1 Introduction

Infill walls are usually considered non-structural elements, though they may increase the lateral strength, stiffness and energy dissipation capacity of a structure, as well as limiting drift and deformations. However, they may also cause soft story mechanisms, short columns and eccentricities in plan and elevation. Dolšek and Fajfar (2008) take a critical conclusion, stating that “infill walls can have a beneficial effect on the structural response, provided that they are placed regularly throughout the structure, and that they do not cause shear failures of columns.” Significant seismic performance enhancement can be observed in retrofitted infilled frames, in terms of inter-story drift, lateral load and stiffness capacities, energy dissipation capacity, equivalent damping and observed damages (Özkaynak et al. 2011, 2013).

Polyakov (1960) presented one of the pioneering studies on the seismic response of infilled panels surrounded by RC and steel frames. An equivalent diagonal strut was first proposed for modeling the infill panels. Holmes (1961) suggested that the equivalent strut should have a width equal to 1/3 of the length of the masonry panel. Smith and Carter (1969) related the width of the equivalent diagonal strut to the infill-to-frame-stiffness ratio. Žarnic and Gostic (1997) proposed an elastic, perfectly plastic equivalent strut model for infills, which is known as the “multi-strut model”. Chrysostomou et al. (1992) and Hashemi and Mosalam (2006), suggested simplified models based on the equivalent strut approach, which take account of the slip along the interface of the frame and masonry infill. The models use empirically determined correction factors to calculate effective strut dimensions. Dhanasekhar and Page (1986), Mosalam (1996) and Shing and Lotfi (1991) used FEM to predict the general behavior of infilled frames. Madan et al. (1997) proposed a method for computing the in-plane hysteretic force deformation behavior of the masonry infilled frame, based on a tie-and-strut approach, in which the infill is modeled as a combination of three non-parallel struts in each direction of loading. A smooth hysteretic model was developed that uses degrading control parameters for stiffness, strength and slip. Saneinejad (1990) developed an analytical model based on nonlinear FEA and experimental results, taking account of various lower-bound solutions. Saneinejad and Hobbs (1995) developed a method, based on the equivalent diagonal strut approach, for the analysis and design of infilled frames subjected to in-plane forces. This method takes into account the elastoplastic behavior of the infilled frame, considering the limited ductility of the infill wall. Infill aspect ratio, shear stress at the frame-infill interface, and beam and column strength are all accounted for in the method. Smyrou et al. (2011) performed a verification study using the fiber-based FE program and a double-strut nonlinear cyclic model for unreinforced masonry panels. The capability of the model for predicting the cyclic seismic response of the multi-story infilled RC frames was then verified through comparisons with experimental results. Erkoseoglu et al. (2014) proposed a piecewise linear capacity curve, including cracking, maximum and ultimate points based on the experimental data collected from the literature. The defined parameters were verified for unreinforced and confined masonry walls that reasonably matched with the experimental results. This analytical approach was used to conduct a parametric study for the comparison of the behavior of these two distinct types of masonry wall. The concept of simulating the infill with single or multiple diagonal struts under compression is widely accepted as a simple and rational way to describe the influence of the infills on the surrounding frame, and has been adopted in many documents and new guidelines, such as S304.1 (CSA 2004), SEI 41-06 (ASCE 2007), NZSEE (2006) and MSJC (2011).

Although several studies concerning the analytical modeling of masonry infill walls have been completed in the past, only a few of them have concentrated on retrofitted infills. The rationale of this paper is to propose a straightforward empirical model for bare and CFRP-based retrofitted infills made of perforated clay bricks, to be used especially in the performance evaluation of existing low-rise RC buildings in earthquake-prone areas. The scope of the study is based on the literature review and on-hand experimental consequences. Subsequent to the validation of the proposed empirical model with the results of two sovereign tests, the model is employed in the earthquake performance evaluation of an existing three-story RC building. The main objective of this paper is to generate a piecewise tri-linear capacity curve model to be used as an envelope for load-vs.-displacement hysteresis of perforated clay brick infills without CFRP retrofitting in RC frames.

