Analysis and design of FRP composites for seismic retrofit of infill walls in reinforced concrete frames

Composites: Part B 38 (2007) 575–583 www.elsevier.com/locate/compositesb

Analysis and design of FRP composites for seismic retrofit of infill walls in reinforced concrete frames Baris Binici a

a,*

, Guney Ozcebe

a,1

, Ramazan Ozcelik

b,2

Middle East Technical University, Inonu Bulvari, Department of Civil Engineering, 06531 Ankara, Turkey b Akdeniz University, Department of Civil Engineering, 07058 Antalya, Turkey Received 20 May 2006; accepted 1 August 2006 Available online 21 December 2006

Abstract There is an urgent need to retrofit deficient mid-rise reinforced concrete (RC) frame buildings in Turkey. For this purpose, an efficient FRP retrofit scheme has been developed previously, in which hollow clay brick infill walls can be utilized as lateral load resisting elements after retrofitting. The main premise of this practical retrofit scheme was to limit inter-storey deformations by FRP strengthened infill walls that are integrated to the boundary frame members by means of FRP anchors. Based on the analytical model that was previously verified extensively by comparison with test results, a simplified model was proposed for use in displacement based design of FRPs for deficient RC frame buildings. FRP retrofit design and analysis of an actual deficient RC building located in Istanbul are presented herein both for the local design spectrum and Duzce ground motion. It was observed that the FRP retrofit reduced the damage induced to deficient columns by controlling story deformations. In this way, it was possible to satisfy the collapse prevention performance state in an efficient and economical manner.  2006 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibre; B. Stress transfer; C. Computational modeling; Retrofit

1. Introduction The vulnerability of existing structures in Turkey to large seismic demands became apparent in recent earthquakes (Kocaeli 1999, Duzce 1999, Bingo¨l, 2003). Most of the vulnerable structures in Turkey were either not designed for prescribed earthquake forces or else they lack the necessary detailing [1,2]. This calls for the establishment of reliable strengthening methodologies so that the expected loss in future earthquakes can be minimized. With the objective of unifying the evaluation and rehabilitation procedures and guiding engineers in determining vulnerable members or parts of a structural system, a new section *

Corresponding author. Tel.: +90 312 210 2457; fax: +90 312 210 7991. E-mail addresses: [email protected] (B. Binici), [email protected] (G. Ozcebe), [email protected] (R. Ozcelik). 1 Tel.: +90 312 210 2461; fax: +90 312 210 2451. 2 Currently graduate student at Middle East Technical University. 1359-8368/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2006.08.007

on seismic evaluation and rehabilitation has been added to the recent draft version of the Turkish Earthquake Code (TEC) [3]. Different rehabilitation methods (i.e. use of FRPs, addition of shear walls or precast panels) were examined at Middle East Technical University [4–7] in the last two decades in order to place a number of alternatives at the service of practicing engineers. Among available seismic retrofit schemes, adding shear walls is the most commonly chosen alternative for current applications in Turkey. However, the construction work involved for this scheme is tremendously demanding. Furthermore, it results in lengthened retrofit time and necessitates relocating the occupants of the building involved. In order to overcome these shortcomings, alternative retrofit schemes are needed to enhance the in-plane load carrying capacity of an immense number of deficient reinforced concrete frames. Fiber reinforced polymers have been used in strengthening infill and masonry walls in a number of studies [8–10]. Both

