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Effect of slenderness on fibre reinforced polymer wrapped reinforced concrete columns.


Reinforced concrete columns confined with FRP composites exhibit higher compressive strength, axial strain and lateral strain at ultimate state. The ductility values are also higher for FRP confined columns. The effect of FRP wrap is not the same for columns with different slenderness ratios, although the available equations for predicting compressive strength do not consider slenderness ratio as a parameter. Most of the results for FRP confined concrete and theoretical models published in the literature are based on short stubs for which slenderness ratio is very minimal.

The effect of slenderness ratio on the performance of reinforced concrete columns with FRP wrap at yield level and ultimate level were studied. The combined effect of slenderness ratio and thickness of FRP wrap on stresses, axial strains and lateral strains for the columns were studied. The data obtained from the experimental investigation was used for performing a multi-variate regression analysis which incorporated components for the effect of slenderness in addition to those related to the strength of concrete and FRP.

Mirmiran et al. (2001) investigated the slenderness limit for hybrid FRP confined concrete columns. Seven Concrete Filled FRP Tube (CFFT). Specimens having slenderness ratios of 4, 11, 18, 22, 30, 34 and 36 were prepared and tested uniaxial compression. Typical failure of specimens was characterized by rupture of FRP wrap at points of maximum stress concentration, which were away from the centre of the columns. It was shown that slenderness did not affect the stiffness of the hybrid system, but resulted in reduced compressive strength and axial strain characteristics. An analytical model was also proposed for estimating the strength of FRP confined concrete columns.

Girard and Bastien (2002) studied the behaviour of reinforced concrete columns confined by lateral ties using a finite element bond slip model. The model was capable of accounting for the confinement provided by hoop reinforcement, softening of concrete and for the gradual loss of bond between concrete and steel. The results of finite element simulation agreed well with experimental results reported by other researchers.

Challal et al. (2003) carried out extensive experimental investigations on short columns of square and rectangular shape, on a total of 90 specimens. Three ratios of shorter face to longer face of cross sections were adopted at 1.000, 0.654 and 0.500 with constant area and corner radius of 25.4 mm. Two grades of concrete at 20.7 MPa and 41.4 MPa were adopted with zero, one, two, three and four layers of CFRP wrapping. The investigation found that the rate of gain of strength fell down with increase in level of confinement, while the ductility levels showed remarkable increase with increasing confinement. The researchers categorized the behaviour of confined concrete as bilinear with three distinct regions: i) initial behaviour similar to plain concrete, ii) transition zone in which CFRP exerted confining pressure on the core, as the core deteriorated and iii) constant stiffness zone where the confinement effect of CFRP stabilized to a constant value. The poison's ratio for the columns was stable around 0.2 while the dilation ratio for plastic response was influenced by level of confinement.

Hadi and Li (2004) investigated the behaviour of high strength concrete columns with FRP confinement. The specimens were confined using carbon, glass and kevlar fibre reinforced polymer of varying thicknesses and subjected to concentric as well as eccentric loading. All columns failed in a brittle manner. The failure of unconfined columns was highly explosive. Under concentric loading conditions, confinement using kevlar FRP resulted in some increase of deflection and ductility over the unconfined specimens. Carbon fibre wrapped specimens with single layer failed explosively, while those with three layers seemed to appear integral without any damage to the wrap even after failure of the column. Under eccentric loading, carbon FRP confined columns failed explosively, while kevlar and glass FRP confined specimens showed adequate warning in the form of white patches on FRP surface at the time of initiation of failure.

