CFRP-Confined Reinforced Concrete Elements Subjected to Cyclic Compressive Loading

Transcription

1 SP CFRP-Confined Reinfored Conrete Elements Subjeted to Cyli Compressive Loading by J.A.O. Barros, D.R.S.M. Ferreira, and R.K. Varma Synopsis: The effetiveness of disrete and ontinuous CFRP wrapping arrangements for reinfored onrete (RC) short olumn subjeted to monotoni and yli ompressive loading is assessed in this work. The experimental program is omposed of four series of RC olumns with disrete wrapping arrangements and one series of full wrapped RC olumns. Eah series is omposed of a monotoni and a yli test. Strain gauges were installed along the height of eah olumn to measure the strain field in the CFRP during the test. The variation of the stiffness of the unloading and reloading branhes of eah loading yle was determined. A onstitutive model to simulate FRP-onfined RC onrete elements subjeted to yli ompressive loading was developed and implemented into a omputer program based on the finite element method. This model was appraised with the data obtained from the arried out experimental program. Keywords: arbon fiber-reinfored polymers; olumns; onrete onfinement; yli onstitutive model; yli loading; FEM wrapping 85

2 86 Barros et al. Joaquim A.O. Barros is an Assoiate Professor and Diretor of the Laboratory of the Strutural Division of the Department of Civil Engineering, University of Minho, Portugal. He is a Member of ACI Committees 44, Fiber Reinfored Polymer Reinforement, and 544, Fiber Reinfored Conrete. His researh interests inlude strutural strengthening, omposite materials, fiber reinfored onrete, and finite element method. Debora R.S.M. Ferreira is a PhD Student in the Strutural Division of the Department of Civil Engineering, University of Minho. Her researh interests inlude strutural strengthening with omposite materials. Rajendra K. Varma is a PhD Student in the Strutural Division of the Department of Civil Engineering, University of Minho. His researh interests inlude the development of onstitutive models to simulate the material nonlinear behavior or reinfored onrete strutures strengthened by FRP omposite materials, using finite element method and omputational mehanis. INTRODUCTION Wrapping reinfored onrete (RC) olumns with wet lay-up arbon fiber reinfored polymer (CFRP) sheets, using disrete (strips in between the existent steel hoops) or ontinuous (full wrapping) onfinement arrangements, has proven to be an effetive strategy to inrease the load arrying apaity, ultimate deformability and energy absorption apaity of RC olumns. The inrease in terms of the energy that an RC olumn an dissipate before its ollapse, due to the onrete onfinement provided by CFRP arrangements, is one of the main reasons justifying the appropriateness of these omposite materials to retrofit RC olumns of the built heritage loated in zones of high seismi risk 1-4. To preserve the global strutural stability of buildings loated in these zones, it is mandatory to assure that their olumns do not fail when subjeted to a seismi event. When this type of event ours, the olumns are subjeted to yli ompressive loading. To explore the potentialities of CFRP-onfinement arrangements to inrease the load arrying apaity and energy absorption ability of RC olumns subjeted to yli ompressive loading, an experimental program was arried out with RC olumn speimens having a ross setion of mm (7.88 in.) diameter and a height of 6 mm (23.64 in.). The influene of the CFRP onfinement arrangement on the yli ompressive behavior of onrete was evaluated. Prediting the behavior of CFRP-onfined RC olumns submitted to seismi loading is a omplex task, requiring sophistiated onstitutive models able of reproduing the behavior of the intervening materials up to their ollapse, and FEM-based omputer programs that inlude the algorithms assoiated to the material nonlinear analysis of RC strutures. However, the development of these numerial tools is mandatory sine their use an avoid the exeution of too expensive experimental programs and an help the designer on the seletion of the best strengthening strategies to adopt. To give a ontribution in this domain, a CFRP-onfined onrete yli onstitutive model was developed and implemented into a FEM-based omputer program. The results from the experimental program were used to alibrate some variables of this model and to appraise its performane. CONFINEMENT ARRANGEMENTS AND EXPERIMENTAL PROGRAM The present work is part of a researh program that aims at developing guidelines for the design of disrete and ontinuous FRP onfinement arrangements to RC olumns submitted to monotoni and yli loadings. In previous works 5,6, the most effetive disrete onfinement arrangements were seleted, taking into aount the inrement in terms of load arrying and energy absorption apaities provided by disrete and ontinuous onfinement onfigurations, as well as the labor time and materials these arrangements require. The present work deals with the most effetive disrete onfinement arrangements and ompares their performane with that obtained from ontinuous onfinement arrangements. These arrangements are shematially represented in Table 1. Eah speimen is designated as WiLk_/m, where Wi represents the strip width and Lk the number of CFRP layers per eah strip. To distinguish yli from monotoni tests, a letter was attributed to a speimen submitted to yli tests, while an m letter was used to designate monotoni tests. Eah series of diret ompression tests (WiLk) was omposed of two speimens, one submitted to monotoni loading (WiLk_m) while the other was submitted to yli loading (WiLk_). Figure 1 shows the onfinement arrangements adopted in this work. A detailed desription of the onfinement proedures an be found elsewhere 7.