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in plane and out-of-plane behavior of strengthened walls have been investigated in these studies. The post earthquake reconnaissance surveys [1] showed that a typical feature of most of the deficient RC building frames in Turkey is the large extent of infill walls in residential construction. In most cases, these walls are susceptible to out of plane failure and not considered in the design. However, the examination of a number of buildings revealed that presence of infill walls can be beneficial and they enable the building to avoid collapse by limiting inter-storey deformations and providing additional base shear capacity to the existing structural system having lack of lateral resistance. In order to rely on these infill walls in avoiding collapse during an earthquake, they need to be strengthened so that they contribute to lateral load-carrying capacity. Recently, a novel technique that makes use of fiber reinforced polymers (FRPs) in the upgrading of reinforced concrete frames with infill walls was developed as a part of an extensive research project [11] jointly sponsored by the NATO Science for Peace Division and the Turkish Scientific and Technological Research Council. The method was based on the premise of limiting inter-story deformations and increasing the base shear capacity of the existing weak frame using FRPs bonded on infill walls that are integrated to the boundary frame members with FRP anchors. Quasi-static cyclic tests were performed on multi-bay multi story structures in order to experimentally validate the effectiveness of the FRP strengthening system [11–15]. The proposed method was found to be appealing due to its speed and ease of application with little or no disturbance to the occupants. Subsequently, an analytical model that is capable of estimating the nonlinear static response of the FRP strengthened infill wall was proposed [16]. The detailed explanation and extensive experimental verification of this analytical model has been provided elsewhere [12,16], hence only a brief discussion of the original model will be presented in the next section. The main objective of this paper is to propose a simplified design oriented version of the original analytical model that can be used in the performance based retrofit design of RC frames with hollow clay tile infill walls strengthened with FRPs and to present a case study for the performance of an actual building with and without FRP retrofit. First, a brief summary of the previously developed analytical model based on experimental findings is presented. Second, a simplified model to use in displacement based nonlinear evaluation procedures is proposed and an example retrofit design is presented for an actual building frame both for the design spectrum and Duzce ground motion. The results presented herein should enable structural engineers to assess the feasibility of the retrofit procedure, as also the design and detail of FRPs for building retrofit. 2. FRP retrofit scheme and analytical model For a reinforced concrete frame with masonry infill walls that is subjected to lateral deformations, the infill wall

acts as a diagonal strut, while the separation of the infill occurs on the opposite side. The idea of the FRP retrofit scheme is to reduce inter-story deformation demands by using FRPs to act as tension ties similar to a steel crossbrace configuration. In order to achieve this, diagonal FRPs bonded on the infill wall are tied to the framing members using FRP anchors as shown in Fig. 1. The tension tie formed in this way provides additional contributions to the load carrying capacity and the lateral stiffness of the existing RC frame structure, in addition to the strength and stiffness provided by the compression strut formed along the infill diagonal. Special embedded fan type FRP anchors formed by rolling FRP sheets are connected in the corner region in order to achieve efficient use of FRP materials (Fig. 1). To eliminate premature debonding of FRP from the plaster surface anchor dowels are used along the thickness of the infill wall (Fig. 1). In a previous study, the infill wall strengthened using FRPs was proposed to be modeled using a compression strut and a tension tie (Fig. 2), which adequately represents the load transfer mechanism observed from the experiments and finite element analysis [16]. A trilinear stress– strain response was employed for the truss members to simulate the behavior of the strengthened infill wall (Fig. 2). The presence of plaster on the infill wall surfaces was taken into account for accurate estimation of stiffness and strength. It was assumed that FRP, infill material and plaster on the infill wall surface could contribute to the stiffness of the tension tie. The cracking stress of the tie, fcrt, was defined as V crt wf ðtf þ tp þ tin Þ   Ef ¼ fpt wf ðtin þ tp Þ þ tf Em

fcrt ¼

ð1Þ

V crt

ð2Þ

In Eq. (1), wf and tf are the width and thickness of the FRP, respectively, and tin and tp are the thickness of the brick infill and plaster, respectively. In Eq. (2), fpt is the tensile strength of the plaster; Ef and Em are the moduli of elasticity of FRP and mortar. The cracking strain (Fig. 2), ecrt, is the cracking strain of the plaster which can be determined from uniaxial tension tests. Beyond cracking, the contribution of mortar and plaster to load carrying capacity gradually decreases (Fig. 2). The tensile strength, fut, can be computed from Eq. (3) based on the capacity of the FRP at the effective strain obtained from experimental results, ef,eff (taken as 0.004 for debonding failures as shown in Fig. 2), at which failure initiates fut ¼ ef;eff ðtf ÞðEf =ttie Þ

ð3Þ

where in Eq. (3), ttie is equal to the sum of tf, tin, and tp. The strain at which complete failure of FRP occurs (etu) was defined as three times the effective strain (ef,eff). The strut stress–strain model is also a trilinear model with a perfectly plastic plateau and limited deformation

B. Binici et al. / Composites: Part B 38 (2007) 575–583

577

FRPtie tie FRP

Stress

Stress

Fig. 1. FRP strengthening method for reinforced concrete frames with infill walls.

