INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010

Transcription

1 Reliability Study of Concrete Columns Internally Reinforced with Non-Metallic Reinforcements Deiveegan A 1, Kumaran G 2 1- Assistance Professor, 2- Professor, Department of Civil and Structural Engineering, Annamalai University, Annamalai Nagar , Chidambaram, Tamil Nadu,India deiveejaya@yahoo.co.in doi: /ijcser Abstract This study focuses on the behaviour of full scale size concrete columns reinforced internally with non-metallic reinforcements i.e Glass Fibre Reinforced Polymer (GFRP) reinforcements combined bending and axial loads. The experimental investigation consists of Series A and B. Each series has twenty four column specimens with different parameters like shape of columns, reinforcement ratios, types of GFRP reinforcements, slenderness of the columns and grades of concrete. Based on this study, the strength expressions are derived using the equilibrium, strain compatibility, and stress-strain relationship for the constituent materials. For a known eccentricity, the expressions for axial thrust-moment interaction relations are developed for slender columns and the effect of secondary moments incorporated in the analytical study. Also Finite element modelling and analysis of GFRP reinforced concrete columns are performed to simulate the behaviour of the columns under various parametric conditions. A probabilistic framework is necessitated because of the presence of a large number of uncertainties pertaining to the theoretical models and the inherent randomness in the various design parameters. The full range of possible values of load eccentricity, from axial load to pure bending is investigated in the study. Finally, based on the reliability index, appropriate resistance factors are arrived at using the concepts of reliability based design. Keywords: Glass Fibre reinforced Polymer reinforcements (GFRP), concrete columns, Interaction curves, Eccentric loadings. 1. Introduction The use of non-corrosive reinforcements (Glass Fibre Reinforced Polymer- GFRP reinforcements) in the place of conventional steel reinforcements has become a vital alternative which can improve the life span of concrete structures (ACI 2007; ASTM-D; Cho 2006; Nanni 1993; Sivagamasundari 2008). Therefore the present study discusses mainly the behaviour of concrete columns reinforced internally with Glass Fibre Reinforced Polymer (GFRP) reinforcements. First part of this study covers the experimental investigation of GFRP/Steel reinforced concrete columns of series A and B. Each series consists of twenty four specimens with identical dimensions, geometry and reinforcing arrangement. The maximum length (L = 2200 mm) of column is decided based on the experimental limitations. The second part of this study is pertains to the theoretical sectional analysis of concrete columns reinforced with GFRP reinforcements. 270

2 For slender columns the effect of secondary moments are incorporated in the analytical study (Amir Mirmiran 2001; Bank C Lawrence 2006). The interaction curves for various parametric conditions are derived and plotted. Finally, the results of the analytical methods are compared with experimental predictions. The third part of this study relates to the reliability analysis and design of concrete columns reinforced with GFRP reinforcements. A new resistance model is developed to assess the probability of failure and hence reliability index of concrete columns reinforced with GFRP reinforcements. The statistical parameters of column resistance are simulated based on Monte Carlo method. A computer program is developed in visual C++ to perform simulations (Deiveegan 2009; Maria 2005). Sensitivity analysis is performed to determine the design variables that have the highest influence on the reliability index. The level II reliability method is employed to evaluate the risk underlying a structural design in terms of a reliability index. Finally, based on the reliability index, appropriate resistance factors are arrived at using the concepts of reliability based design (ACI 2007; ASTM-D; Bank C Lawernce 2006; Deiveegan 2009; Sivagamasundari 2008). 2. Materials 2.1 Concrete Normal Strength Concrete (NSC) of grades M20 and M30 are used to cast the concrete columns. The mix proportions of the NSC are carried out as per Indian Standards (IS) and the average compressive strengths are obtained from laboratory tests (Deiveegan 2009; Sivagamasundari 2008). 2.2 Reinforcements The mechanical properties of all the types of GFRP reinforcements as per ASTM-D Standards and steel specimens as per Indian standards are obtained from laboratory tests are shown in Figure.1 and the results are tabulated in Table.1. Table 1: Tensile strength of reinforcements Properties Tensile strength (MPa) Longitudinal modulus (GPa) Strain Threaded GFRP rod (F T ) Sand coated GFRP rod (F S ) Steel Fe 415 rod (Fe)