3 Seismi Strengthening of Conrete Buildings 87 MATERIALS CFRP sheets with the trade name of Mbrae CF-1 ( g/m 2 (.28 lb/in. 2 ) of fibers) were used in the present experimental program. These sheets had.113 mm (.446 in.) of thikness, a tensile strength of 3539 MPa (514.5 ksi), an elastiity modulus and an ultimate strain in the fiber s diretion of 232 GPa (33728 ksi) and 1.53%, respetively. To evaluate these properties, samples of the CFRP sheet were tested in ompliane with the ISO reommendations 8. To determine the values of the properties that haraterize the tensile behavior of used steel bars, five tensile tests for eah steel bar diameter were arried out aording to the NP-EN reommendations 9. The average values of the obtained results are the following: for the steel hoops of 6 mm (.236 in.)diameter, a yield stress ( sy ) of MPa (68.4 ksi), a tensile strength ( su ) of MPa (89.58 ksi), an elastiity modulus (E s ) of GPa (3849 ksi) and an ultimate strain ( su ) of 8%; for the longitudinal steel bars of 8 mm (.315 in.) diameter, sy =517.2 MPa (75.19 ksi), su =67.9 MPa (88.38 ksi), E s =199.8 GPa (2961 ksi) and su =11%. The onrete ompressive strength was determined aording to NP-EN From tests on 15 mm (5.91 in.) ubes, an average ompressive strength of 3 MPa (4.36 ksi) was obtained at 28 days. TEST SETUP The yli and monotoni diret ompression tests were arried out using a losed-loop test mahine of 225 kn (55.8 kilo-lb) maximum load apaity. Speimen axial deformation was measured by means of LVDTs lamped to the steel load platens of the equipment, as shown in Figure 2. Strains in the CFRP fiber diretion were measured by strain gauges (SG) plaed aording to the shemes presented in Table 1. The speimens subjeted to yli ompressive load were tested under fore ontrol at a load rate of 15 kn/s (3372 lb/s), aording to the loading history shematially represented in Figure 3. The last test proedure onsisted of a ramp in displaement ontrol up to the rupture of the speimen. The speimens subjeted to monotoni loading were tested under displaement ontrol at a displaement rate of 5 m/s (.2 in/s), using an external LVDT of mm (.79 in.) of measuring length. The test was stopped when the measuring length of the LVDT was reahed. EXPERIMENTAL RESULTS The main effetiveness indiators for the adopted onfinement systems are inluded in Table 2, where f is the URC CRC maximum onrete ompressive stress, f and f are the ompressive strength of unonfined and onfined CRC URC CRC reinfored speimens, is the speimen axial strain at f, and are the speimen axial strain at f URC and f, respetively, and fmax is the maximum tensile strain in the CFRP fiber s diretion. The variation of W and L leads to speimens with different values for the CFRP volumetri ratio, f, whih is evaluated from: W L S t f f 4 (1) D H where t f is the thikness of the CFRP sheet and D and H represent, respetively, the diameter and the height of the speimen. In Table 2, UPC represents the unonfined plain onrete speimens and URC the speimens reinfored with longitudinal and transversal steel bars, without any CFRP onfinement arrangement. From the analysis of the results inluded in Table 2 the following observations an be outlined: The speimen load arrying apaity rises with the inrease of f. Taking as basis of omparison the f URC CRC URC values of URC speimen ( f ) it is observed that f f ratio varied between 1.5 for f =.31 and 2.68 for CRC URC f =.68. Regardless of the loading type, a tendeny of f f ratio to inrease with the inrease of f is noted;