Model [16]

f ut

Simplified model

Infill Infillstrut stru str utt

fus Plastic hinge Plastic with hing hingeefiber elements element with fiber discretization discretization

0.003 E f f crt

Esm elastic fram e frame Elastic frame elements elements

Immediate Life Safety Collapse Prevention Occupancy

ε crs

ε so

ε fs

Ef

ε crt

Strain

0 .4

0 .6

ε tu

Strain (%)

Fig. 2. Structural model and stress–strain response of compression struts and tension ties: (a) structural model, (b) infill compression strut model and (c) FRP tension tie model.

capacity. The ultimate strength, fus, of the strut can be computed by minðfmv L; 250f mc Þ ws ð1  aÞah ws ¼ cos h

fus ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðM pj þ 0:2M pc Þ a¼ h2 tst fmc

ð6Þ

ð4Þ ð5Þ

In Eq. (4), fmv is the shear strength of mortar (or plaster) bed joint, fmc is the uniaxial compressive strength of plaster (in MPa), and L is the width of the infill wall. It should be noted that Eq. (4) defines the failure of the compression state as the smallest of the two capacities based on sliding shear and corner crushing, respectively. In Eq. (5), h is the height of the infill wall, h is the strut inclination angle and a is a dimensionless parameter to account for the frame infill contact length computed by

in which tst is equal to the sum of tin and tp, Mpj is the minimum of the moment capacities of the column or the beam, Mpc is the moment capacity of the column and fmc is the compressive strength of the infill plaster composite. As shown in Fig. 2, the slope of the stress–strain curve (Esm), can be obtained from uniaxial compression tests of plastered infill walls. Finally, the following relationship was proposed for the deformation capacity of the strut  eso ¼

ecrs 2ef;eff

without FRP with FRP

ð7Þ

B. Binici et al. / Composites: Part B 38 (2007) 575–583

δ

L

2 f

ε f,ef

δ

θ

θ= cos h

θ s in / h

Drift Ratio (%)

578

1.5

0.006

1

0.005 0.004

0.5

0.003 0.002

0 30

45

θ (degrees)

60

Fig. 3. Deformations of the wall and maximum allowable drift deformations: (a) infill wall deformations in pure shear and (b) allowable drift ratios for different FRP critical strains and wall angles.

The failure strain of the compression strut, (efs), was taken as 0.01 for the infill walls without any strengthening and it was assumed as 0.02 when failure of the FRP tie occurs. The analytical model summarized above was verified extensively by comparing its estimations with the experimental results obtained from two-story one- to three-bay structures [16]. Hence, experimental validation of the above proposed model is not repeated herein, however, the practical implications of the model, recommended simplifications for design and applications for a case study building are presented below. 3. Allowable drift deformations In order to establish a practical limit on wall deformations, the behavior of a single retrofitted wall was examined assuming that the induced deformations to be in the form of pure shear (Fig. 3). Subsequently, the interstory drift ratio can be related to the effective strain of FRP corresponding to ultimate limit state in the following form: DR ¼

d ef;eff ¼  2ef;eff h cos h sin h

ð8Þ

where DR is the interstory drift ratio and ef,eff is the effective strain at which FRP becomes inactive due to either of the failure modes discussed above. The relationship given in Eq. (8) is plotted for different values of effective FRP strain in Fig. 3. It can be observed that aspect ratio of the infill wall (i.e. angle h) does not significantly influence the allowable drift ratio. Hence the critical drift deformation can safely be taken as twice the effective FRP strain. In addition, assuming an FRP strain of about 0.004 for the onset of FRP debonding, a drift ratio of 0.8% can be accepted safely as the drift deformation limit beyond which significant damage will be induced in the FRP strengthened wall. This drift limit can be instructive to the design engineer with regards to the order of magnitude of expected deformation levels. 4. Simplified analysis and design recommendations Defining a softening region in the force-deformation response of ties or struts presents a difficulty in the numer-

