ANALYTICAL MODELS FOR FRP CONFINED CIRCULAR CONCRETE COLUMNS

Transcription

1 ANALYTICAL MODELS FOR FRP CONFINED CIRCULAR CONCRETE COLUMNS R. Kumutha a, K. Vijai a a Department o Civil Engineering, Sona College o Technology, Salem, Tamilnadu, India ABSTRACT Jacketing a reinorced concrete column by Fibre Reinorced Polymer (FRP) wraps primarily improves column perormance, not because the jacket itsel carries some raction o the axial load applied to the column, but rather because, it provides lateral conining pressure to the column. This conining pressure places the concrete in a triaxial state o stress, altering the loaddeormation characteristics o concrete. But contribution o wraps in improving the load carrying capacity o columns still remains controversial and there is need to develop suitable conining models or FRP wraps.simple analytical equations based on coninement model developed by Richart et al. with modiied value o coninement eectiveness co-eicient were proposed to predict the axial load carrying capacity o FRP conined circular columns under axial loading. The proposed equations were validated through the previous experimental database available in literature. A good correlation is obtained between the proposed equations and the existing experimental results. The conined concrete strength rom tests was compared with the results rom the developed empirical equations and the comparisons are avorable. Keywords: Jacketing; column; ibre reinorced polymer; conining pressure; wraps; load carrying capacity; conining models address o the corresponding author: (R. Kumutha)

2 258 INTRODUCTION Strengthening o R.C. columns represent an engineering problem, which, like all engineering problems, involves several solutions, each having their own advantages and disadvantages and their own limits to applicability and practicality. For instance, there is a possibility to remove deicient columns and construct new columns in their place. Another solution is to place reinorcing steel and orm work around an existing column and pour additional concrete. Yet another solution is to use a jacketing technique wherein the column is encased by some reinorcing material. Traditionally steel has been used to conine R.C. columns, but recently iber reinorced polymer (FRP) has become a viable alternative to steel in some applications. The lateral pressure exerted by FRP will increase the compressive strength o concrete resulting in higher load carrying capacity. The lateral coninement provided by FRP will also provide additional support against buckling o the longitudinal bars. In the case o a circular crosssection, the jacket exerts a uniorm conining pressure resulting in a uniorm tri-axial stress ield. Amir Mirmiran, Mohsen Shahawy conducted series o uniaxial compression tests on concrete illed FRP tubes and the results were compared with the available coninement models in the literature. The study indicates that ibre composites are an eective means o coninement, as they signiicantly increase both strength and ductility o concrete. A comparison o test data with available coninement models indicates that while they produce acceptable results or steelencased concrete, they overestimate the strength o FRP encased concrete. The study also shows a unique characteristic o coninement with ibre composites in that, unlike steel, FRP curtails the dilation tendency o concrete, as it reverses the direction o volumetric strains [1]. The behavior o FRP wrapped concrete cylinders with dierent wrapping materials and bonding dimensions has been studied by Kin-Tak Lau and Li-min Zhou using Finite Element

3 (FEM) and analytical methods [2]. It was ound that, the load carrying capacity o the 259 wrapped concrete structure is governed by the mechanical properties such as modulus and Poisson s ratio, o the wrapping sheet. The delection o the wrapped concrete cylinder in the load direction decreases with increasing the length thickness and modulus o the wrapping sheet. An analytical equation was provided to estimate the shear stress distribution o an adhesive material or dierent wrapping geometries. The results o the equation compared well with FEM solutions. Shahawy et al veriied a coninement model which was originally developed or concrete illed glass FRP tubes by conducting axial compression tests on a total o 45 carbon- wrapped concrete stubs o two batches o normal and high strength concrete and ive dierent number o wraps. It was concluded that, the wrap signiicantly enhanced the strength and ductility o concrete by curtailing its lateral dilation and the adhesive bond between concrete and the wrap would not signiicantly aect the coninement behaviour [3]. The analytical compressive behaviour o concrete members reinorced with FRP was examined by Campione and Miraglia. The variation in the shape o cross section was analysed. The bearing capacity and the increase in the maximum strain or members having a cross-section which was circular, square or square with round corners reinorced with FRP were determined. An analytical model is proposed to validate the conining pressure in ultimate conditions and to determine the ultimate strain corresponding to FRP ailure. Analytical results show good agreement with experimental values available in literature [4]. A study on the compressive behaviour and strength o elliptical concrete specimens wrapped with CFRP has been described by Teng and Lam[5]. From the study it is ound that, the axial