Aire et al. (2005) investigated the stress-strain behaviour of axially loaded concrete cylinders with compressive strengths of 30 MPa and 70 MPa. Confinement was provided with GFRP and CFRP. The number of layers was 1, 3 and 6 for 30 MPa concrete core and 1, 3, 6, 9 and 12 layers for 70 MPa concrete. It was observed that CFRP was more effective in providing confinement and led to more compressive strength when compared to corresponding number of layers of GFRP. The failure of columns confined with CFRP was explosive while the failure of columns confined with GFRP was less explosive, although sudden in nature. The results indicated that hardening type failure was noticed in confined concrete with multiple layers of FRP. Both compressive strength and axial strain capacities improved due to confinement. It was observed that FRP confinement was more effective for normal strength concrete than for high strength concrete. An analytical model was also proposed as part of the work and the results from the model agreed well with experimental results.

Kaminski and Trapko (2006) investigated the effect of varying configurations of FRP strengthening on the performance of reinforced concrete columns having square and circular cross sections. External CFRP strips in the longitudinal direction, CFRP longitudinal strips combined with transverse bands, CFRP longitudinal strips combined with full length transverse CFRP wraps, CFRP transverse wraps alone. Internal adhesive bonding of CFRP longitudinal strips,CFRP strips combined with bands and CFRP strips combined with wrap. The increase in load-carrying capacity was attributed to the lower strain in CFRP confined columns compared to unconfined columns at the same load levels. The specimens with longitudinal CFRP without bands or wraps showed that the failure was induced by damage at the contact surface. Some of band wraps failed in the case of longitudinal strips combined with band wraps.

Saenz and Pantelides (2007) proposed a strain-based model for FRP confined concrete. The model estimated the stress corresponding to the given strain level. The secant modulus with a softening mechanism was used in the model. The fundamental behaviour of FRP under loading was described. Volumetric contraction was exhibited in the linear elastic axial response zone. As the concrete softened, the volumetric strain reached zero marking the transfer of load from concrete core to the FRP confinement. The radial strain at zero volumetric strain marked the activation of FRP confinement. The model consisted of linear elastic response regime, transition regime and ultimate axial stress-radial strain regime. The ultimate radial strain of the FRP confined column was expressed as a function of the confinement effectiveness.

Research Significance

The present study attempted to investigate the relationship between column parameters like slenderness ratio and thickness of FRP wrap and performance parameters like yield stress, axial yield strain, lateral yield strain, ultimate compressive stress, ultimate axial strain and ultimate lateral strain. The combined effect of slenderness and FRP wrap on the performance of concentrically loaded concrete columns was not so clearly established in the literature yet.

A multi-variate regression analysis was performed using the components for compressive strength of plain concrete confined by FRP (based on the model proposed by Mander et al., 1988), the slenderness ratio and the strength of steel reinforcement.

Experimental Investigation

Specimen Geometry

Reinforced concrete column specimens having 150 mm diameter and different heights of 300 mm, 600 mm, 900 mm and 1200 mm were prepared. The nominal slenderness ratios for the columns were 8, 16, 24 and 32 for the columns of 150 x 300 mm, 150 x 600 mm, 150 x 900 mm and 150 x 1200 mm respectively.

Three specimens were cast for each slenderness ratio. For each slenderness ratio, one specimen was tested without any wrapping, one specimen with 3 mm GFRP wrap and the third specimen with 5 mm thick GFRP wrap. The total number of specimens was 12.


The columns were cast using concrete of mix ratio 1:1.54:3:0.5 (cement: FA: CA: water), having characteristic compressive strength of 23.64 MPa.


Steel used for longitudinal reinforcement had yield strength of 415 MPa and that used for lateral ties had yield strength of 250 MPa. The columns were reinforced with 6 rods, 8 mm diameter in the longitudinal direction. Lateral circular ties were provided using 6 mm diameter mild steel rods spaced at 115 mm c/c.

Glass Fibre Reinforced Polymer (GFRP)

The GFRP used for the present investigation consisted of randomly oriented chopped strands distributed at 450 gram/ square metre of the mat. The fibres had average aspect ratio of 4800. The Chopped Stand Mat Glass Fibre Reinforced Polymer (CSMGFRP) was wet laid on the column specimens using iso-phthalic resin. The mechanical properties of the CSMGFRP are presented in Table 1.