4 88 Barros et al. Comparing the results of speimens of equal f subjeted to yli loading, it an be onluded that fullwrapping is more effetive than disrete onfinement arrangements. Similar tendeny was expeted for the speimens subjeted to monotoni loading, as previous researh has already proved 5, but W6L3_m speimen presented a too abnormal low load arrying apaity, whih might have been aused by a defiient appliation of the CFRP system or an inorret position of this speimen in the testing mahine, resulting some eentriity of the applied load. The lower effetiveness of disrete onfinement systems an be justified by the aumulated damage in the unonfined onrete between strips. This effet is more pronouned in speimens subjeted to yli loading, sine the onrete plasti strain inreases in subsequent yles of the series of yles of same load amplitude (see Figure 4). However, it should be noted that, in omparison with the full wrapping onfinement system, the partial onfinement arrangements are easier and faster to apply; CRC URC If the W6L3_m speimen is exluded from the analysis, the ratio has a tendeny to rise with the inrease of f (a negative signal attributed to the onrete ompressive strain). Due to the aumulation of the onrete ompressive plasti strain, mainly in between CFRP strips in subsequent loading yles, values of the CRC URC ratio were larger in the speimens submitted to yli loading than in the speimens under monotoni loading; There was a tendeny for maximum CFRP strains (a positive signal attributed to the CFRP tensile strains) to our in the top half of the speimen, in spite of a large dispersion within the obtained results, sine these measures are restrited to the influene area of the SGs and they an be even affeted by loalized ourrenes. A similar tendeny has, however, already been reported by other authors 11,12. In fat, failure ours, in general, by the rupture of the CFRP strips loated in the upper half of the speimen, mainly in the first and/or seond strips. Figure 4 shows the urves that relate the onrete axial ompressive stress (f ) with the onrete axial ompressive strain ( ) in the speimens submitted to yli (WiLk_) and monotoni (WiLk_m) loadings. In Figure 4, the relationship between f and the average strain in the CFRP strips ( fm ) is also inluded for both monotoni and yli tests (the strains were not measured in the W6L3_ test due to the malfuntioning of the SG data aquisition system). Figure 4 shows that: the urve of the monotoni test an be regarded as the envelope of the urve of the orresponding yli test; In eah series of load yles, both the onrete axial strain and the average CFRP strain inreased from the first to the third yle. The inrease of the onrete axial strain an be justified by onrete dilation, mainly at the zones in-between CFRP strips, while the inrease of the CFRP tensile strain an be justified by the inrease of onrete plasti strain in subsequent load yles. In fat, the reovered strain in the unloading branh of eah yle is only a part of the strain inrement ourred in the reloading branh of the previous yle, whih means that an inrement of strain is installed in the CFRP in subsequent load yles; In general, the maximum load attained in the reloading branh of the 1 st load yle of eah series of load yles was higher than the load arrying apaity (for equal level of axial deformation) of the homologous speimens submitted to monotoni loading. Due to the inrease of tensile strains in the CFRP in subsequent load yles of eah series of load yles, an inrease of onfinement pressure is introdued into onrete by the CFRP system, leading that the reloading branh of the last yle of eah series of load yles (the returning to the monotoni phase) presents higher load arrying apaity. As expeted, this ourrene was more pronouned in the fullwrapped speimens; From the analysis of the onfiguration of the f - unloading and reloading branhes of eah load yle, it is verified that the unloading branh is eminently non linear, while the reloading branh is formed by nonlinear segments of redued amplitude at its extremities, onneted by a linear part. To evaluate the variation of the stiffness of the unloading and reloading phases of the load yles along the test, it was assumed that both the unloading and reloading phases ould be modeled by linear branhes, as shown in Figure 5 (r for the reloading branh and u for the unloading branh).

