Composites: Part B 43 (2012) 825–831

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Composites: Part B

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Effect of confinement level, aspect ratio and concrete strength on the cyclicstress–strain behavior of FRP-confined concrete prisms

R. Abbasnia ⇑, R. Ahmadi, H. ZiaadinyDepartment of Civil Engineering, Iran University of Science and Technology, Tehran 16844, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 May 2010Received in revised form 13 September2011Accepted 1 November 2011Available online 10 November 2011

Keywords:A. Polymer fiberB. StrengthD. Mechanical testingRectangular columns

1359-8368/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.compositesb.2011.11.008

⇑ Corresponding author. Tel.: +98 21 77240399; faxE-mail address: abbasnia@iust.ac.ir (R. Abbasnia).

Behavior of rectangular concrete columns confined with FRP composites depends on several parameters,including unconfined concrete strength, confinement level, aspect ratio of cross-section (defined as thedepth/width of the cross-section), and the sharpness of the section corners. For modeling the cyclicstress–strain behavior of FRP-confined rectangular concrete columns, effect of column parameters onthe cyclic behavior of these columns should be examined properly. In this paper, effects of unconfinedconcrete strength, confinement level and the aspect ratio of cross-section are studied. The test databaseincludes 10 prisms from recent study of authors and 18 prisms from a new experiment. Results of testsshow that some aspects of cyclic behavior of FRP-confined concrete prisms such as envelope curve andstress deterioration are unaffected by the considered parameters. Results also indicate that the plasticstrain decreases as the unconfined concrete strength increases, but it is independent of the aspect ratioand the confinement level. While the reloading path in all specimens was almost linear, the unloadingpath was highly nonlinear and was affected by unconfined concrete strength.

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1. Introduction

Over the years, different techniques have been used for retrofit-ting of existing reinforced concrete columns, such as sectionenlargement using reinforced concrete jacket, providing passiveconfinement for the column using steel jacketing, and the use of fi-ber reinforced polymer (FRP) composites as wraps or jackets forthe confinement of reinforced concrete (RC) columns. Among thesetechniques, the use of FRP composites has become increasinglypopular due to their high strength-to-weight ratio and excellentcorrosion resistance.

The use of FRP composites as confining material for concretecolumns can enhance their strength and ductility. Thus for design-ing the concrete columns confined with FRP composites properly,the behavior of these columns under both monotonic and cycliccompression needs to be properly investigated.

A large number of studies have been reported in the literature onthe monotonic behavior of FRP-confined concrete cylinders andrectangular concrete columns confined with FRP composites[1–17]. In the recent years, some researchers have also studied thebehavior of FRP-confined concrete cylinders under cyclic compres-sion [18–20]. Shao et al. [19] proposed a constitutive model basedon an experimental database for cyclic loading of FRP-confined con-crete cylinders. Their model includes cyclic rules for loading and

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unloading, plastic strains, and stiffness and strength degradations.However Lam et al. [18] has shown that this model is inadequatein predicting the unloading path and the cumulative effect of loadinghistory on the stress–strain response of FRP-confined concrete cylin-ders. Thus Lam and Teng [20] developed a model which predicts thestress–strain hysteresis loops of FRP-confined concrete cylindersexperiencing all patterns of cyclic loading.

In the recent years few studies, however, have addressed the cyc-lic stress–strain behavior of FRP-confined concrete prisms [21].Behavior of rectangular concrete columns confined with FRPcomposites depends on several parameters, including unconfinedconcrete strength, confinement level, aspect ratio of cross-section(defined as the depth/width of the cross-section), and the sharpnessof the section corners. For modeling the cyclic stress–strain behaviorof FRP-confined rectangular concrete columns, effect of columnparameters on the cyclic behavior of these columns should be exam-ined properly.

In this paper, an experimental database is used to investigate theeffects of unconfined concrete strength, confinement level and theaspect ratio of cross-section on the cyclic behavior of FRP-confinedconcrete prisms. The test database includes 10 prisms from recentstudy of authors and 18 prisms from a new experiment.

2. Experimental database

In this study results from the study of Abbasnia and Ziaadiny[21] are used together with the results of a new experiment in

(a) rectangular section

(b) strain gauge layout

(c) test setup

Fig. 1. Rectangular section, instrumentation and test setup.