3 Poisson s ratio F T Threaded type GFRP reinforcements; F S Sand Sprinkled type GFRP reinforcements; F e Steel reinforcements Figure 1: a) GFRP reinforcements with end anchorages b) Failure of GFRP reinforcements c) Test setup for GFRP stirrups d) Failure of GFRP stirrups The tensile strength properties are validated by conducting the tensile tests at different testing agency CIPET (Central Institute for Plastic Engineering and Technology), Chennai, Govt. of India. Also from the laboratory tests (Figure. 1), the compressive modulus of elasticity of GFRP reinforcing bars are smaller than its tensile modulus of elasticity (Deiveegan 2009; Sivagamasundari 2008). It varies between GPa which is approximately 70% of the tensile modulus for GFRP reinforcements. Under compression GFRP reinforcements have shown a premature failure resulting from end brooming and internal fibre micro-buckling. No standard test method exists in composite literature. In this study, GFRP stirrups are manufactured by Vacuum Assisted Resin Transfer Moulding process, using glass fibres reinforced with Epoxy resin (Sivagamasundari 2008; Deiveegan 2008; Deitz 2003; ACI 2007). Based on the experimental study, it is observed that the strength of GFRP bent bars/stirrups at the bend location (bend strength) is as low as 50 % of the strength parallel to the fibres. However, the stirrup strength in straight portion is comparable to the yield strength of conventional steel stirrups. The stress strain curves of steel/gfrp reinforcements are shown in Figure 2. Other related tests such as shear tests, thermal coefficient expansion, creep, fatigue and other durability tests are conducted and reported (Sivagamasundari 2008; Deiveegan 2009; Benmokrane 2001; Deitz 2003; Agarwal 1990) 272

4 Stress Mpa steel bar 0 2 Strain Figure 2: Typical Stress-Strain Curves steel/gfrp Reinforcements 3. Test set up and instrumentation All the test specimens are instrumented to measure their overall axial shortening and lateral deflections using strain gauges, deflectometers and LVDTS. All test specimens in each series are cast with the bulk heads in order to prevent local failure of columns. The static loads are applied with the help of hydraulic jacks manually and are monitored by proving ring or load cells. Wedge supports are provided in order to observe the uniaxial bending. A Data acquisition system is used to record all LVDT and electrical strain gauge signals. All test specimens in test series-a & B are applied with a seating load which is followed by monotonically increasing load with an increment of 1 kn up to the failure of the columns. All specimens in series A & B are tested by applying monotonically increasing axial compression with an eccentricity (e) of 20 mm until failure. Table 2: Parameters involved in Construction of Rectangular Columns (series-a) Parameters Description Designation Threaded GFRP Ft Types of Sand coated GFRP F reinforcements S Conventional Fe Concrete grade M 20 &M30 m 1 & m 2 Column sizes Rectangular column (150 x 200 mm) &Rectangular column ( mm) R 1 & R 2 Rectangular column 150x % (6-12 Reinforcement mm bars bars) Rectangular column 230 R 1 p ratios 1 & R 1 p % (6-12 mm bars) 273

5 m 1 M20 Grade of concrete; m 2 M30 Grade of concrete; R 1 Rectangular Column of size 150 mm 200 mm; R 2 Rectangular Column of size 230 mm 300 mm; p 1 Percentage of reinforcements 2.26%; p 2 Percentage of reinforcements 0.98%; Table 3: Parameters involved in Construction of Circular Columns (series-b) Parameters Description Designation Threaded GFRP Ft Types of Sand coated GFRP F reinforcements S Conventional Fe Concrete grade M 20&M30 m 1, m 2 Column sizes Circular column (150 mm Diameter) & Circular column(230mm Diameter) C 1& C 2 Circular column 150 -Diameter Reinforcement -3.8% (6-12 mm bars bars) & C 1 p 1 ratios Circular column 230 -Diameter & C 2 p2, % (6-12 mm bars) m 1 M20 Grade of concrete; m 2 M30 Grade of concrete; C 1 Circular column of size 150 mm dia; C 2 Circular column of size 230 mm dia; p 1 Percentage of reinforcements 3.8%; p 2 Percentage of reinforcements 1.63%. The parameters involved in this study for casting series-a and series-b columns are tabulated in Table. 2. & 3.. Figure 3: Experimental Test setup with instrumentation 274