Specimen Details

Wrapping of Specimens

The columns were wrapped using CSMGFRP fibre mat after cleaning the surface. The specimen surfaces were rubbed using grinding stone and blown with compressed air. Isophthalic resin was applied in measured quantities, the wrapping mat was applied and the excess resin was oozed out using rubber roller. Figs. 1.a to 1.e show the process of wrapping a typical set of specimens.






Experimental Investigation

The test set ups for S8, S16, S24 and S32 columns are shown in Figs. 2.a and 2.b.



The instrumentation for S32 columns included a deflectometer at bottom, a deflectometer at top, one Linear Variable Dielectric Transducer (LVDT) at top, three LVDTs at top portion of the column to measure lateral expansion, and one deflectometer at mid height of the specimen for measuring lateral movement Instrumentation for S24 columns was slightly different in that an extensometer (with least count of 0.00254 mm) was employed for measuring the lateral expansion.

The instrumentation for S8 and S16 columns included a deflectometer at bottom, one LVDT for measing axial deflection, extensometer at mid height of the column to measure lateral expansion.

All the specimens were testing with two electrical strain gauges, one in the axial direction and the other in the lateral direction to measure the strains.

The S8 and S16 columns were tested in a Compression Testing Machine (CTM) of 2000 kN capacity at load increments of 10 kN and the S24 and S32 columns were tested on a loading frame having 2000 kN capacity at load increments of 5 kN. The loading was monotonic and readings were noted for each load increment.

Experimental Results And Discussion

The stress-strain behaviour of the experimental specimens is presented in Fig. 3.


The stress-strain curves for columns with lower slenderness ratio and higher thickness of FRP wrapping went higher on both the stress axis and the strain axis, indicating improvement in both strength and deformability. The entire family of curves were dominated by the stress-strain curve for S8CSM5 specimen.

The post yield deformation capacities for unwrapped columns were very low and the failure occurred just after the yield point, indicating the lack of sustained resistance after the concrete core failed. In the case of CSMGFRP wrapped columns, the failure was preceded by sufficient post yield deformation, with considerable reduction in the slope of the stress-strain curve. But, the failure was sudden, accompanied by rupture / tearing of the wrap either at top or at the bottom portion of the column. Although the post yield deflection capacity was satisfactory, pre-failure warning was not so clear.

Experimental results pertaining to yield point and ultimate point are presented in Tables 3 and 4 respectively. Figs. 4.a to 4.c show the performance values at yield point and Figs. 5.a to 5.c show the performance values at ultimate point.







The influence of wrap thickness was calculated taking the results for unwrapped columns as reference, keeping the slenderness ratio constant. The influence of slenderness ratio was calculated with reference to the columns having slenderness ratio of 32, keeping the wrap thickness constant.

Effect of Wrap Thickness on Performance at Yield Point

The increase in yield stress for 3 mm thick CSMGFRP wrapped columns was in the range of 17.95% to 29.73%, while that for 5 mm thick CSMGFRP was in the range of 46.15% to 78.38%. The increase in compressive stress at yield point higher for columns with thicker wrap.

Columns with 3 mm thick CSMGFRP wrap showed increase in the range of 16.99% to 50.00%, while those with 5 mm thick CSMGFRP showed increase in the range of 47.71% to 80.56%, when compared to the unwrapped columns with the same wrap thickness.

The unwrapped reinforced concrete columns clearly showed a trend of increase in lateral yield strain values by a margin of 14.50% to 32.57% with reduction in slenderness ratios. The increase in lateral yield strain ranged from 0.93% to 49.52% for 5 mm thick CSMGFRP.

The effect of wrap thickness on lateral yield strain was significant. Increased thickness of GFRP wrapping resulted in higher lateral yield strain. The columns with 3 mm thick CSMGFRP wrapping showed increase in lateral yield strain in the range of 10.53% to 50.00%.