826 R. Abbasnia et al. / Composites: Part B 43 (2012) 825–831

order to investigate the effects of unconfined concrete strength,confinement level and the aspect ratio of cross-section on the cyc-lic behavior of FRP-confined concrete prisms. Details of these stud-ies are presented in the following subsections.

2.1. Abbasnia and Ziaadiny’s tests [21]

Abbasnia and Ziaadiny’s study included a total of 10 CFRP-confined concrete prisms which were subjected to various cyclicloading patterns [21]. All of the specimens were 152 � 152 mmin cross section and 305 mm in height and Corner radius of allspecimens was 29 mm. One batch of concrete was used in theirstudy. All the specimens were wrapped with three layers of CFRPusing wet lay-up process and were subjected to axial compression.The compression tests were achieved with load control at a rateapproximately equal to 4 kN/s.

2.2. New tests

In this experimental program a total of 18 CFRP-confined con-crete prisms were prepared and subjected to axial compressive load-ing. All of the specimens were 305 mm in height but with differentaspect ratios. Three aspect ratios of 1, 1.266 and 1.688 were consid-ered in this study. In order to have the same edge sharpness of cross-section, the ratio of corner radius to the width (r/b), (see Fig. 1a) in allthe specimens had a constant value of 0.19. Other variables whichwere considered in the preparation of specimens were the uncon-fined concrete strength and the number of CFRP layers. In additionto the confined specimens, for each batch of concrete three uncon-fined concrete cylinders were prepared as control specimens. Theproperties of specimens and the key results of tests are presentedin Table 1. This table contains six categories of specimens. The spec-imens which have similar characteristics are listed in the same cat-egory. The categories are named as CxS (or Ry)Jz, where Cx refers tothe concrete types, S and Rx refer to the square and rectangularcross-sections respectively, and Jz refers to the two FRP jackets.

After uniform mixing in the mixer, concrete was poured into theforms. Forms for prismatic specimens were made in a manner sim-ilar to that used in the recent study of authors [21]. One day aftercasting, the specimens were removed from the forms and put inwater for curing. After 28 days, the specimens were removed fromthe water and their surface was cleaned with water and left to dry.When the surface of specimens was completely dried, specimenswere wrapped with three or four layers of CFRP using wet lay-upprocess and each layer had a single lap 150 mm in length.

2.2.1. Material propertiesThree batches of concrete were prepared in this study to inves-

tigate the effect of unconfined concrete strength on the cyclicbehavior of FRP-confined concrete prisms. Ordinary PortlandCement (OPC) was used with a water/cement ratio of 0.63, 0.48and 0.42 for the target strengths at 28 days of 25, 43, and50 MPa, respectively. River sand and coarse aggregate with a max-imum size of 19 mm were used in the preparation of concrete.

Unidirectional carbon fiber sheets and epoxy-based primer andresin were used in this study. The nominal thickness of carbon fibersheets was 0.176 mm. The mechanical properties of CFRP materialhave been obtained from flat coupon tensile tests in accordancewith ASTM D3039 and are summarized in Table 2.

2.2.2. Instrumentation and testingIn this study, axial displacements of specimens were measured

by two linear variable differential transformers (LVDTs). The LVDTswere mounted at 180� apart onto two steel frames that were fixedat the top and bottom of the specimens, and mid-height region of200 mm was covered (see Fig. 1c).

In some specimens four strain gauges were bonded at the mid-height of them. Two horizontal strain gauges were bonded outsidethe overlapping zone (180� apart) in order to measure lateralstrains and two vertical strain gauges were bonded 180� apart tomeasure longitudinal strains (see Fig. 1b). For some specimensloading was applied monotonically, and for the other specimens,cyclic loading involving a single or several complete unloading/reloading cycles at each prescribed displacement level was applied(see Ref. [21]). Loading and unloading in the compression testswere achieved with load control at a rate approximately equal to4 kN/s. The axial load was measured using a load cell that wasplaced under the specimens. A data logging system was used forrecording the readings of the load cell, strain gauges and LVDTs.

2.2.3. Test resultsThe actual concrete strengths at the testing ages were obtained

from the testing of control specimens simultaneously along with

Table 1Details of CFRP-confined specimens and key results.