6 Figure 4: Failure of GFRP Reinforced Columns The entire set with all instrumentation and failure of columns are shown in Figures.3. & 4. The results of the experimental study are depicted in the form of graphs (Figure. 7. to 14.) and are summarized. Figure 7: Load verses strain Figure 8: Moment verses Curvature (R 1 p 1 m 1 F e, R 1 p 1 m 1 F t, R 1 p 1 m 1 F t ) (R 1 p 1 m 1 F e, R 1 p 1 m 1 F t, R 1 p 1 m 1 F t ) 275

7 Figure 9: Load verses strain Figure 10: Moment verses Curvature (R 2 p 2 m 2 F e, R 2 p 2 m 2 F t, R 2 p 2 m 2 F t ) (R 1 p 2 m 2 F e, R 2 p 2 m 2 F t, R 2 p 2 m 2 F t ) Figure 11: Load verses strain Figure 12: Moment verses Curvature (C 1 p 1 m 1 F e, C 1 p 1 m 1 F t, C 1 p 1 m 1 F t ) (C 1 p 1 m 1 F e, C 1 p 1 m 1 F t, C 1 p 1 m 1 F t ) 276

8 Figure 13: Load verses strain Figure 14: Moment verses Curvature (C 1 p 2 m 2 F e, C 1 p 2 m 2 F t, C 1 p 2 m 2 F t ) (C 2 p 2 m 2 F e, C 1 p 2 m 2 F t, C 2 p 2 m 2 F t ) 4. Experimental results 1. From the experimental study it is seen that two types of failures (Figure. 4.) are observed for columns reinforced with GFRP reinforcements, namely,concrete crushing, rupture of GFRP reinforcements under tension and rupture of GFRP reinforcements under compression. 2. For the specimens in series A when the percentage of reinforcements is 0.98%, these columns fail by rupture of GFRP reinforcements in tension leading to violent failure. It is primarily due to the ultimate tensile strains of the GFRP reinforcements reach ultimate strain values before the column reaches the pure bending, and this failure is governed by brittle tension failures of GFRP reinforcements devoid of concrete crushing. 3. It is also evident from the experimental study that in series A & B when the percentages of reinforcements are 2.26% and 3.8% for rectangular and circular columns respectively, these columns fail due to concrete crushing. But none of columns fail due to rupture of GFRP reinforcements in compression prior to concrete strain reaches ultimate. It is probably due to the fact that the ultimate compressive tensile strains of GFRP reinforcements are greater than the ultimate compressive strains of concrete. The experimental values are 8 to 22% higher than the theoretical capacities. 4. It is evident from the experimental tests that the GFRP reinforcements are stressed up to 20 to 35% of its ultimate strength in compression. But higher percentage of utilization is seen under flexural condition (more than 75%). 5. After failure, all tested slender columns, reinforced with GFRP reinforcements are damaged at the compression face because the excessive concrete cover spalling in proximity of the collapse section. It is mainly due to larger deflection curvature where as conventional columns show a limited spalling of cover concrete.. But no stirrups failure is observed in any of the specimens. 277