ical solution of the nonlinear procedures and requires the implementation of special algorithms to accommodate for the negative tangent stiffness. In addition, most of the commercially available software [20] cannot generally accommodate a softening region in the definition of plastic hinge or link elements. Furthermore, it is more practical to assume elasto-plastic relationships for the inelastic elements as suggested by FEMA 356 [17] and TEC [3] guidelines. In this way, consistency with the aforementioned guidelines can be established. For these purposes, further simplifications are introduced herein for the FRP ties and infill strut elements as shown in Fig. 2. According to the simplified model, the initial stiffness of the FRP ties are taken equal to the stiffness of the FRP sheets neglecting the presence of hollow clay tile and plaster prior to cracking. At a tensile strength corresponding to an FRP strain of 0.003, plastic flow is assumed to take place up to a strain level of 0.006 at which complete strength deterioration occurs. The relevant performance points are defined as shown in Fig. 2 for the FRP ties. For the infill strut, complete strength degradation is assumed to take place at a strain of 0.012 (i.e. twice the strain at FRP tie failure) consistent with Eq. (7). With these simplifications, additional conservatism is introduced in the model while preserving the accuracy of the original model. Based on the extensive testing of the developed FRP retrofit scheme a number of detailing rules should be provided. It has been found that in order to reduce stress concentrations and provide a uniform stress transfer from the diagonal FRP sheet to the frame connection locations, it is beneficial to use square flag FRP sheets with a width not smaller than 1.5 times FRP diagonal sheet width. In this way, it is possible to use a number of FRP anchors and distribute the forces transferred from the diagonal sheet to the boundary frame. The test results revealed that FRP application should be performed on both sides of the infill wall and FRP dowels (rolled from at least 100 mm wide FRP sheets) should be placed at a spacing preferably less than or equal to 600 mm [16]. In order to investigate the pull-out strength of FRPs, Ozdemir and Akyuz [18] conducted a detailed experimental program consisting of 120 pull-out tests on concrete specimens having a concrete compressive strength of 10 to

Relative Ultimate Strength (Pu/Pfrp)

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onal FRP sheet can be transferred uniformly to the framing elements. The anchor capacity can be computed as the smallest of 20 kN (as the upper limit obtained from experiments corresponding to cone failure in the range of FRP sheet widths, 100–200 mm) and 30% of the tensile strength of an FRP sheet formed into an FRP anchor. In this way, it is possible to ensure that FRP anchor failure can be eliminated prior to FRP debonding failure at a strain of about 0.004 followed by wall sliding failure.

0.6

0.4

0.2

40

60

80 100 120 Embedment depth (mm)

140

160

Fig. 4. FRP anchor pull-out strength [18].

30 MPa. It was found that depending on the embedment depth, different failure modes, concrete cone failure for shallow anchors (depth less than 100 mm) and FRP anchor rupture for deep anchors (depth greater than 100 mm), have been observed. Fig. 4 summarizes the normalized anchor capacities as a function of embedment depth for a concrete uniaxial compressive strength of 15 MPa. The results show that beyond an embedment depth of about 100 mm the tensile strength of the anchor stabilizes safely at about 40% of the ultimate strength of the FRP, regardless the diameter of anchors. Hence it is recommended herein to use an embedment depth of at least 150 mm and utilize four FRP anchors so that the force in the diag-

5. Displacement based FRP retrofit design example In this section, the performance based design of a retrofit scheme for an existing building located in the Zeytinburnu district of Istanbul is presented. The building under consideration is a reinforced concrete frame structure with one basement, three floors and a penthouse (Figs. 5 and 6). It is important to mention here that Zeytinburnu is established in the highest seismic hazard zone of Istanbul. Moreover, the seismic risk of the built environment is also very high. The loss estimation studies carried out jointly by the Istanbul Metropolitan Municipality and the Japan International Cooperation Agency – JICA [19] indicated that in a future severe earthquake 16.6% of the 15,500 buildings are estimated to experience heavy damage or collapse and consequently 1.9% of a population of 240,000 would be lost. Within this study, a performance evaluation method based on nonlinear pushover analysis

Fig. 5. Floor plan of the case study building located in Istanbul.