Category Specimenname

Dimensions(mm)

Aspect ratio (h/b)

Corner radius, r(mm)

Number of FRPlayers

Loadingpattern

f 0co

(Mpa)fcu

(Mpa)ecu (%) eh,rup

(%)a

Abbasnia and Ziaadiny [20]C1SJ1 C1-L1 152 � 152 � 305 1 29 3 Monotonic 30 1.7587 58.86 1.2134

C1-L2-a 152 � 152 � 305 1 29 3 Cyclic 30 2.40875 66.23 1.1664C1-L2-b 152 � 152 � 305 1 29 3 Cyclic 30 1.2575 53.12 1.1837C1-L4-a 152 � 152 � 305 1 29 3 Cyclic 30 1.7588 58.56 b–C1-L4-b 152 � 152 � 305 1 29 3 Cyclic 30 2.545 63.03 1.0231C2-L1 152 � 152 � 305 1 29 3 Monotonic 27 2.5623 61.76 1.0071C2-L3-a 152 � 152 � 305 1 29 3 Cyclic 27 3.0088 65.61 1.3633C2-L3-b 152 � 152 � 305 1 29 3 Cyclic 27 2.6113 61.58 1.0266C2-L5-a 152 � 152 � 305 1 29 3 Cyclic 27 2.765 63.99 b–C2-L5-b 152 � 152 � 305 1 29 3 Cyclic 27 2.2175 61.14 b–

New testsC1SJ2 C1SJ2L2 152 � 152 � 305 1 29 4 Cyclic 30 2.67 65.08 .85

C1SJ2L3a 152 � 152 � 305 1 29 4 Cyclic 30 2.80 65.22 1.051C1SJ2L3b 152 � 152 � 305 1 29 4 Cyclic 30 2.61 65.96 –

C2SJ2 C2SJ2L1 152 � 152 � 305 1 29 4 Monotonic 50 1.2 77.08 –C2SJ2L2a 152 � 152 � 305 1 29 4 Cyclic 50 1.18 75.34 –C2SJ2L2b 152 � 152 � 305 1 29 4 Cyclic 50 1.22 76.65 0.76C2SJ2L3 152 � 152 � 305 1 29 4 Cyclic 50 1.24 78.98 –

C3SJ2 C3SJ2L2a 152 � 152 � 305 1 29 4 Cyclic 56 – – –C3SJ2L2b 152 � 152 � 305 1 29 4 Cyclic 56 – – –C3SJ2L3 152 � 152 � 305 1 29 4 Cyclic 56 – – –

C1R1J1 C1R1J1L1a 152 � 90 � 305 1.688 17.5 3 Monotonic 30 1.78 49.72 .827C1R1J1L1b 152 � 90 � 305 1.688 17.5 3 Monotonic 30 2.25 55.80 –C1R1J1L2 152 � 90 � 305 1.688 17.5 3 Cyclic 30 2.38 54.17 0.84C1R1J1L3a 152 � 90 � 305 1.688 17.5 3 Cyclic 30 2.85 55.286 1.073C1R1J1L3b 152 � 90 � 305 1.688 17.5 3 Cyclic 30 2.74 51.877 –

C1R2J1 C1R2J1L2 152 � 120 � 305 1.266 23 3 Cyclic 30 1.75 53.34 –C1R2J1L3a 152 � 120 � 305 1.266 23 3 Cyclic 30 1.75 55.27 –C1R2J1L3b 152 � 120 � 305 1.266 23 3 Cyclic 30 2.29 61.39 1.007

a FRP hoop rupture strain.b No strain gauges were bonded.

Table 2Mechanical properties of CFRP.

Ultimate tensile strain (%) Tensile strength (MPa) Elastic modulus (GPa) Primary fiber direction Specimen number Specimen type

1.64 3969.2 242 Unidirectional 1 CFRP coupon1.67 3941.1 236 Unidirectional 2 CFRP coupon1.60 3920.2 245 Unidirectional 3 CFRP coupon1.63 3943.5 241 – – Average

Fig. 2. Typical failure modes of the specimens.