Effect of Slenderness Ratio on Performance at Yield Point

The effect of slenderness on yield performance was calculated using S32 specimens as reference. The effect of slenderness ratio on yield stress for unwrapped columns was in the range of 4.23% to 9.86%. The reinforced concrete columns with 3 mm CSMGFRP wrapping exhibited increase in yield stress in the range of 4.55% to 9.09% and those with 5 mm thick CSMGFRP exhibited increase by 4.72% to 24.53%.

The axial yield strains for CSMGFRP wrapped columns showed increase in the range of 4.68% to 57.89% for 3 mm thick wrap and in the range of 4.63% to 48.61% for 5 mm thick CSMGFRP wrap.

The unwrapped reinforced concrete columns clearly showed a trend of increase in lateral yield strain values by a margin of 14.50% to 32.57% with reduction in slenderness ratios. The same clarity of increasing lateral yield strain values was shown in the case of 5 mm thick GFRP wrapped columns, where the increase ranged from 0.93% to 49.52% for CSMGFRP. The lateral yield strains increased and decreased for the same wrap thickness and material with varying slenderness ratios. For the columns with 3 mm thick GFRP wrapping and slenderness ratios 24, 16 and 8, the lateral yield strain values were in the range of -8.82% to 43.28% compared to those having slenderness ratio of 32

Effect of Wrap Thickness on Performance at Ultimate Point

The columns with 3 mm thick CSMGFRP wrap exhibited increase in ultimate stress up to 66.67%, while those with 5 mm thick CSMGFRP wrap showed increase up to 115.69%.

The increase in ultimate axial strain for 3 mm thick CSMGFRP was up to 268.65% and that for 5 mm thick CSMGFRP wrap was up to 621.35%. The columns with 3 mm thick CSMGFRP wrap showed increase in ultimate lateral strain by a maximum of 422.39% and those with 5 mm thick CSMGFRP attained up to 889.79% increase.

Effect of Slenderness on Performance at Ultimate Point

The unwrapped columns with slenderness ratios of 24, 16 and 8 showed increase ultimate stress values by 7.41%, 15.05% and 25.93% over the columns having slenderness ratio of 32. The columns with 3 mm thick CSMGFRP wrapping showed up to 25.00% increase in ultimate stress, while those with 5 mm thick CSMGFRP showed up to 39.24% increase.

The axial strain values for unwrapped columns showed the maximum sensitivity to the slenderness ratio, where the increases were in the range of 51.35% to 181.08% and were progressively higher for decreasing slenderness ratios. Columns with CSMGFRP wrap showed up to 62.46% increase in ultimate axial strain levels. The ultimate lateral strain values attained by the unwrapped columns were 22.83%, 44.29% and 111.07% for S24R0, R16R0 and S8R0 over the column S32R0. The ultimate lateral strain values increased up to 54.08% for 3 mm thick CSMGFRP wrap and up to 47.23% for 5 mm thick CSMGFRP wrap.

Regression Analysis for Compressive Strength

The compressive strength of FRP wrapped columns was estimated using the model proposed by Mander et al. (1988). While the results were in good agreement with predictions obtained from the model, the predictions were not sensitive to the slenderness ratio of the column. Since the experimental results showed sensitivity to the variation in slenderness, a multi-variate linear regression analysis was carried out to incorporate the slenderness of FRP confined reinforced concrete column as a parameter in the equation for estimating compressive strength. The data used for the regression analysis is shown in Table 5.

The basic form of the regression equation with unknown coefficients was,


Equation 1 has separated the contribution of longitudinal steel into a passive component which is unaffected by the regression process, in keeping with the ACI 440.2R (2002). The value of fl may be estimated using,

[f.sub.l] = 2nt[[epsilon].sub.fe][E.sub.f]/D (2)

The values for the unknown regression coefficients [a.sub.0], [a.sub.1] and [a.sub.2] are presented in Table 6.