5 Seismi Strengthening of Conrete Buildings 89 Figure 6 shows the relationship between the onrete axial strain and the stiffness of the unloading and the reloading branhes of the load yles (seant stiffness). The following observations an be pointed out: In eah series of load yles, in the onseutive yles the stiffness of the unloading and reloading branhes shows a tendeny to derease and to inrease, respetively. The stiffness inrement of the reloading branhes is due to the inrease of the onfinement pressure applied by the CFRP to the onrete in the onseutive yles. However, this tendeny of inrease is not as pronouned as the tendeny of derease reported for the unloading branhes; In the suessive series of load yles, a tendeny for a derease of the stiffness of both the unloading and reloading branhes is observed in all tested speimens. The dereased level of the stiffness of these branhes diminished with the inrease of the speimen axial deformation. This is more pronouned in the full-wrapped speimens, whih presented a variation that an be simulated by an exponential law (see Figure 6e). The stiffness of the unloading and reloading branhes seems to approah a onstant value (residual stiffness). In ase of fully wrapped speimens, this value is almost the same for both the unloading and reloading branhes, while in the speimens with disrete onfinement arrangements the residual stiffness of the unloading branhes is higher than that of the reloading branhes. This an be justified by the dilation of the unonfined onrete inbetween CFRP strips. Figure 7 shows the urves orresponding to the relationship of the onrete axial ompressive stress with both the onrete axial ompressive strain and the CFRP tensile strain in the fiber s diretion, for the partially onfined W6L5 and fully onfined W6L3 series, both series with equal f (see Table 2). To make the figure legible, only the strains reorded by SG2 were inluded in this graph, one the speimen rupture ourred in the zone where SG2 was installed (see Table 1 and Figure 8). Although partial wrapping arrangements were not as effetive in terms of load arrying apaity as full wrapping arrangements, they provided a signifiant inrease of the speimen load arrying apaity (up to two times the ompressive strength of its orresponding unonfined speimen). Furthermore, partial wrapping arrangements assured a high level of deformability at the speimen failure, ensured easier and faster appliation and prevented the rupture modes from being as violent as those of the fully wrapped speimens, sine part of the internal energy was gradually dissipated due to the ompression strain-softening behavior of the onrete in-between CFRP strips. The shape of the unloading and reloading branhes seems to be similar in both partially and fully onfined speimens. After rupture, the partially and fully wrapped speimens of equal f presented the appearane shown in Figure 8. Failure mode ourred with a violent CFRP rupture, whih tended to be more violent as the volume of unonfined onrete between the CFRP strips dereased. This an be justified due the aumulation of plasti deformation of the onrete in these areas. Figure 9 shows the tensile strains measured in the strain gauges (SG) installed on W6L5 and W6L3 speimens (of equal f ), submitted to yli and monotoni loadings, for a load level near the failure of these speimens. In spite of the diffiulty in finding a tendeny, in general, the maximum strains in the CFRP ourred at the top of the speimens. Sine a steel hinge was used at the top of the speimens to transfer the load applied by the mahine, the redued restrain provided by this hinge has allowed SG1 to reord the highest gradient of strains (see Figure 9), whih justifies the prevalene of the failure of the speimen due to the rupture of the CFRP strip near the loation of this SG. Nonetheless, the strains varied from.3% up to 1.2%, and the average strain, taking into aount the measures registered in all SG of the tested speimens, was approximately.7%. This value may be even higher sine the strain values registered in the CFRP only represent the areas where the strain gauges are plaed, and, onsequently, they are too dependent on the speimen failure mode onfiguration. Figure 1 represents the relationship between the onrete axial ompressive stress and the average strain in the SGs of W6L5 and W6L3 speimens for both the monotoni and yli tests. The envelope urve of the yli test follows approximately the urve of the monotoni test of the orresponding speimen. However, in general, the envelope stress-strain urve of the yli test reveals a higher load arrying apaity than the one of the orresponding monotoni test. This is justified by the pre-stress applied in the CFRP in the onseutive load yles, whih inreased the speimen axial stiffness, resulting in higher load arrying apaity of the speimen.