2 Compilation of the existing data

An assessment of the existing literature demonstrates that there exists a significant number of experimental works which aim to determine the cyclic behavior of the infilled frames. The main characteristics of the specimens selected from the literature are brought together in Table 1. The literature review yields some significant data for the current study, in terms of the estimation of ultimate displacement and strength capacities, which are represented in columns 8 and 10 of Table 1, respectively. Based on the compiled data, the following conclusions could be drawn:

Table 1 Summary of the existing literature
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  1. 1.

    For bare infills, the average drift corresponding to the ultimate strength is in the range of 0.90–1.00 %.

  2. 2.

    For the retrofitted infills, the average drift corresponding to the ultimate strength is in the range of 0.70–1.15 %.

Various equations exist in the literature to determine the ultimate strength of infills. The equation proposed in FEMA-356 (2000) for bare infills, and the equation proposed by Triantafillou (1998) for CFRP-based retrofitted infills, are shown on Table 2, along with a definition of their variables.

Table 2 Shear strength of the infill and retrofitted infill wall
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The equation given in FEMA-356 (2000) to determine the ultimate loading capacity of bare infills is used here for its simplicity. The contribution of CFRP is added to the infill wall capacity. The shear capacity provided by CFRP can be determined from Eq. (1):

$${\text{V}} =\upvarepsilon{\text{Ewt}}$$
(1)

where V is the ultimate shear capacity provided by the CFRP sheet, ε is the ultimate strain, E is the modulus of elasticity of CFRP, and w and t are the width and thickness of CFRP, respectively.

3 The experimental background

A group of 1/3-scale specimens, consisting of infilled and CFRP-retrofitted infilled RC frames, were tested in the Structural and Earthquake Engineering Laboratory at Istanbul Technical University. Two discrete types of retrofitting—namely cross bracing and diamond cross bracing—were studied, experimentally. The details of the study can be found elsewhere (Yüksel et al. 2009; Özkaynak et al. 2011). The dimensions, reinforcing details and pictures of the tested specimens are presented in Fig. 1. The average compression strength of concrete obtained from the standard cylinder tests was 19 MPa. The yield strength of the reinforcing bars was 420 and 500 MPa for 8 and 6 mm diameters, respectively. Clay hollow bricks with dimensions of 88 × 84 × 57 mm were used in the production of the infill wall, which has an aspect ratio of 1.17. The compression tests performed on 350 × 350 mm wall mock-ups yielded compression strengths of 5.0 and 4.1 MPa in two perpendicular directions. The diagonal shear tests performed on the same-sized wall specimen resulted in 0.95 MPa of shear strength. A unidirectional type of CFRP sheet was used in the retrofitting. As per the technical data provided by the manufacturer, the unit weight of the CFRP was 300 g/m2, the fiber density was 1.79 g/cm3 and the modulus of elasticity of the CFRP was 230 GPa. Tensile strength and ultimate elongation capacities were 3900 MPa and 1.5 %, respectively. For the wall mock-ups that were retrofitted with CFRP, the average compressive and shear strengths were 7.5 and 1.8 MPa, respectively. Additionally, the modulus of elasticity was determined as 7600 MPa.

Fig. 1
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Dimensions, reinforcing details and pictures of the specimens. a Dimensions and reinforcing retails. b Infilled frame. c Cross braced frame. d Diamond cross braced frame

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A servo-controlled, 280 kN-capacity hydraulic actuator, aligned to the center of the beam, was utilized to generate cyclic displacement reversals in quasi-static (QS) tests (Fig. 2). The rigid foundation of the specimen was fixed to the strong floor.