9 6. GFRP reinforcements do not have yield point, and its stress- strain response shows linear-elastic up to failure. In some cases, GFRP reinforced columns exhibit a failure point before it reaches pure bending condition and is classified as brittle tension failure. This is due to the outer most concrete fibre reaches its limiting strain GFRP reinforced columns exhibit this type of failure when lower reinforcement ratios are considered. Therefore reinforcement ratio limits may be re-fixed for GFRP reinforced concrete column sections. However it must be checked to ensure that compressive failure does not occur in GFRP reinforcements especially in compression zone. 4.1 Analytical investigation This study is confines to a sectional analysis of columns under eccentric loading. Here, the cross sectional strength expressions are derived based on the equilibrium, strain compatibility, and stress-strain relationship for the constituent materials for rectangular and circular concrete columns subjected to an eccentric load (Amir mirmiran 2001; Deiveegan 2009). b d D centroidal axis A si) d highly compressed edge least compressed edge COLUMN SECTION d D centroidal axis d neutral axis y i y i A si x u neutral axis x u si FAILURE STRAIN PROFILE cu = PIVOT si 3D/ cu D/14 C si STRESS RESULTANTS C si 0.67f ck 0.67f ck C c x (a) x u D (b) x u > D Figure 15: Strength of a Rectangular Column Section under Eccentric Compression C c x 278

10 C d D 2 highly compressed edge least compressed edge D centroidal axis highly compressed edge centroidal axis y i d i th row of steel (total area = A GFRPi) ) y i d A GFRPi x u neutral axis x u neutral axis si FAILURE STRAIN PROFILE cu = PIVOT si 3D/ cu D/14 C si STRESS RESULTANTS C si 0.67f cu 0.67f cu C c x (a) x u D (b) x u > D Figure 16: Strain Distribution for Circular Section under Eccentric Compression C c x The derivations are carried out for the symmetrically reinforced concrete sections and compression is assumed to be positive and tension is assumed to be negative as shown in Figures 15 &16. For slender columns the effect of secondary moments are incorporated in the analytical study (Amir mirmiran 2001; Choo 2006; Deiveegan 2009). The interaction curves for various parametric conditions are derived and plotted. Finally, the results of the analytical methods are compared with experimental predictions. Applying the condition of static equilibrium, the two design strength components for GFRP reinforced concrete columns are obtained as follows: M GFRP M C M P GFRP GFRP C C af c cu GFRP af cu n i 1 bd f f n i 1 GFRP bd( D / 2 x) ci AGFRPi fgfrpi fci AGFRPi yi 0.54 xu D for xu D 0.416xu xu D where, a & x 0.67(1 4g 21) for xu D (0.5 8g 49) D (1 4g 21) xu D ; g 16 7 xu D 3 2 ( ) Where, A GFRPi area of GFRP rebars in the i th row (of n rows) ; y i distance of i th row of steel/gfrp from the centroidal axis, measured positive in the direction towards the highly compressed edge; f si stress in the i th row (corresponding to the strain si ) obtainable from stress-strain curves for steel reinforcement; f GFRPi stress in the i th row (1) (2) 279

11 (corresponding to the strain GFRPi ) obtainable from stress-strain curves for GFRP reinforcement; si/ GFRPi strain in steel/gfep at the i th row, obtainable from strain compatibility conditions ( si/ GFRPi and f si/ f GFRPi are assumed to be positive if compressive, and negative if tensile); f ci compressive stress in concrete, corresponding to the strain ci = si( GFRPi) adjoining the i th row of steel/gfrp bars, obtainable from the design stressstrain curve for concrete. 4.2 Construction of Interaction curve for Slender Columns In this study, the effect of secondary moments for slender columns is considered for the GFRP reinforced column sections (Amir mirmiran 2001; Choo 2006; Deiveegan 2009). GFRP reinforcements are considered symmetrically on each side of the column cross section. Columns are assumed to have pin supports at both ends. Effects of torsion, biaxial bending, creep and shrinkage of concrete, and creep and relaxation of reinforcement are ignored in this study. A simple excel (spread sheet) routine is developed to obtain lateral displacement of a column based on the nonlinear axial load moment curvature relations. The lateral displacements, i and slopes i at points x i on the column are successively calculated for an assumed initial slope, o at initial conditions x o, for a given combination of P and M at x o. 1 2 i i 1 i 1( x i xi 1) i 1( xi xi 1) (3) 2 ( i i 1 i x 1 i xi 1) (4) Using the axial load-moment (P-M) and moment curvature relationship (M- ) developed for the column cross section in the previous section, the curvature at every point is computed as a function of the axial load and moment f ( M, P) (5) i The procedure is repeated by changing o until the correct displacement is obtained. The correct displacements are those for which the slope at mid height equals zero for symmetrical end conditions, or for which the displacement equals zero at the end of a column subjected to an axial load P with unequal moments at the member ends. The moments along the column, including the maximum moment, can be determined from the lateral displacements. Repeating the aforementioned procedure for increasing values of P, the corresponding displacements along the column can be computed and, thus, tables of axial force-displacement and axial force-maximum moment resistance can be generated 3,13. The interaction curves for various parametric conditions are derived and plotted. i 280