6 9 Barros et al. CONSTITUTIVE MODEL FOR FRP-CONFINED CONCRETE SUBJECTED TO CYCLIC COMPRESSION LOADING The developed model is omposed by an envelope and yli branhes. Compressive Envelope Curve The envelope urve for ompression is derived from Lam and Teng model 13. The stress-strain relationship of the envelope urve (Figure 11) for ompression, f, an be desribed as follows (ompression stresses and strains are assumed with positive sign): E 2 E E E2 f E and E t E if t ; (2) 4 f 2 f o o f fo E2 and E t E2 for t ; (3) where f o is the ompressive strength of unonfined plain onrete (UPC) in MPa, E is the onrete initial Young s modulus, is the strain at the transition between the domain of the equation (2) and (3), t is the ultimate strain of onfined plain onrete () and: 2 f o t (4) E E2 E is the tangential Young s modulus determined by: 2 f fo E2 (5) From experimental results it was verified that the ompressive strength of onfined plain onrete ( f ) and its orresponding strain ( Cyli Hystereti Shemes ) an be obtained from: f ( f.9431) fo (6) 2 ( ) (7) f f o The hystereti branhes of the proposed yli model inlude nonlinear unloading/reloading, arbitrary yli loading and stiffness degradation resulting from yli loading. The shape of all possible yli branhes (omplete or partial) is predited by the transition urve proposed by Chang and Mander 14 : R f ( )[ fa a Ea A a ] (8) where R is the parameter governing the urvature of the hystereti branh and A is a internal parameter: Eb E se E se Ea fb fa R, A and E R se = E se Ea b a b (9) a where E se represents the seant modulus, E a and E b are the tangent Young s Modulus at the initial (A) and target (B) points (see Figure 11), and f a and f b are the ompression stresses at A and B points, respetively. The proposed ompressive yli mode, shown in Figure 11 with all the possible hystereti shemes, an be broadly ategorized as: omplete unloading (AB); partial unloading (AB ); omplete reloading (BCD) and; partial reloading (B C D ). Unloading from point A ( un, f un ) with reversal slope E un (= 2E, see Figure 11), will target point B ( pl, ) with target slope E pl, whose harateristi parameters an be determined as follows:

7 Seismi Strengthening of Conrete Buildings 91 E se = E f un.57 E o, E =.1 exp 2 un pl E un o.57 o fun and pl = un (1) E se The transition urve Eq. (8) is used to join the initial point A and the target point B. A reversal from any point in between A and B will initiate the starting of a reloading branh. The omplete reloading urve is desribed by three points (initial point B, intermediate point C and target point D), and two onneting transition urves. The first transition urve onnets point B ( pl, ) with starting slope E, to an intermediate point C ( un, f new ) with slope E new. Similarly, the seond transition urve onnets intermediate point C to the return point D ( re, f re ) with target slope E re. The parameters required for omplete reloading are derived from the following Eqs. (see Figure 11): f f f (11) E E new un new fnew un pl (12) re un (13) E and fre f re re re (14) un f.9 fun and.1992 un (15) o For reloading followed by partial unloading, a modified returning point is defined, whih is alulated from the modified form of Eqs. (11-15), as desribed elsewhere 14. Numerial Simulation A fibrous model with yli onstitutive laws for CFRP-onfined onrete and steel bars was implemented into FEMIX omputer program, whih is based on the finite element method (FEM). This model is apable of analysing the nonlinear yli behaviour of three-dimensional RC frames, sine the beams and olumns are simulated by 3D Timoshenko finite elements. Eah element is disretized in fibres along its longitudinal diretion. Model Appraisal To verify the apabilities of the proposed model on the simulation of CFRP-onfined RC olumns submitted to yli ompressive loading, the arried out tests are simulated, and the experimental and numerial axial stressstrain urves are ompared. The values of the model parameters used on the numerial simulations are the following ones: E = 3 GPa ( ksi), f o = 3.2MPa (4.39 ksi) and o =.4 (mm/mm). All the simulated olumns were disretized in three isoparametri Timoshenko finite elements of three nodes eah. An integration sheme of two Gauss integration points per finite element was adopted for the evaluation of both the stiffness matrix and internal fores. Every ross setion was disretized in forty-eight quadrilateral elements of eight nodes for the onfined onrete, and four quadrilateral elements of four nodes to simulate the steel bars, using an integration sheme based on 2 2 Gauss integration points. Figures 12a- show that the proposed model simulates with satisfatory auray the experimental urves. In spite of prediting the envelope urve with high auray the analysis tends to predit a slightly less stiffness and underestimates the energy dissipation apaity of the struture due to the assumption of perfet bond between onrete and steel bars.