Fig. 2
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One-cycle and three-cycle displacement protocols used in QS tests

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The general damage patterns and envelopes of force–displacement hysteresis obtained from the QS tests are presented in Fig. 3. The critical events, such as first cracking in RC members, first diagonal cracking in infill, rupture or tearing of CFRP, and buckling of re-bar, are designated on the curves.

Fig. 3
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QS test results. a Damage pattern. b 1-cycle protocol. c 3-Cycle protocol

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Some of the damage indications and corresponding drifts are compiled in Table 3.

Table 3 Critical drifts (%) determined from QS tests
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Based on Tables 2 and 3, the generalized drift corresponding to the ultimate shear strength could be proposed as given in Table 4.

Table 4 The generalized drifts corresponding to the ultimate shear strength
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According to the experimental data extracted from the unidirectional strain gauge measurements in the QS tests, the CFRP tears when the strain reaches 0.6 %. This critical value was used in the calculation of the CFRP’s contribution to the ultimate shear strength of the infill wall (Eq. 1).

4 Development of the “DUVAR” capacity curve model

To develop the capacity curve model that we have called “DUVAR”, three sets of piecewise linear envelopes were generated from the QS test results. The breaking points on the envelopes correspond to the cracking, maximum and ultimate strength, and displacement couples (Figs. 4, 5, 6).

Fig. 4
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Envelopes of infilled frames. a 1-Cycle QS. b 3-Cycle QS

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Fig. 5
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Envelopes of cross-braced frames. a 1-Cycle QS. b 3-Cycle QS

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Fig. 6
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Envelopes of diamond cross-braced frames. a 1-Cycle QS. b 3-Cycle QS

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The contribution of the bare and CFRP-retrofitted infills to the system behavior is represented by the proposed “DUVAR” model (Fig. 7). The model consists of three piecewise linear segments: namely, pre-cracking, post-cracking and descending branches. The self-determining parameters of the model are Vmax, δmax, β, ϕ and μ, which appear in the rectangles in Fig. 7. These parameters are decisive in expressing initial stiffness, effective stiffness and ductility.

Fig. 7
figure 7

Parameters of the “DUVAR” capacity curve model

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The definitions of all the variables used in the “DUVAR” model are listed in Table 5. The lines corresponding to the self-determining parameters are indicated with gray shading.

Table 5 Variables of the proposed “DUVAR” capacity curve model
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The numerical assignments to the parameters are presented in Tables 6 and 7 for the one-cycle and three-cycle QS tests, respectively.

Table 6 Numerical assignments to the model variables for the one-cycle QS tests
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Table 7 Numerical assignments to the model variables for the three-cycle QS tests
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ϕ, β and μ are unitless parameters which were generated to characterize imperative features of infills without CFRP strips. The overall values which are deliberated as the average of pushing and pulling directions are presented in Table 8.

Table 8 The overall unitless parameters of the proposed “DUVAR” capacity curve model
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The ultimate shear strength of the infill (Vmax) was determined using the FEMA-356 (2000) approach, as given in Table 2. Based on the results of the experimental study and the literature review summarized in Table 1, the drift ratio (δmax/h) corresponding to the ultimate shear was assigned at 1.0 % for bare infills and 1.20 % for the retrofitted infills (see Table 4).

In order to generate the proposed model, the following steps should be traced:

Step 1::

The ultimate shear strength (Vmax) of the infill wall without CFRP retrofitting is determined according to FEMA-356 (2000) (see Table 2)

Step 2::

The drift ratio (δmax/h) corresponding to the Vmax is taken from Table 4. The displacement (δmax) is calculated by multiplying the drift ratio by the story height (h) (Eq. 2)

$$\updelta_{\hbox{max} } =\Delta _{\hbox{max} } \times {\text{h}}$$
(2)
Step 3::

The secant stiffness (Ksec) is calculated by dividing the ultimate shear strength (Vmax) by the corresponding displacement (δmax) (Eq. 3)

$${\text{K}}_{ \sec } = {\text{V}}_{ \hbox{max} } /\updelta_{ \hbox{max} }$$
(3)
Step 4::