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Fig. 6. Elevation view and computational model of the building: (a) computational model and (b) elevation view.

is carried out using structural data obtained from site measurements of an existing residential building. Following the assessment procedure, the strengthening of the building based on the methodology described in this paper is performed. In order to obtain the performance point, Turkish Earthquake Code Draft-2006 (TEC) [3] and the Duzce ground motion (DGM) are employed. The peak ground acceleration, velocity and displacement of the DGM were 375.54 cm/s2, 47.62 cm/s and 108.57 cm, respectively. Mechanical properties of concrete and steel were determined by a local construction company obtained from at

Normalized Base Shear

0.30

0.20

Strengthened with FRP Deficient building DGM Performance Point TEC [3] Performance Point

least five cores and a sufficient number of steel coupon samples per floor. Accordingly, for concrete, a uniaxial compressive strength of 9 MPa and a modulus of elasticity of 23,750 MPa were obtained whereas the yield strength of reinforcing steel was found as 220 MPa. The dimensions of the building in the x and y direction are 9.9 and 10.1 m, respectively. The building consists of 150 · 500 mm beams and 250 · 400, 270 · 750, 250 · 600, 350 · 400 mm columns. The orientation and also size of the beams and columns are shown in Fig. 5. The stirrup spacing is 260 mm for all beams and 280 mm for all columns with a clear cover of 25 mm. It is important to note that the stirrup spacing of columns and beams does not satisfy the provisions of the current TEC [3]. Moreover, the in situ concrete strength is lower than the code specified minimum. 1.4 TEC

0.10

Strengthened with FRP X dir.

1.2

Strengthened with FRP Y dir.

0.00 0.000

Deficient building X dir.

0.005

0.010

1.0

0.015

Deficient building Y dir.

Overall Drift Ratio

DGM (%5 damping)

S a (g)

Normalized Base Shear

0.30 Strengthened with FRP Deficient building DGM Performance Point TEC [3] Performance Point

0.20

0.8

0.6

0.4

0.10

0.2 0.00 0.000

0.005

0.010

0.015

Overall Drift Ratio Fig. 7. Normalized pushover capacity curves and performance points of the building in x and y directions: (a) x direction and (b) y direction.

0.0 0.00

0.10

0.20 S d (m)

0.30

0.40

Fig. 8. Summary of the performance based evaluation procedure.

B. Binici et al. / Composites: Part B 38 (2007) 575–583

Nonlinear static pushover analyses were performed in order to estimate displacement capacity of the building for the required evaluation techniques. The 3D computer model of the building was generated using SAP2000 [20] from the original drawings of the building (Fig. 6). All the joints on each floor were constrained in order to model the diaphragm effect. Moment–rotation properties derived from sectional analyses with the plastic hinge length (taken equal to half the member depth in the direction of loading as suggested by TEC [3]) idealization were assigned to the beam and column ends. Axial force–moment yield surfaces obtained from interaction diagrams were used for column plastic hinge regions. Triangular load distributions were used for pushover analysis for x and y directions separately. Prior to conducting the pushover analyses, gravity loads and 30% of the live load on the structure were applied. The displacement-controlled pushover analysis was then conducted to obtain performance point of the

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building and plastic deformations (rotations) of the members. Results of pushover capacity curves are presented in Fig. 7 for x and y directions separately. After performing the pushover analysis and obtaining the capacity curve, the performance points of the building in x and y directions were calculated using two different methods as SDOF approach employing the DGM and TEC [3]. Pushover curves were converted into the acceleration displacement response spectrum (ADRS) representation of demand, Fig. 8, by using Eq. (9) Sa ¼