8 92 Barros et al. CONCLUSIONS The present work ompares the effiay provided by ontinuous and disrete onfinement arrangements for reinfored onrete (RC) olumn elements subjeted to monotoni and yli ompressive loading. URC Taking the ompressive strength obtained in the unonfined reinforement onrete (URC) speimens ( f ) for basis of omparison, a signifiant inrease in the speimen load arrying apaity was provided by the adopted CRC URC onfinement systems provided, sine f f varied between 1.5 for f =.31 up to 2.7 for f =.68, where f is the ompressive strength of the orresponding onfined speimen. CRC CRC URC The ratio inreased with f, having varied from 7 up to 1, where unonfined reinfored onrete speimen and onfined speimen, respetively. URC and CRC are the strains of Comparing the results obtained in speimens of equal f it was verified that the load arrying apaity of partially onfined speimens (W6L5) was a little bit lower than that of the fully onfined speimens (W6L3). However, it should be kept in mind that partial onfinement arrangements were easier and faster to apply than full onfinement arrangements. The obtained stress-strain urves indiate that the urve orresponding to the monotoni test an be onsidered as the envelope of the urve of the yli test. Regarding the variation of the stiffness of the unloading and reloading branhes of the load yles, it was notied that the stiffness of the unloading branhes was higher than the stiffness of the reloading branhes. In the onseutive yles of a series of yles with the same load amplitude, the stiffness of unloading branhes dereased, while the stiffness of the reloading branhes presented a tendeny to inrease. Finally, a tendeny was observed for a derease in the stiffness of both the unloading and reloading branhes in suessive series of load yles. The data obtained from the experimental program was used to appraise a model proposed to simulate the yli behavior of CFRP-onfined RC olumns. The model simulated with high auray the arried out tests. ACKNOWLEDGEMENTS The authors of the present work wish to aknowledge the materials supplied by S&P Clever Reinforement and MBT Bettor Portugal. The seond author would like to thank the finanial support by PRODEP ation 5.3/N/199.14/1. The third author aknowledges the grant obtained in the ambit of the researh projet CUTINSHEAR - Performane assessment of an innovative strutural FRP strengthening tehnique using an integrated system based on optial fibre sensors, Referene: POCI/ECM/57518/4. REFERENCES 1. Seible, F.; Priestley, M. J. N.; Hegemier, G. A., and Innamorato, D., Seismi retrofit of RC olumns with ontinuous arbon fiber jakets, ASCE, Journal of Composites for Constrution, Vol. 1, No. 2, pp , Mirmiran A., and Shahawy M., Behaviour of onrete olumns onfined by fiber omposites, ASCE Journal of strutural Engineering, Vol 123, nº5, pp , Saadatmaneh, H.; Ehsani, M.R, and Jin, L., Repair of earthquake-damage RC olumns with FRP wraps, ACI Strutural Journal, Vol. 94, No. 2,, pp , Marh-April Pantelides, P. C.; Gergely, J., Carbon fiber reinfored polymer seismi retrofit of RC bridge bent: design and in situ validation, ASCE Journal of omposites for onstrution, Vol. 6, No. 1, pp. 52-6, February Barros, J.A.O., and Ferreira, D.R.S.M. (8), Assessing the effiieny of CFRP disrete onfinement systems for onrete olumn elements, ASCE Journal of Composites for Constrution, Vol. 12, No. 2, pp

