniaxial ompression stress strain relation of onrete. J Strut Eng 1988;114(9): [24] Menegotto M, Pinto PE. Method of analysis for ylially loaded reinfored onrete plane frames inluding hanges in geometry and non-elasti behaviour of elements under ombined normal fore and bending. In: IABSE symp. on resistane and ultimate deformability of strut. Ated on by welldefined repeated loads. Final report [25] Stevens NJ. Analytial modelling of reinfored onrete subjeted to monotoni and reversed loadings. Report No ISBN University of Toronto [26] CEB. CEB-FIP model ode Comite Euro-International du Beton. Thomas Telford (ed.). Bulletin d Information n o 213/214; 1993.