12 (a) E GFRP-C / E GFRP-T =1 (b) E GFRP-C / E GFRP-T =0.5 Figure 17: Load verses Moment- Interaction diagrams(r 1 p 1 m 1 F e, R 1 p 1 m 1 F t, R 1 p 1 m 1 F t ) (a) E GFRP-C / E GFRP-T =1 (b) E GFRP-C / E GFRP-T =0.5 Figure 18: Load verses Moment- Interaction diagrams (R 2 p 2 m 2 F e, R 2 p 2 m 2 F t, R 2 p 2 m 2 F t ) 281

13 (a) E GFRP-C / E GFRP-T =1 (b) E GFRP-C / E GFRP-T =0.5 Figure 19: Load verses Moment- Interaction diagrams (C 1 p 1 m 1 F e, C 1 p 1 m 1 F t, C 1 p 1 m 1 F t ) (a) E GFRP-C / E GFRP-T =1 (b) E GFRP-C / E GFRP-T =0.5 Figure 20: Load verses Moment-Interaction diagrams (C 2 p 2 m 2 F e, C 2 p 2 m 2 F t, C 2 p 2 m 2 F t ) 5. Results of Analytical study The results of the theoretical analysis are 1. It is observed from the experimental study that the compressive modulus is 50% lesser than tension modulus. The axial thrust verses moment interaction diagrams for GFRP reinforced columns are drawn for two ratios of elastic moduli i.e E GFRP- C/E GFRP-T = 1 (ratio of elastic modulus in compression to tension =1) and E GFRP- C/E GFRP-T = 0.5 (ratio of elastic modulus in compression to tension =0.5) for various 282

14 parameters and are shown in Figures. 17 to 20. But the variations in elastic moduli do not have remarkable changes in the capacities of the columns cross sections. 2. From the theoretical sectional analysis results, it is observed that the maximum capacities of the column sections for various parametric conditions are comparable with the experimental values. It is observed from the study that the slender columns have reduced capacities by 10 to 20% when compared to the steel reinforced concrete columns. 3. It is clear from the theoretical results that the GFRP reinforcement ratio in compression zone has not remarkable increase in the capacities, even if it is ignored in the compression zone that leads to conservative values. 5.1 Reliability Analysis In reliability analysis, the main components of structural reliability pertains to two random variables (i) R is a random variable represented in terms of several resistance variables and design constants, and (ii) Q is another random variable in terms of load variables and design constants Resistance model The possible sources of uncertainty with reference to the resistance considered here are defined as the product of a nominal resistance and three factors namely material factor, fabrication factor and professional factors (Maria 005; Deiveegan 2009; Sivagamasundari 2008). The detailed calculations are carried out based on the available input and are validated with the current standard procedures Load Model In the present study statistical data pertaining to the dead and live loads variables are obtained from the literature based on the Indian standards (Sivagamasundari 2008). The reliability analysis of concrete columns under the axial load and the bending moment is a path dependent problem because the column resistance depends on the loading eccentricity or on the point where load effect (effect) crosses the boundary between the safe and the failure regions. In this study four simple criterions are followed, viz. the axial capacity criterion, moment capacity criteria, the shortest distance from the interaction curve criterion, and criterion of the shortest distance (shortest load path) from the initial loading condition (Deiveegan 2009). The developed computer program allowed for calculation of reliability indexes for the full range of possible column failure modes. The analysis is performed for two grades of concrete strengths, four selected reinforcement ratios, and two selected strength reduction factors., viz., φ = 0.70 and φ =