The pre-cracking stiffness (K0) is calculated by multiplying the secant stiffness (K sec ) by ϕ, which is given in Table 8 (Eq. 4)

$${\text{\rm K}}_{ 0} =\upphi \times {\rm K}_{ \sec }$$
(4)
Step 5::

The cracking strength (V cr ) is calculated by multiplying the ultimate strength (Vmax) by β, which is given in Table 8 (Eq. 5)

$${\text{V}}_{\text{cr}} =\upbeta \times {\text{V}}_{ \hbox{max} }$$
(5)
Step 6::

The cracking displacement (δcr) is calculated by dividing the cracking strength (Vcr) by the pre-cracking stiffness (K0) (Eq. 6)

$$\updelta_{\text{cr}} = {\text{V}}_{\text{cr}} /{\text{K}}_{0}$$
(6)
Step 7::

The ultimate displacement (δu) is determined by multiplying the cracking displacement (δcr) by μ, given in Table 8 (Eq. 7)

$$\updelta_{\text{u}} =\upmu \times\updelta_{\text{cr}}$$
(7)
Step 8::

The strength (Vu) corresponding to the ultimate displacement is calculated as a 20 % drop in Vmax (Eq. 8)

$${\text{V}}_{\text{u}} = 0.80 \, \times {\text{V}}_{ \hbox{max} }$$
(8)

5 Verification of the “DUVAR” capacity curve model

The verification of the proposed “DUVAR” capacity curve model was accomplished for three discrete cases. The first and second cases involved QS and pseudo-dynamic tests (PsD), respectively, of the 1/3-scale one-bay/one-story infilled frames. The third example related to the ½-scale one-bay/two-story infilled RC frame. For all cases, the analytically obtained force-versus-displacement curves were compared with the experimental results.

The nonlinear spring-type link element, which is available in most analysis packages (such as SAP 2000), was used for the application of the infill model. The nonlinear behavior of the RC members was represented by the plastic hinges assigned at both ends of the members. The sectional analysis of the RC members was performed by XTRACT (2006).

Material nonlinearity is accounted for in the pushover analysis, in which lateral displacement increments were applied to story levels.

Case 1

QS tests of one-bay/one-story 1/3-scale specimens

The analytical model consists of three frame elements which represent the nonlinear behavior of columns and beams, and a nonlinear spring that represents the nonlinear behavior of the infill without CFRP retrofitting (Fig. 8).

Fig. 8
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Analytical models of one-bay/one-story 1/3-scale specimens. a Infilled frame. b Cross braced frame. c Diamond cross braced frame

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The characteristic points of the bi-linear moment–curvature relations generated for the plastic hinges defined at both ends of the frame elements are given in Table 9.

Table 9 Characteristic points of the plastic hinges defined on the RC members
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The terms of the bare and retrofitted infill capacity curves for the one-cycle and three-cycle QS tests were determined using the procedure defined above (Fig. 7). The overall parameters listed in Table 8 were used in the determination of the model variables. The calculated model variables are given in Table 10.

Table 10 Characteristic points of “DUVAR” for Case #1 and Case #2
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The force-vs.-displacement curves obtained from the pushover analyses for the three cases—namely, the infilled frame, cross-braced frame and diamond cross-braced frame—were compared with the backbone curves of the corresponding experimental hystereses (Fig. 9).

Fig. 9
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Comparisons of the analytical results with the experimental backbone curves

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It could be concluded that the force-versus-displacement curves obtained from the pushover analyses are close enough to represent the experimental results. The initial stiffness, load-bearing capacity and slope of the descending branch fit rather well with the test results.

Case 2

PsD tests of one-bay/one-story 1/3-scale specimens

Details of the PsD testing can be found elsewhere (Altın et al. 2008a). The acceleration record shown in Fig. 10 was used in the PsD tests. The record was multiplied by two coefficients (0.5 and 1.5) to scale down and up to reach 0.2 and 0.6 g records, respectively.