4 260 compressive strength o FRP conined concrete in elliptical specimens is controlled by the amount o conining FRP and the major to minor axis length ratio a/b o the column section. The conining FRP becomes increasingly less eective as the section becomes more elliptical but substantial strength gains rom FRP coninement can still be achieved even or strongly elliptical sections. The ultimate axial strain o the conined concrete is also shown to increase as the FRP coninement becomes larger. Based on the test results, a simple compressive strength model or FRP conined concrete in elliptical columns is proposed, in which the eect o the section shape is taken into account by a shape actor. Hadi carried out experiments to evaluate the eectiveness o the various types o external reinorcement on the circular columns where eccentric loading was applied through especially designed loading mechanism. The experimental results clearly demonstrate that composite wrapping can enhance the structural perormance o concrete columns under eccentric loading to some extent. However, the enhancement is not as signiicant as that o columns under concentric loading as suggested by previous studies. The test results also indicated that the carbon ibres provided the greatest amount o coninement, and had signiicantly better results, i the external coninement was achieved by the application o FRP in tape. The external coninement with galvanised steel straps improved the strength o the column to a certain extent. The brittle, sudden, soundless ailure o the galvanised steel strap wrapped columns showed that the galvanised steel straps had very little eect on improving the ductility o the columns [6]. Teng and Lam presented a large database assembled rom an extensive survey o existing studies and employed the same to assess available axial strength models or FRP conined concrete. The test database is also deployed to examine the eect o various actors on the perormance o FRP conined concrete. This study shows that the coninement eectiveness o

5 FRP, based on reported test results depends little on unconined concrete strength, size, and 261 length to diameter ratio o test specimens and FRP type, but depends signiicantly on the accuracy o the reported tensile strength o the FRP [7]. Literatures indicated that attempts have been made by dierent authors to improve the strength and other engineering properties like energy absorption capacity, and ductility o plain concrete circular columns strengthened with FRP. In this paper,on the basis o experimental investigations carried out on Glass Fibre Reinorced Polymer (GFRP) conined circular columns and based on the model developed by Richart et al simple analytical equations with modiied value o coninement eectiveness co-eicient are proposed to predict the strength o FRP conined concrete columns with circular cross-sections under axial loading. ANALYTICAL INVESTIGATION Conined Concrete Strength According to Richart et al or circular concrete columns conined with FRP composite wraps, the conined core concrete strength can be given as cc co k1 (1) l where co = Strength o unconined concrete k 1 = Coninement eectiveness co-eicient. l = Lateral conining pressure. Evaluation o lateral pressure o coninement For circular specimens, l is uniormly distributed and the concrete in FRP wrapped specimens is uniormly conined. For the case o concentrically loaded cylindrical columns, the lateral pressure

6 262 o coninement can be evaluated by simple considerations o equilibrium o orces. As the axial stress increases, the corresponding lateral strain increases and the conining jacket develops a tensile hoop stress which is assumed to be equal to the ultimate tensile strength o FRP ( rp ), balanced by the radial pressure l, which reacts against the concrete lateral dilation as shown in Figure 1. By equilibrium considerations, the ollowing equation can be derived: l 2t D rp rp rp (2) 2 where t D = thickness o FRP jacket = Diameter o the concrete core rp = Tensile strength o FRP in hoop direction 4t rp = FRP volumetric ratio D Figure 1. Coninement Pressure due to FRP Coninement Ratio (CR) and Stengthening Ratio (SR) The coninement ratio o FRP conined concrete is deined as ratio o the maximum conining pressure to the unconined concrete strength. It is given by

7 263 l CR (3) co Strengthening ratio or coninement eectiveness is deined as the ratio between the strength o conined concrete to that o unconined concrete, that measures how eectively the concrete is conined in a given cross section. It is given by cc SR (4) co Parameters or coninement eect The main parameters that are likely to inluence the coninement eect are the volumetric ibre reinorcement ratio, yield strength o ibre reinorcement, core concrete shape and the strength o unconined concrete. The eect o coninement on these parameters was determined based on the test results. The test results o GFRP conined plain concrete cylinder specimens are given in Table 1. It can be seen that the peak stress o the conined concrete depends on the value o the lateral coninement pressure l. Figure 2 shows the relation between coninement ratio and the ratio o the peak stress to the strength o the unconined concrete or the plain concrete circular specimens o the test series together with the respective linear regression. The peak strength cc o the conined specimens was normalized by the strength o unconined concrete co. It can be seen that, the normalized conined compressive strength, approximately, increase linearly with the increase o the normalized conining lateral pressure. Thereore the relationship may be approximated by a linear unction, with the slope depending on the crosssectional shape. Making use o the experimental results, rom the regression analysis, the relation between coninement ratio and strengthening ratio is written as

8 Strenghtening ratio 264 cc co l (5) co 3 Data set 2 1 y = x Coninement ratio Figure 2. Strengthening Ratio Vs Coninement Ratio-Plain concrete cylinders Table 1 Test results o GFRP conined plain concrete circular specimens S.No. D (mm) L (mm) Fibre type co t (mm) rp E rp l l / co cc cc / co CSM CSM CSM CSM CSM CSM WRM WRM WRM WRM WRM WRM