R. Abbasnia et al. / Composites: Part B 43 (2012) 825–831 827

the tests of confined specimens. The actual strengths were 30, 50,and 56 Mpa which are somewhat higher than the mix design targetstrengths. For a given number of CFRP layers and a constant uncon-fined concrete strength, the compressive strength of specimenswith higher aspect ratio (C1R1J1 and C1R2J1) was smallerthan those for specimens with lower aspect ratio (C1SJ1). The

confinement efficiency to lower-strength concrete prisms washigher. The load capacity of specimens with the concrete strengthof 56 Mpa (C3SJ2) was higher than the capacity of load cell, thusthe ultimate condition of these specimens are not given in Table1. Both the square and rectangular specimens failed by the suddenrupture of the CFRP jacket at the middle portion of them. Rupture

Fig. 3. Cyclic stress–strain curves of specimens in comparison with monotonic stress–strain curves for the same concrete.

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of CFRP jacket in the a majority of specimens was occurred near thecorners of cross-section due to the stress concentration, but insome of the specimens with square cross-section the rupture didnot necessarily occur at the corner. Similar observation was madeby Wang and Wu [12]. This mode of failure may be due to the ef-fect of overlapping zone in the stress distribution in the specimens.The typical failure modes of the specimens are shown in Fig. 2.

3. Discussion of tests results

3.1. Column parameters and the envelope curve

Previous studies on the cyclic behavior of unconfined concrete,steel-confined concrete and FRP-confined concrete in cylindricalspecimens [18–23], have suggested a hypothesis that the mono-tonic stress–strain curve of these specimens can be considered asthe envelope of the cyclic stress–strain curve. Recent study ofAbbasnia and Ziaadiny [21] indicated that the hypothesis of enve-lope curves is also valid for FRP-confined concrete in square pris-matic specimens. The results of the present tests clarify that thishypothesis is independent of column parameters. The monotonicand cyclic stress–strain curves of specimens with different charac-teristics are shown together in Fig. 3. It should be noted that theaxial stress–lateral strain curves of specimens which had straingauges are also presented in this figure (Fig. 3a and c). It is clearin Fig. 3 that the monotonic stress–strain curve is tangent to upperboundary of cyclic stress–strain curve and the hypothesis ofenvelope curve is valid for all specimens. Thus it can be concludedthat the considered parameters including the aspect ratio of cross-

section, concrete strength and the confinement level may not affectthe hypothesis of envelope curve.

3.2. Effect of column parameters on the plastic strain

For modeling the unloading/reloading cycles it is necessary toknow the residual axial strains (or plastic strains) of concrete whenit is unloaded to the zero stress. Previous studies on the steel-confined concrete and FRP-confined concrete [18,21,22], haveshown that the relationship between the plastic strain in the firstunloading/reloading cycle at each prescribed displacement level,epl,1, and the strain at the starting point of unloading from envelopecurve, eul,env is linear. Since behavior of rectangular concrete col-umns confined with FRP composites depends on several parame-ters, thus these parameters may affect the relationship betweenthe plastic strain and the envelope unloading strain. This sectionis concerned with the effect of confinement level, aspect ratio andunconfined concrete strength on the plastic strain of FRP-confinedconcrete prisms.

3.2.1. Effect of confinement levelConfinement level (i.e. amount of FRP) is a parameter which

strongly affects the monotonic stress–strain behavior of FRP-confined concrete. However Lam et al. [18] suggested that thisparameter has an insignificant effect on the plastic strain ofFRP-confined concrete cylinders. The insignificant effect of lateralconfinement on plastic strain was noted by Buyukozturk and Tseng[24] based on their biaxial cyclic compression tests on flat concreteplates, and by Sakai and Kawashima [22] based on their tests onsteel-confined concrete [20]. In the present study, in order to

Fig. 4. Correlations between plastic strain versus envelope unloading strains ofspecimens in the categories of C1SJ1 and C1SJ2.

(a) Specimen C1SJ1 and C1R1J1

(b) Specimen C1SJ1 and C1R1J1

Fig. 5. Correlations between plastic strains versus envelope unloading strains.

Fig. 6. Correlation between epl,1 and eul,env, for the specimens C1SJ2, C2SJ2 andC3SJ2.

(a) Lam and Teng [20]

(b) Present study

Fig. 7. Correlation between epl/eul,env and f 0co .