After incorporating the values of regression coefficients, equation 1 becomes,


The predictions obtained using the above regression equation had fitness value of 0.925, produced Root Mean Square Error (RMSE) of 3.25 and Root Mean Square Percentage Error (RMSPE) of 9.77%. A comparison of the results obtained from regression equation and the experimental results is shown in Fig. 6. The comparison shows that the predictions of the regression equation are sensitive to the variations in slenderness ratio and agree well with experimental results.

Abbreviations And Notations

[A.sub.g]     --Gross cross sectional area of concrete column
[]    --Area of longitudinal steel reinforcement
[A.sub.t]     --Area of steel tie
CSMGFRP       --Chopped Strand Mat Glass Fibre Reinforced Polymer
D             --Diameter of reinforced concrete column
[E.sub.f]     --Elasticity modulus of FRP
[f']   --Compressive strength of unconfined concrete
[f.sub.l]     --Confining pressure
[f.sub.rc]    --Compressive strength of FRP confined reinforced
[f.sub.y]     --Yield strength of longitudinal steel reinforcement
[]    --Yield strength of lateral steel ties
n             --Number of layers of FRP wrap
RC            --Reinforced Concrete
[S.sub.t]     --Spacing of steel ties
t             --Thickness of each layer of FRP wrap
[[].sub.fe]   --Effective ultimate strain in FRP wrap at failure
[]            --Slenderness ratio


The authors wish to acknowledge the financial support offered by the University Grants Commission, New Delhi for carrying out this research investigation.


The experimental investigation established the fact both slenderness ratio and thickness of FRP wrap have a considerable influence on the compressive behaviour of reinforced concrete columns. The yield stresses and ultimate stresses were higher for columns with thicker FRP wrap and lower slenderness ratio. The following conclusions are drawn from the investigation:

1. Columns with CSMGFRP wrap exhibited increase in ultimate compressive stress by a maximum of 66.67% for 3 mm thickness of wrap and 115.69% for 5 mm thickness of wrap.

2. The ultimate axial strain capacity of the columns increased by up to 621.35% and the lateral strain capacity increased by up to 889.79% due to CSMGFRP wrapping.

3. Reduction in slenderness led to higher ultimate compressive stress values. The increase due to reduction of slenderness from 32 to 8 was up to 25.93% for unwrapped columns and 39.24% for CSMGFRP wrapped columns.

4. The ultimate axial strain and lateral strain values were affected by the slenderness ratio. Columns without wrap showed up to 181.08% increase in axial strain capacity and 111.07% increase in lateral strain capacity for reduction in slenderness ratio from 32 to 8..

5. CSMGFRP wrapped columns showed increase in ultimate axial strain due to slenderness ratio by up to 62.46%.

6. The regression equation proposed in the present study incorporates slenderness component for estimating the compressive strength of reinforced concrete columns, thus permitting more accurate estimation of compressive strength.

7. The errors in the results obtained from the regression equation were very small, with Root Mean Square Percentage Error (RMSPE) of 9.77%.


[1] ACI, 440.2R, (2002), Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures,, pp. 1-45.

[2] Aire, C., Gettu, R., Casas, J.R., Marques, S. and Marques, D., (2005), "Compressive Behaviour of Concrete Confined with Fibre Reinforced Polymer Wraps", Proc. Advances in Concrete and Composites, SERC, Chennai, India, pp. 825-832.

[3] Challal, O., Shahawy, M. and Hassan, M. (2003), "Performance of Axially Loaded Short Rectangular Columns Strengthened with Fiber Reinforced Polymer Wrapping", ASCE Jl. of Compos. for Constr., 7(3), 200-208.

[4] Girard, C. and Bastien, J. (2002), "Finite Element Bond Slip Model for Concrete Columns under Cyclic Loads", ASCE Jl. of Structural Engg., 128(12), 1502-1510.