9 Comparison o conined strength 265 The strength o the FRP conined concrete predicted rom the proposed analytical equation (5) was compared with the experimental results as shown in Table 2. It was ound that a good correlation was obtained between the experimental results and those got rom the equation. It can be seen that the proposed equation predicts the behaviour o conined concrete with most accuracy. The same model can also be used to ind the ultimate strength o concrete conined with all types o ibre sheets namely carbon, aramid etc. Table 2 Comparison o experimental and analytical results S.No Spec.ID cc From Experiment equation (5) cc,cal / cc,exp 1 C C C C C C W W W W W W Validation o proposed equation with existing experimental data base in literature A large number o tests have been reported in the literature on the axial compressive strength o circular concrete specimens conined by FRP.A database containing test results [6] built rom a survey o existing studies ( Kabhari 1994, Watanable et al 1997, Harries et al 1998, Matthys et al 1999, Mirmiran et al 1998, Harmon and Slattery 1992, Demers and Neale 1994, Nanni and Bradold 1995, Soudki and Green 1996, Miyauchi et al 1997, Toutanji and Balaguru 1998, Miyauchi et al 1999, Purba and Muti 1999, Toutanji 1999, Saai et al 1999) is presented in Table 3.

10 266 Only test results on circular specimens without steel reinorcement were considered. These data are all or ully conined plain concrete circular specimens with unconined concrete strengths not greater than 60MPa.All these specimens ailed by FRP rupture. Carbon Fibre Reinorced Plastics (CFRP) and Glass Fibre Reinorced Plastics (GFRP) have been used in these tests. The coninement ratio varies rom 0.03 to The experimental results o conined concrete strength reported in the existing database ound in the literature were compared with those o the conined strength computed rom equation (5). The comparison is shown in Table 4 and is ound to be avorable. Hence, equation (5) can be satisactorily applied to determine the axial compressive strength o FRP conined concrete circular specimens.

11 S. No. Source o Data D (mm) L (mm) L D Type o FRP t (mm) rp E rp co l co cc From Experiment equation (5) CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP Watanable et al CFRP Watanable et al CFRP Harries et al GFRP Harries et al GFRP Harries et al CFRP Matthys et al CFRP Matthys et al CFRP Matthys et al CFRP Matthys et al CFRP Mirmiran et al GFRP Mirmiran et al GFRP Mirmiranet al GFRP Mirmiran et al GFRP Mirmiran et al GFRP Harmon and CFRP cc, cal/ cc,exp

12 258 Slattery Harmon and Slattery CFRP Demers and Neale CFRP Nanni and Bradold GFRP Nanni and Bradold GFRP Nanni and Bradold GFRP Nanni and Bradold GFRP Nanni and Bradold GFRP Nanni and Bradold GFRP Soudki and Green CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Toutanji and Balaguru GFRP Toutanji and Balaguru CFRP Miyauchi et al CFRP Miyauchi et al CFRP Miyauchi et al CFRP Purba and Muti CFRP

13 48 Toutanji GFRP Toutanji CFRP Saai et al GFRP Saai et al GFRP Saai et al CFRP Saaiet al CFRP

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15 CONCLUSIONS Simple analytical equations based on coninement model developed by Richart et al. were proposed to predict the axial load carrying capacity o FRP conined circular columns under axial loading. The proposed equations were validated through the previous experimental database available in literature. A good correlation is obtained between the proposed equations and the existing experimental results. The conined concrete strength rom tests was compared with the results rom the developed empirical equations and the comparisons are avorable. REFERENCES 1. Amir Mirmiran and Mohsen Shahawy. Behaviour o concrete columns conined by ibre composites.journal o structural Engg, (1997) Kin-tak Lau and Li-min Zhou (2001). The mechanical behaviour o compositewrapped concrete cylinders subjected to uniaxial compression load. Composite Structures, 52 (2001) Shahawy M, Mirmiran A. and Beitelman T. Tests and modeling o carbon-wrapped columns. Composites: Part B, 31(2000) Campione G. and Miraglia N. Strength and strain capacities o concrete compression members reinorced with FRP. Cement and Concrete composites, 25(2003) Teng JC and Lam L.Compressive behaviour o Carbon Fibre Reinorced Polymerconined concrete in elliptical columns. Journal o structural Engg, (2002) Hadi M N S. Behaviour o wrapped HSC columns under eccentric load. Asian Journal o Civil Engineering, 4(2003) Teng JC and Lam L. Strength models or Fibre Reinorced Plastic Conined concrete. Journal o structural Engg, (2002)