R. Abbasnia et al. / Composites: Part B 43 (2012) 825–831 829

evaluate the effect of confinement level on the plastic strain, thecorrelations between the plastic strain versus envelope unloadingstrains of specimens in the categories of C1SJ1 and C1SJ2, whichare confined by 3 and 4 CFRP layers respectively, are shown inFig. 4. This figure shows that the trend lines of these specimens al-most coincide. This indicates that the plastic strain of FRP-confinedconcrete prisms is also independent of the confinement level.

3.2.2. Effect of aspect ratioThe aspect ratio defines the shape of a rectangular section. A

number of existing studies have been concerned with the effectof aspect ratio on the monotonic stress–strain behavior of FRP-

confined concrete prisms. Results of these studies have shown thatthe confinement effectiveness decreases when the aspect ratioincreases. Wu and Wei [17] suggested that as the aspect ratioincrease from 1 to 2, the strength gain in confined concrete col-umns decreases until it becomes insignificant at an aspect ratioof greater than two.

In the present study, in order to evaluate the effect of aspect ratioon the plastic strain, the correlations between epl,1 and eul,env, for thespecimens with different aspect ratios, are shown in Fig. 5. In thisfigure it is obviously seen for specimens C1SJ1 (h/b = 1) andC1R1J1 (h/b = 1.688), it is difficult to distinguish between the trendlines, and for specimens C1SJ1 (h/b = 1) and C1R2J1 (h/b = 1.266),the trend lines almost coincide. Thus it can be concluded that thechange in cross-sectional aspect ratio may not affects the plasticstrain.

Fig. 8. Stress deterioration in the first cycle.

830 R. Abbasnia et al. / Composites: Part B 43 (2012) 825–831

3.2.3. Effect of unconfined concrete strengthSakai and Kawashima [22] suggested that the plastic strain of

steel-confined concrete is independent of unconfined concretestrength, and proposed a linear relationship between epl,1 andeul,env for each of the two regions of 0.001 < eul,env 6 0.0035 andeul,env > 0.0035. Lam and Teng [20] examined the cyclic behaviorof FRP-confined concrete cylinders with different unconfined con-crete strengths based on the test results from Lam et al. [18] andother studies on the FRP-confined concrete. They concluded thatthe plastic strain of FRP-confined concrete strongly depends onthe unconfined concrete strength, because they observed that theslope of linear relationship between plastic strain and envelopeunloading strain decrease linearly with increase in the concretestrength (Fig. 7a).

Fig. 6 shows the correlation between epl,1 and eul,env, for thespecimens C1SJ2, C2SJ2 and C3SJ2 with the unconfined concretestrengths of 30, 50 and 56 Mpa respectively. It is clear from this fig-ure that the slope of trend lines decreases with the increase in theconcrete strength. Thus it can be concluded that the plastic strainof FRP-confined concrete prisms depends on unconfined concretestrength. The slope of trend lines is a linear function of the uncon-fined concrete strength as shown in Fig. 7b.

3.3. Effect of column parameters on the stress deterioration

A number of existing studies on the cyclic behavior ofunconfined and confined concrete [18–22] have shown that bothunconfined and confined concrete under unloading/reloading cy-cles, are subjected to stress deterioration. In the present study, inorder to evaluate the degree of stress deterioration for the firstunloading/reloading paths of each cycle, a stress deterioration ratiois defined as follows:

b1 ¼fnew;1

ful;envð1Þ

where, ful,env is the envelope unloading stress, and fnew,1 is the stresswhere the first reloading path reaches to the point corresponding toeul,max (see Fig. 8a). Fig. 8b depicts the correlation between eul,env

and b1, for the specimens C1SJ1, C2SJ2 and C1R1J1. This figureshows that for small envelope unloading strains b1 is almost equalto 1, and strength degradation is negligible. As eul,env increase, b1

tends to decreases and reaches a constant value of about 0.9 ateul,env P 0.0035. This ratio was proposed by Lam and Teng [20] tobe 0.92 based on the tests on FRP-confined concrete cylinders. Shaoet al. [19] suggested that after the bend point in the envelope curve,the stress deterioration ratio is 0.9.

Fig. 8b also indicates that, for specimens with different charac-teristics, the stress deterioration ratio has the same trend, thus itcan be concluded that the stress deterioration is independent ofthe column parameters.