9 Seismi Strengthening of Conrete Buildings Ferreira, D.R.S.M., and Barros, J.A.O., Confinement effiay of partially and fully wrapped CFRP systems in RC olumn prototypes, 2nd International fib Congress, Naples, June 5-8, Artile 1- in CD, Ferreira, D.R.S.M., and Barros, J.A.O., Disrete and full onfinement of onrete elements with CFRP sheets, Tehnial Report, 4-DEC/E-29 Dep. Civil Eng. University of Minho, 165 p, 4. (in Portuguese). 8. ISO TC 71/SC 6 N, Non-onventional reinforement of onrete-test methods- Part 2: Fiber reinfored polymer (FRP) sheets, International Organization for Standardization (ISO), Geneva, Switzerland, NP-EN 1 2-1, Metalli materials - Tensile testing. Part 1: Method of test (at ambient temperature), European Standard, CEN, Brussels, Belgium, pp. 35, NP-EN , Testing hardened onrete - Part 3: Compressive strength of test speimens, European Standard, CEN, Brussels, Belgium, pp. 1, Rodrigues C.C., and Silva, G.M., Behaviour of GFRP reinfored onrete olumns under monotoni and yli axial ompression, Int. Conf. Composites in Constrution, Balkema, Porto, pp , Otober Triantafillou, T.C, Seismi retrofitting of strutures with fibre-reinfored polymers, Prog. Strut. Engng Mater., vol.3, 57-65, Lam, L., and Teng, J.G., Design-oriented stress-strain model for FRP-onfined onrete, J. Constrution and Building Materials, Elsevier, vol. 17, , Chang, G.A., Mander, J.B., Seismi energy based fatigue damage analysis of bridge olumns: Part I-Evaluation of seismi apaity, Teh. Report NCEER-94-6, NOTATION CFRP = arbon fiber reinfored polymers = onfined plain onrete CRC = onfined reinfored onrete D = diameter of the olumn ross setion E s = elastiity modulus of the steel bars E = initial Young modulus of onrete E new = tangent modulus at the new stress point E pl = tangent modulus when the stress is released E re = tangent modulus at the returning point ( re, f re ) E t = tangent modulus for onrete on ompression envelope f = onrete ompressive stress f = ompressive strength of onfined onrete f o = ompressive strength of UPC f new = new value of stress orresponding to the unloading strain ( un ) f re = stress on returning strain ( re ) f un = stress on FRP onfined onrete envelope at unloading strain( un ) CRC f = ompressive strength of onfined onrete speimen f = ompressive strength of onfined plain onrete f = ompressive strength of unonfined reinfored onrete URC H = height of the speimen L k = number of CFRP layers per eah strip S j = number of strips along the speimen

10 94 Barros et al. SG = Strain gage t f = thikness of the wet lay-up CFRP sheet UPC = unonfined plain onrete URC = unonfined reinfored onrete W i = strip width = onrete axial ompressive strain at f CRC axial strain at ompressive strength of onfined reinfored onrete ( f ) CRC axial strain at ompressive strength of onfined plain onrete ( f ) URC = axial strain at ompressive strength of unonfined reinfored onrete ( f ) URC o = axial strain at ompressive strength of unonfined plain onrete (f o ) pl = onrete plasti strain re = strain on the FRP onfined onrete envelope orresponding to the return point un = strain on FRP onfined onrete envelope at unloading (reversal) point fm = Average tensile strain in the CFRP fiber s diretion fmax = maximum tensile strain in the CFRP fiber s diretion su = Steel ultimate strain f = CFRP volumetri ratio sy = Steel yield stress su = Steel tensile strength

11 Seismi Strengthening of Conrete Buildings 95 Table 1 - Experimental program Speimen designation (WiLk_/m) W45L3_ W45L3_m W45L5_ W45L5_m W6L3_ W6L3_m Loading type yli monotoni yli monotoni yli monotoni W [mm] s [mm] L mm Confinement arrangement mm SG1 s' SG2 SG3 w SG4 Ø6//96 CFRP W6L5_ yli 6 4 SG5 W6L5_m monotoni 5 SG6 4Ø8 mm W6L3_ yli SG1 SG2 6-3 SG3 SG4 6 mm W6L3_m monotoni SG5 SG6 Note: 1 mm =.394 in.

12 96 Barros et al. Table 2 - Main indiators of the effetiveness of the onfinement systems Speimen designation f [%] f (MPa) f f Conf URC Conf URC SG1 SG2 SG3 SG4 SG5 SG6 UPC_ UPC_m URC_ URC_m W45L3_ W45L3_m W45L5_ W45L5_m W6L3_ W6L3_m W6L5_ W6L5_m W6L3_ W6L3_m Note: 1 MPa = psi. fmax a) b) ) Figure 1- Confinement arrangements: a) strips of 45 mm width; b) strips of 6 mm width; ) full wrapping (1 mm =.394 in.).