Vb a1 W

Sd ¼

and

Dr C1 /r;1

ð9Þ

where W is the total weight of the MDOF structure, Vb is the base shear, Dr is the roof displacement of the MDOF structure, a1 is the modal mass coefficient for the first mode (first fundamental mode), and C1 is the modal participation factor for the first fundamental mode. /r,1 is the amplitude

120

120

Deficient Building

Deficient Building 101

Strengthened with FRP

100

Strengthened with FRP

100

92

Number of Member

Number of Member

87 80

60

40

80

73

60

40 29

20

20

15 10

1 0

IO

0

LS

IO

Performance Level

LS

Performance Level

60

60

Deficient Building Strengthened with FRP

50

40

30 23 20

20

Strengthened with FRP

50

46

Number of Member

Number of Member

Deficient Building

40 34

30

19 20

16

14

14 8

10

9 9

10

10 4

11

2

1 0

0 IO

LS

CP

Performance Level

Total Collapse

IO

LS

CP

Performance Level

Total Collapse

Fig. 9. Performance states of beams and columns of the examined building for DGM in x and y directions: (a) damage state of beams for analysis in x direction, (b) damage state of beams for analysis in y direction, (c) damage state of columns for analysis in x direction and (d) damage state of columns for analysis in y direction.

B. Binici et al. / Composites: Part B 38 (2007) 575–583

of the first fundamental mode at the roof, Sa is spectral acceleration, and Sd is the spectral displacement. For the SDOF approach, the elastic and post-yield stiffness of the building are evaluated from bilinear idealization of the load–deformation curve. The mass of the building is taken as the mass corresponding to the governing x and y modes and 5% critical damping is assumed. Using the bilinear idealization with elastic unloading a SDOF analysis is conducted using the DGM to obtain the top displacement (performance point). The displacement value obtained from SDOF analysis is converted to the roof displacement and plotted on the pushover curve (Fig. 7). The second method of evaluation according to the TEC [3] was performed using the response spectrum defined for Zone 1 with the soft soil type Z2 (Fig. 8). The response spectrum was then converted into ADRS format and plotted in the same figure with the capacity curve. According to TEC 2006, if the period is greater than the corner period, TB, which is approximately 0.40 s (this is valid for both cases of before and after retrofit since the fundamental period for the deficient and retrofitted structure are 0.77 and 0.56 s, respectively) then the equal displacement rule is employed, otherwise an equal energy approach is used. Hence, the inelastic displacement demand is estimated by S di1 ¼ C R1 S de1

ð10Þ

in which Sdi1 is the inelastic spectral displacement estimate for the fundamental mode and the spectral displacement ratio CR1, and spectral displacement, Sde1, are computed by 2

S de1 ¼ S ae1 =ð2p=T Þ ( 1 if T P T B C R1 ¼ ð1 þ ðRy  1ÞT B =T Þ=Ry

ð11Þ

otherwise

In order to avoid the collapse and decrease the member damage levels of the deficient building, the strengthening technique previously presented in this paper was applied. The locations of infill walls with FRP strengthening are shown in Fig. 5. A custom made CFRP sheet having a uniaxial strength of 3400 MPa with a modulus of elasticity of 230,000 MPa and a thickness of 0.16 mm was used in the design of the FRP diagonals. The values of FRP width and number of layers were obtained as a result of a trial and error procedure to satisfy the target performance level of collapse prevention. For all diagonal FRP anchor dowels, an FRP width of 200 mm was used to be inserted in a hole having a diameter of 15 mm. The depth of the anchors was designed as 150 mm in compliance with the previously suggested value [18]. The pushover curve of the retrofitted structure and the deformation demands imposed by TEC and DGM are shown in Fig. 7. It can be observed that as a result of the FRP retrofit, the strength of the structure increased about 100% and 150% in the x and y directions, respectively. In addition, the deformation demand at the roof level corresponds to about 0.7% overall drift. The beam and column performance states at the performance point are shown in Fig. 9 for the retrofitted structure. It can be seen that the number of columns in the total collapse state were reduced by a factor of two upon applying the proposed strengthening technique. This results in controlling the damage in columns by controlling the interstory deformations. The interstory drift profiles for x and y directions obtained from pushover analysis at performance points of DGM are shown in Fig. 10. It can be observed that highest interstory drift ratio, which was about 2% in the x direction, occurred in the second floor