Fig. 10
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The acceleration record used in the PsD tests

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The analytical force–displacement curves are illustrated in Fig. 11, together with the force–displacement hysteresis obtained from the PsD tests, which represents the results of three successive runs: namely, 0.2, 0.4 and 0.6 g. In general, the analytical results converge with the test results in terms of initial stiffness, ultimate strength and descending branches.

Fig. 11
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Comparison of theoretical results with the PsD test results. a Infilled frame. b Cross braced frame. c Diamond cross braced frame

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Case 3

One-bay/two-story ½-scale specimens

A number of one-bay/two-story ½-scale RC frames were tested in the Structural and Earthquake Engineering Laboratory at ITU, within the framework of a research project (Karadogan et al. 2003). The experimental results obtained from the bare, infilled and cross-braced frame tests were used here to evaluate the success of the “DUVAR” model. The dimensions and reinforcement details of the specimens are demonstrated in Fig. 12a. No confinement reinforcement existed in or around the beam-column connections.

Fig. 12
figure 12

The dimensions and reinforcement details of the specimen (all dimensions are in mm). a Dimensions and reinforcement details. b Analytical model

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The yielding and ultimate strengths of longitudinal reinforcement in the RC members used were 270 and 290 MPa, respectively. The compression strength for the concrete was 14, 11 and 10 MPa, obtained from 150 × 300 mm standard cylinder tests for bare, infilled and cross-braced frames, respectively.

The clay perforated brick used in the infill wall had dimensions of 88 × 84 × 56 mm. Both sides of the infill wall were plastered 10 mm thick. Compression tests performed on the 350 × 350 mm brick infill mock-ups yielded a compression strength of 5.0 and 4.1 MPa, in two perpendicular directions. The tests performed on the same-sized specimens resulted with 0.95 MPa shear strength. The unit weight and fiber density of the CFRP used were 300 g/m2 and 1.79 g/cm3, respectively. Furthermore, the modulus of elasticity, tensile strength and ultimate elongation capacity of CFRP were 230 GPa, 3900 MPa and 1.5 %, respectively.

The specimens were subjected to constant vertical and varying lateral forces. In the lateral direction, reversal displacement cycles were applied at various ductility levels. The lateral loading system seen in Fig. 13 could handle the force distribution ratio between the lower and upper stories being 1:2.

Fig. 13
figure 13

One-bay/two-story infilled frame tests (Karadogan et al. 2003). a Testing set-up. b Damage condition

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The analytical model, which consists of six beam-columns and two shear spring-type nonlinear elements, is illustrated in Fig. 12b. The characteristic points of bi-linear moment–curvature relations generated for the plastic hinges defined at both ends of the RC members are listed in Table 11.

Table 11 Characteristic points of the plastic hinges defined on RC members
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The “DUVAR” model parameters prepared for the bare and retrofitted infills are tabulated in Table 12.

Table 12 Characteristic points of the “DUVAR” model for Case #3
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The base-shear-versus-top-displacement relations obtained through nonlinear static analysis, in which constant vertical and incremental lateral displacements were used, were compared with the backbone curves of the experimental hysteresis (Fig. 14).

Fig. 14
figure 14

Theoretical and experimental results of the bare frame and infilled frame. a Bare frame. b Infilled frame. c Cross braced frame

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For each distinct case, the initial stiffness, ultimate strength and descending branch are comparable between the experimental and analytical results. Hence, the “DUVAR” model can represent the effects of bare and retrofitted infill on the general response.