13 Seismi Strengthening of Conrete Buildings 97 LVDT Ø Ø46 Ø2 LVDT Steel Load plate LVDT LVDT LVDT Conrete speimen LVDT Speimen Steel Load plate Teflón Figure 2 - Position of the LVDTs.. Load [kn] displaement ontrol 3 Figure 3 - Cyli loading onfiguration (1N =.2248 lb.). time

14 98 Barros et al. W45L3_ W45L3_m W45L3_m W45L3_ Stress (MPa) W45L5_m W45L5_ W45L5_m W45L5_ Stress (MPa) Axial Strain (mm/mm) Strain in CFRP (mm/mm) Axial Strain (mm/mm) Strain in CFRP (mm/mm) 8 7 W6L5_m W6L5_m 7 W6L3_m W6L3_ W6L3_m W6L3_ Stress (MPa) W6L5_ W6L5_ Stress (MPa) Axial Strain(mm/mm) Strain in CFRP (mm/mm) Axial Strain (mm/mm) Strain in CFRP (mm/mm) W6L3_ W6L3_m W6L3_m W6L3_ Stress (MPa) Axial Strain (mm/mm) Strain in CFRP (mm/mm) Figure 4: Relationship between onrete stress and both the axial strain and the CFRP strain for the monotoni and yli tests (1 MPa = psi). 1

15 Seismi Strengthening of Conrete Buildings u r Stress (MPa) Axial Strain (mm/mm) Figure 5: Proedure to evaluate the stiffness for unloading and reloading phases (1 MPa = psi ; 1 mm =.394 in.).

16 1 Barros et al Axial Strain (mm/mm) Stiffness (GPa) st Unloading (1 nd Unloading (2 st Reloading (1 nd Reloading ( Axial Strain (mm/mm) Stiffness (GPa) st Unloading (1 Unloading (2 nd st Reloading (1 nd Reloading ( Axial Strain (mm/mm) a) W45L3 b) W45L Stiffness (GPa) st Unloading (1 nd Unloading (2 Unloading (3 rd st Reloading (1 Reloading (2 nd Reloading (3 rd Axial Strain(mm/mm) ) W6L3 d) W6L Axial Strain (mm/mm) e) W6L3 Figure 6: Variation of the stiffness of the unloading and reloading branhes in the yli tests (1 MPa = psi ; 1 mm =.394 in.) Stiffness (GPa) Unloading (1 st Unloading (2 nd rd Unloading (3 th Unloading (4 th Unloading (5 st Reloading (1 nd Reloading (2 rd Reloading (3 th Reloading (4 th Reloading ( Stiffness (GPa) st Unloading (1 Unloading (2 nd rd Unloading (3 th Unloading (4 st Reloading (1 Reloading (2 nd rd Reloading (3 th Reloading (4

17 Seismi Strengthening of Conrete Buildings 11 W6L3_ W6L3_m W6L3_SG2_ W6L5_SG2_m 8 7 W6L5_m W6L5_ W6L3_SG2_m W6L5_SG2_ Stress (MPa) Axial Strain (mm/mm) Strain in CFRP (mm/mm) Figure 7: Relationship between the onrete stress and both the onrete axial strain and the CFRP strain in series with equal f : W6L5 and W6L3 (1MPa = psi ; 1 mm =.394 in.). W6L5_ W6L5_m W6L3_ W6L3_m Figure 8: Failure modes of speimens with equal f.

18 12 Barros et al. SG1 Y 1 SG2 SG3 SG yli test monotoni test SG5 5 5 SG f a) W6L5 Y SG1 1 SG2 SG3 SG yli test monotoni test SG5 5 SG f b) W6L3 Figure 9: Tensile strains in the CFRP for speimens: a) W6L5; b) W6L3. 8 W6L5_m W6L5_ Average Strain in CFRP (mm/mm) Stress (MPa) W6L3_m W6L3_ Average Strain in CFRP (mm/mm) a) W6L5 b) W6L3 Figure 1: Relation between stress,, and axial average strain in CFRP,, under monotoni and yli tests, for speimen: a) W6L5; b) W6L3 (1 MPa = psi ; 1 mm =.394 in.).

19 Seismi Strengthening of Conrete Buildings 13 Compression f A D f f o UPC f C C' 2E D' FRP onfined onrete B' O E o B t Epl Not to sale Figure 11: Shemati representation of the FRP-onfined onrete onstitutive model.

20 14 Barros et al. 6 5 Experimental Simulation Axial stress (MPa) Axial strain (mm/mm) 6 5 Experimental Simulation a) Axial stress (MPa) Axial strain (mm/mm) Experimental Simulation b) Axial stress (MPa) Axial strain (mm/mm) ) Figure 12: Numerial simulation of: a) W45L3_, b) W45L5_, and ) W6L5_ (1 MPa = psi.; 1 mm =.394 in.).