15 5.1.3 Sensitivity analysis A wider variation in the reliability index can be seen (Table 4 & Table 5), depending on the mode of failure (concrete crushing, rupture of GFRP reinforcements under tension and rupture of GFRP reinforcements under compression). In concrete crushing failure, the reliability index has got considerable variation with regard to the concrete strength. This can be attributed to different values of the bias factor for concrete strength. In rupture of GFRP reinforcements under tension, influence of concrete on the overall capacity of a column decreases and the GFRP reinforcement controls the capacity and hence higher reliability indices are obtained. S.No Table 4: Resistance factors for GFRP Reinforced Columns Specification of Columns R e/d ratio for Possible Resistance Factors = 0.7 = R1 p1m1fs R1 p1m1ft R1 p1m2fs R1 p1m2 Ft R2 p2m1fs R2 p2m1ft R2 p2m2fs R2 p2m2ft C1 p1m1fs C1 p1m1ft C1 p1m 2Fs C1 p1m2 Ft C2 p2m1fs C2 p2m1ft C2 p2m2fs C2 p2m2ft R Reinforcement ratio; e Eccentricity; D Depth of column or Diameter of the column; Resistance factor; Reliability Index 284

16 S.No Table 5: Resistance factors for Steel reinforced columns Specification of Columns R e/d ratio for Possible Resistance Factors = 0.7 = R1 p1m1fe R1 p1m 2Fe R2 p2m1fe R2 p2m2fe C1 p1m1fe C1 p1m 2Fe C2 p2m1fe C2 p2m2fe R Reinforcement ratio; e Eccentricity; D Depth of column or Diameter of the column; Resistance factor; Reliability Index 5.2 Strength reduction factors The reliability analysis for all design cases resulted to frame a rational approach to select the new resistance factors for the design of GFRP reinforced concrete columns. The selected resistance factors are related to predefined target reliability indices. Surfaces presenting the distribution of strength reduction factor as a function of load ratio and load eccentricity, or tensile strain in steel, are plotted for preselected values of target reliability indices β = 3.5 and 4.0. The sensitivity analysis shows that the resistance factor falls below 0.70 for higher strength concrete columns with lower reinforcement ratio. The selection of resistance factors for columns can be decided based on the all design cases (with different concrete strengths, reinforcement ratios, and load proportions) and shows that the preselected values of target reliability indices β = 3.5 and 4.0 encompasses all possible cases under consideration taking into account the tensile strain in GFRP rebars. Based on the previous reliability indices applicable for conventionally reinforced concrete columns, and because of the fact that failure of a column can be more brittle (compared to a beam in pure bending), higher reliability index for columns is suggested. 6. Conclusions The following conclusions are summarized as follows: 1. In this study, Load and Resistance Factor Design (LRFD) format is adopted to carry out the design of GFRP reinforced concrete columns. 2. Results indicated that β values for the uni-axial bending cases are relatively constant, also, β increases as the percentage of reinforcement value increases. But it is 285