6 Application of the “DUVAR” model to an existing structure

The three-story RC building, constructed in the 1970s, consists of seven spans in a longitudinal direction (X) and three spans in a transversal direction (Y). The uniform span lengths are 6 m in two directions. The identical story heights are 4.2 m. While the columns positioned at the façades have sectional dimensions of 30 × 60 cm, all the others have a 30 × 70 cm cross-section. The sectional dimensions of the outer beams are 30 × 80 cm, whereas the inner beams have a section of 30 × 50 cm. The RC slabs have a 15 cm thickness and one can assume that they are infinitely rigid in their own planes.

The structural system involves regular frames with rigid connections. The strong axes of all the columns are parallel on the Y-axis; consequently, the lateral stiffness in each of the two directions is quite different to the other (Fig. 15). The building is used as an office building and located on a firm type of soil.

Fig. 15
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Typical story plan of the building

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The equivalent concrete compressive strength, determined by the means of ϕ94 mm cylindrical specimens extracted from the RC members of the structure, is 18 MPa. The longitudinal and lateral reinforcements are mild steel and have a yielding strength of 220 MPa.

The reinforcing details and moment-vs.-curvature relations are illustrated in Figs. 16 and 17.

Fig. 16
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Column sections and moment-versus-curvature relations

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Fig. 17
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Beam sections and moment-versus-curvature relations

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Although the clay brick infills were not accounted for in the original design phase of the building, beyond their weight and mass, the retrofitted infills were evaluated as structural elements. The bare infills were merely represented by their masses.

The seismic weights calculated for the first two stories of the building were identical and equal to W1 = W2 = 9584 kN, while the calculation for the top story was W3 = 5670 kN. For the existing conditions, free vibration analyses gave periods of 1.78 and 1.19 s for the X and Y directions, respectively. The mass contribution ratios for the first modes in the X and Y directions were 88 and 84 %, respectively.

The code-based acceleration spectrum used in the evaluation process had corner periods of Ta = 0.15 s and Tb = 0.40 s. The PGA level was selected as 0.4 g (Turkish Earthquake Code 2007).

The infill walls marked by a gray color in Fig. 18 are retrofitted with CFRP. The total number of retrofitted walls in each story is 16 and the process is repeated in each story.

Fig. 18
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Position of the retrofitted infill walls on a typical plan

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Diamond cross-braced retrofitting has been applied to both sides of the designated walls. The width of the CFRP sheets is 55 cm, and both faces are connected to each other (Fig. 19a). The analytical model of the retrofitted RC frame is illustrated in Fig. 19b. The potential plastic hinges were defined at both ends of the RC members, as well as the nonlinear shear spring used for the retrofitted infill.

Fig. 19
figure 19

CFRP retrofitting and the corresponding analytical model. a Typical retrofitted detail. b Analytical model

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The moment-versus-curvature relations, produced by XTRACT (2006), were assigned to the plastic hinges at both ends of the RC members (Figs. 16, 17, 20). Mander et al. (1998) concrete model and bi-linear steel hardening model were used in the analyses. The load-versus-displacement relations of the retrofitted infills, determined through the “DUVAR” model, are illustrated in Fig. 20.

Fig. 20
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Nonlinear model of the retrofitted infill wall

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For the retrofitted case, vibration periods of 0.99 and 0.49 s were obtained in the X and Y directions, respectively. If these values are compared with those of the pre-retrofitting case, it is possible to distinguish the effect of retrofitted infills on the lateral stiffness of the building.

The capacity curves corresponding to the pre- and post-retrofitting cases, extracted from the pushover analyses in which the first-mode-compatible lateral loads are increased monotonically, are presented in Fig. 21.

Fig. 21
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Capacity curves in two directions. a X direction. b Y direction

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According to the pushover analyses, the maximum lateral strength in the X and Y directions is 1750 and 2300 kN, respectively, for the pre-retrofitting case. The ultimate displacement is 490 mm for both directions. In the retrofitted case, the maximum lateral strength is 9600 and 7700 kN in the X and Y directions, respectively. The analyses were interrupted when a 20 % strength decrement was observed.