3.4. Effect of column parameters on the unloading and reloading paths

For modeling the unloading and reloading paths, it is necessaryto identify the shape of these paths. It is obvious in Fig. 3 that theunloading paths of FRP-confined concrete prisms are highly non-linear. Similar observations have been reported for steel-confinedconcrete and FRP-confined concrete cylinders. Shao et al. [19] pro-posed that the slope of unloading path at the point of plastic strainis zero and used a polynomial function to present the unloadingpaths of FRP-confined concrete cylinders. A similar approach wasused by Sakai and Kawashima [22] for steel-confined concrete.However Lam and Teng [20] suggested that the slope of theunloading path at zero stress generally has a nonzero value andproposed a new polynomial equation to represent the unloadingpaths of the unloading/reloading cycles of FRP-confined concrete.

Unlike the unloading path, the reloading path for all specimensis almost linear. Fig. 3 shows that although there is some softeningin the early stage of reloading paths, but a major part of reloadingpath is linear, and it approaches the envelope curve non-linearly.Shao et al. [19] modeled the entire reloading path of FRP-confinedconcrete cylinders, as a linear curve. Lam and Teng’s model [20] de-fines a reloading path for FRP-confined concrete cylinders, whichconsists of a straight line from the reloading point to a referencestrain point, and a parabola for the remaining part until it reachesthe envelope curve.

The envelope unloading paths of specimens with different char-acteristics are shown together in Fig. 9. This figure indicates thatthe aspect ratio and the confinement level will not affect the shapeof unloading path. But as the unconfined concrete strength in-crease, the slope of unloading path at the zero stress increases. Inthe Lam and Teng’s model [20], also the slope of the unloading pathat zero stress is related to the unconfined concrete strength.

Eun;0 ¼ min0:5f 0coeul

funeul�epl

8<: ð2Þ

where Eun,0 is the slope of the unloading path at the zero stress.They suggested that in most cases, Eun,0 takes the value of0:5f 0co=eul, and it takes the value of fun/(eul � epl) only when theunloading stress and/or strain are very small. Results of presentstudy indicate that this suggestion is also valid for FRP-confinedconcrete prisms.

4. Conclusion

In this study an experimental database is used to investigate theeffects of unconfined concrete strength, confinement level and the

(a) specimens with different aspect ratios (C1SJ1 and C1R1J1)

(b) specimens with different confinement levels (C1SJ1 and C1SJ2)

(c) specimens with different concrete strengnths (C1SJ1 and C3SJ2)

Fig. 9. Envelope unloading paths of specimens with different characteristics.

R. Abbasnia et al. / Composites: Part B 43 (2012) 825–831 831

aspect ratio of cross-section on the cyclic behavior of FRP-confinedconcrete prisms. These conclusions may be drawn from this work:(a) The hypothesis of envelope curve is valid for all FRP-confinedconcrete prisms with different characteristics. (b) Plastic strain ofFRP-confined concrete prisms is a linear function of the envelopeunloading strain. The plastic strain decreases as the unconfinedconcrete strength increases, but it is independent of the aspect ra-

tio and the confinement level. (c) Strength degradation for thesmall envelope unloading strains is negligible. As eul,env increase,strength degradation tends to increase and reaches a constant va-lue of about 10% at eul,env P 0.0035. (d) For specimens with differ-ent characteristics, the stress deterioration ratio has the sametrend, thus it can be concluded that the stress deterioration is inde-pendent of the column parameters. (e) While the reloading path inall specimens is almost linear, the unloading path is highly nonlin-ear and is dependant to the unconfined concrete strength.

It should be noted that one other parameter that affects mono-tonic stress–strain behavior of rectangular concrete columns con-fined with FRP composites is the sharpness of the sectioncorners. This parameter may also affect the cyclic behavior of thesecolumns. Thus the effect of this parameter on the cyclic behavior ofFRP-confined rectangular concrete columns should be examinedthrough further studies.

Acknowledgments

The authors are grateful for the financial support received fromthe Iran University of Science and Technology. Thanks are also ex-tended to the employees of the Structural Laboratory at the Collegeof Civil Engineering, Iran University of Science and Technology fortheir valuable contribution to the experimental work.

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