17 insignificant to the slenderness ratios of the columns considered in this study (L/D ratios: 9.56 & 14.66). 3. The β values have a significant influence with the increase of grade of concrete, reinforcement ratio, size of the column, eccentricity, shape of the (circular columns). Circular columns have higher reliability indices than the rectangular column due to higher confinement that leads to higher ductility levels. 4. The results of the present study reveals that the statistical properties of GFRP and steel reinforced concrete columns differ based on the expected mode of failure. Columns with higher reinforcement ratios fail by crushing of concrete and hence the resistance models are more influenced by the statistical properties of concrete. 5. Columns with Lower reinforcement ratio impart different resistance models that are influenced by the rupture of GFRP reinforcements. This fact plays an important role in reliability based design which influences the design parameters such as the resistance factor. The bias values are higher for columns that fail by rupture of GFRP bars than columns that fail by crushing of concrete. These bias values are balanced by the fact that the GFRP rupture mode results in higher coefficient of variation. In general the reliability index is more sensitive to the reinforcement ratio rather than the compressive strength of the concrete. In ACI Code, the strength reduction factor is proposed based on the extreme fibre strains of the column cross sections. The present study considers two strength reduction factors. These factors have different values based on the reinforcement ratios. Based on this study, it is observed that the slight increase in the transition zone limits and is expressed as a function of extreme tensile strains ( GFRP ) in GFRP reinforcements. The proposed resistance factors are based on the assumption of the target reliability index of 4.0. In conclusion, both failure modes (i.e., GFRP rupture and concrete crushing) are acceptable for the design of concrete. To compensate for the lack of ductility, the suggested margin of safety against failure is therefore higher than that used in traditional steel reinforced concrete column design. The observed values of are in the range of 3.41 to These values are compared with the previous study for steel reinforced concrete columns 22 and are conservative. Acknowledgement The authors wish to thank the University Grants Commission (UGC) of India for the valuable financial support rendered from the UGC Major Research Scheme. 7. References 1. ACI Committee 440.XR (2007), Report on fiber-reinforced polymer (FRP) reinforcement for concrete. Structures American Concrete Institute. 2. Amir Mirmiran, Wenqing yuan and Xiaobing Chen (2001), Design for slenderness in concrete columns internally reinforced with fibre-reinforced polymer bars. Journal of, Vol.98(12),pp

18 3. Agarwal. B.D and Broutman. L.J (1990), Analysis and performance of fibre composites, second edition, John Wiley & Sons, New York. 4. ASTM-D , Standard Test Methods for Tensile properties of Pultruded Glass- Fibre Reinforced Plastic Rod. 5. Bank C. Lawrence (2006), Composites for Construction: Structural Design with FRP materials, John Wiley & Sons, Inc, New Jersey. 6. Benmokrane. B, Wang. P, Gentry T.R, and Faza. S (2001), Test Method to determine the properties of FRP redo for concrete structural, Proceedings of the International Workshop on Composites in Construction, American society of civil Engineers. 7. Choo. C.C (2006), Strength of Rectangular Concrete Columns Reinforced with Fibre Reinforced Polymer Bars, ACI Structural Journal, Vol.103, May-June, pp Choo. C.C (2006), Minimum Reinforcement Ratio for Fibre Reinforced Polymer Reinforced Concrete Rectangular Columns, ACI Structural Journal, V.103, May-June, pp Deitz. D.H, Harik. E, Asce. M, Gesund. H, Asce. F (2003), Physical properties of glass fibre reinforced polymer rebars in compression, ASCE Journal of Composites for Construction, pp Deiveegan. A and Kumaran. G (2009), Reliability Analysis of Concrete Columns reinforced internally with Glass Fibre Reinforced Polymer Reinforcements, The ICFAI University Journal of Structural Engineering, The ICFAI University Press,India, Vol.2(2), pp Maria. M Szerszen, Aleksander Szwed, and Andrej. S Nowak, (2005), Reliability analysis for eccentrically loaded column, ACI structural journal, Vol.102(69), pp Nanni. A, FRP Reinforcement for bridge Structures (2000), Proceedings of Structural Engineering Conference, University of Kansas, Lawrence, KS. 13. Nanni. A, Okamoto. T, Tanigaki. M, and Osakada. S (1993), Tensile properties of braided FRP rods for Concrete reinforcement, Cement and Concrete Composites, Vol.15 (3), pp Sivagamasundari. R, (2008), Experimental and Analytical Investigations on the Behaviour of Concrete Slabs reinforced with Fibre based Rods as Flexural reinforcements, Ph.D Thesis, Department of Civil & Structural Engineering, Annamalai University, Annamalai Nagar, India. 287