The elastic demand spectra and the capacity curves are presented together in the same spectral era (Fig. 22). Accordingly, the performance points are determined using the procedure defined in FEMA-440 (2005).

Fig. 22
figure 22

Demand and capacity curves in Sa–Sd form. a Pre-retrofitting case. b Post-retrofitting case

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For the pre-retrofitting case, spectral displacements were determined as Sdx = 0.390, Sdy = 0.280 (Fig. 22a). The corresponding top displacements are 370 and 510 mm in the X and Y directions, respectively.

The seismic demand for the retrofitted case is determined using the elastic demand spectra generated for 10 % critical damping, contingent on Özkaynak et al. (2013). The spectral displacements for the retrofitted case were determined as Sdx = 0.085 and Sdy = 0.100 in the two directions. The resultant top displacements are 110 and 130 mm for the X and Y directions, respectively.

FEMA-356 (2000) defines the following performance limits for story drifts: immediate occupancy (IO) 1.0 %, life safety (LS) 2.0 %, and collapse prevention (CP) 4.0 %. The story drift demands of the building corresponding to the performance points are shown in Table 13. With respect to FEMA-356 (2000), although the pre-retrofitting case is in the CP range, the post-retrofitting case is in the IO performance level.

Table 13 Performance evaluation in terms of story drifts
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The plastic rotation limits for RC members given in FEMA-356 (2000) are as follows: immediate occupancy (IO) 0.005 rad, life safety (LS) 0.015 rad, and collapse prevention (CP) 0.020 rad. The distribution of the plastic hinges and range of the plastic rotations are illustrated in Fig. 23. The colored circles with different diameters indicate the magnitude and performance range of the hinge. In the pre-retrofitting case, many columns in the first and second story, especially in their weak directions, reached collapse state in addition to the observed beam damages (Figs. 23a, 24a). After retrofitting, the damages of columns and beams decreased significantly in both directions (Figs. 23b, 24b). The new performance level is in the IO range.

Fig. 23
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Plastic hinge distribution of frame ‘3–3’ in X direction. a Pre-retrofitting case. b Post-retrofitting case

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Fig. 24
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Plastic hinge distribution of frame ‘E–E’ in Y direction. a Pre-retrofitting case. b Post-retrofitting case

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The typical B4 column is assessed at the first story in terms of its plastic rotation demands (Fig. 25). Although the column reaches the CP range in both directions for the pre-retrofitting case, it remains in the IO range in both directions for the post-retrofitting case.

Fig. 25
figure 25

Moment-vs.-plastic-rotation relations of a B4 column at the first story. a Pre-retrofitting case. b Post-retrofitting case

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The story shear capacities corresponding to pre- and post-retrofitting cases are presented in Fig. 26a, b.

Fig. 26
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Story shear capacities. a X direction. b Y direction

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In post-retrofitting case, the story shear capacities increase more than 100 % compared with pre-retrofitting case. Moreover, in the retrofitted case the story shear strengths rise gradually from top to bottom.

7 Conclusions

The following conclusions can be drawn:

  1. 1.

    An empirical behavior model for bare and CFRP-based retrofitted infills was proposed.

  2. 2.

    The proposed “DUVAR” model was evaluated using the different existing experimental results. The model was successful enough to predict the initial stiffness, maximum shear strength and descending branch.

  3. 3.

    The proposed model was utilized in the analysis of an existing 3D RC structure to be retrofitted. The earthquake performance evaluation, made with respect to FEMA-356 (2000), yielded the results that the CFRP-based retrofitting on the infill walls led to rigorous performance increments.

  4. 4.

    According to the story drifts and sectional plastic rotation demands of the three-story building, the CFRP-based retrofitting was exceedingly effective in the performance improvement of the existing structure.

  5. 5.

    The performed pushover analysis of the three-story building showed that the CFRP-based retrofitting of the existing infills is capable of increasing the stiffness and strength capacities of the structure without the need to use any other retrofitting techniques.