ð12Þ

where Sae1 is the elastic spectral acceleration, T is the fundamental period, Ry is the strength reduction factor. For both cases, i.e. before and after retrofit, the modal mass participation of the mode corresponding to the pushover directions was found to be greater than 70%, hence the nonlinear-static procedure is applicable for the seismic evaluation and retrofit. The performance points according to TEC and DGM are shown on the pushover curves in Fig. 7. It can be observed that the building experiences an overall drift ratio of about 1.2% in the x direction prior to retrofit. In the x direction it was observed that the deformation demand imposed by DGM corresponds to the deformation capacity observed from the pushover curve. A member by member evaluation is then conducted to identify the damage level of the members, and the number of columns and beams at different performance levels are presented in Fig. 9. This evaluation indicated that about 75% and 55% of the columns were at the total collapse performance level for x and y directions, respectively. Due to weak columns and strong beams in the building the beam plastic hinges did not form at critical beam sections; hence beam plastic hinges were not fully exploited.

IO

LS

CP

Total Collapse

0 < DR ≤ 0.008

0.008 < DR ≤ 0.02

0.02 < DR ≤ 0.03

0.03 < DR

4

3

Number of Story

582

2

Strengthened with FRP in x- dir.

1

Strengthened with FRP in y-dir. Deficient Building, x-dir. Deficient Building, y-dir.

0 0

0.01

0.02 Drift Ratio

0.03

0.04

Fig. 10. Inter-story drift profiles of the building at the performance point for DGM.

B. Binici et al. / Composites: Part B 38 (2007) 575–583

level of the building without any retrofit. Upon retrofit the drift ratio reduced to about 0.8% and 0.9%, for the x and y directions, respectively. It should be noted that the observed drift ratio is in good agreement with those limits proposed in the previous section based on the simple shear deformation model. This result shows that the FRP retrofit scheme was successful in controlling drift deformations and reducing the demands in the columns. In short, it is possible to say that the FRP retrofit design presented above was found to be successful in preventing collapse of the building by reducing the deformation demands on the columns and controlling the drift deformations. In this way the collapse prevention limit state was satisfied for the building. 6. Conclusions A simplified structural model derived from a previously proposed analytical model has been presented to estimate the behavior of FRP strengthened reinforced concrete frames with infill walls. The performance of the FRP retrofit scheme was demonstrated by analyzing an actual deficient RC building with hollow clay tile infills. It was observed that prior to the FRP retrofit about 75% of the columns were in a total collapse limit state meaning that their deformation capacities were significantly exceeded. Upon FRP retrofit it was observed that drift control was provided and deformation demands on the structure were significantly reduced. In this way it was possible to satisfy the collapse prevention performance state. The proposed model for inelastic static analysis of FRP strengthened reinforced concrete frames can be used in the FRP retrofit design of deficient buildings with hollow clay tile infills. It should be mentioned that this method can be effective when the building is equipped with well distributed infill walls in plan with no prior damage. It is believed that the outcome of this research will help the structural engineers in making a decision on the retrofit scheme as the models developed have proven to provide reasonable estimates of strength and deformation capacities. The extension of the model to estimate cyclic behavior is the future focus of the studies for its use along with nonlinear dynamic analyses. Acknowledgements The study reported in this article was funded, in part, through the European Union project ‘‘LessLoss: A European Integrated Project on Risk Mitigation for Earthquakes and Landslides No. 505448’’ within the framework of the thematic sub-priority 1.1.6.3: Global Change and Ecosystems. We gratefully acknowledge this support. Any opinions and findings cited in this article do not necessarily reflect the position of the funding agency.

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