[5] Hadi, M.N.S. and Li, J. (2004), "External Reinforcement of High Strength Concrete Columns", Elsevier Jl. of Composite Structures, 65, 279-287.

[6] Kaminski, M. and Trapko, T. (2006), "Experimental Behaviour of Reinforced Concrete Column Models Strengthened by CFRP Materials", Jl. of Civil Engineering and Management, 12(2), 109-115.

[7] Mander, J.B., Piestly, M.J.N. and Park, R. (1988), "Theoretical Stress-Strain Model for Confined Concrete." ASCE Jl. of Structural Engg., 114(8), 1804-1826.

[8] Mirmiran, A., Shahawy, M. and Beitleman, T. (2001), "Slenderness Limit for Hybrid FRP Concrete Columns", ASCE Jl. of Compos. for Constr., 5(1), 26-34.

[9] Saenz, N. and Pantelides, C.P. (2007), "Strain-Based Confinement Model for FRP-Confined Concrete", ASCE Jl. of Structural Engg., 133(6), 825-833.

[10]--, (2006), "Statistics Toolbox for Use with MATLAB[R]", Mathworks inc., 3, Apple Hill Drive, Natick, MA 01760-2098, USA.

V. Nagaradjane Research Scholar, Dept. of Civil & Structural Engineering, Annamalai University, Annamalai Nagar--608 002, India; Corresponding author Email:

P. N. Raghunath Professor, Dept. of Civil & Structural Engineering, Annamalai University, Annamalai Nagar--608 002, India.

K. Suguna Professor, Dept. of Civil & Structural Engineering, Annamalai University, Annamalai Nagar--608 002, India.
Table 1: Mechanical Properties of CSMGFRP.

S1.   Type of Fibre   Thickness   Tensile    Ultimate   Elasticity
No.   in GFRP         (mm)        Strength   Elongati   Modulus
                                  (MPa)      (%)        (MPa)

1.      CSM             3          126.20    1.69         7467.46
2.      CSM             5          156.00    1.37        11386.86

Table 2: Specimen Details.

S1.   Specimen      Diameter   Height   Type of   Thickness   Nominal
No.   Designation   (mm)       (mm)     GFRP      of GFRP     Slender-
                                                  (mm)        ness

1.      S8R0         150         300     --          0         8.00
2.      S8CSM3       150         300     CSM         3         8.00
3.      S8CSM5       150         300     CSM         5         8.00
4.      S16R0        150         600     --          0        16.00
5.      S16CSM3      150         600     CSM         3        16.00
6.      S16CSM5      150         600     CSM         5        16.00
7.      S24R0        150         900     --          0        24.00
8.      S24CSM3      150         900     CSM         3        24.00
9.      S24CSM5      150         900     CSM         5        24.00
10.     S32R0        150        1200     --          0        32.00
11.     S32CSM3      150        1200     CSM         3        32.00
12.     S32CSM5      150        1200     CSM         5        32.00

Table 3: Results at Yield Point.

Specimen   Yield   Yield        Lateral      Yield    Axial     Lateral
Desig-     Load    Deflection   Yield        Stress   Yield     Yield
nation     (kN)    (mm)         Deflection   (MPa)    Micro-    Micro-
                                (mm)                  Strain    Strain

S8R0       390       0.60         0.06       22.07    2000.00   372.53

S16R0      370       1.08         0.05       20.94    1800.00   355.60

S24R0      370       1.53         0.05       20.94    1700.00   321.73

S32R0      355       1.84         0.04       20.09    1533.33   281.00

S8CSM3     460       0.90         0.08       26.03    3000.00   558.80

S16CSM3    480       1.36         0.06       27.16    2266.67   423.33

S24CSM3    475       1.79         0.05       26.88    1988.89   355.60

S32CSM3    440       2.28         0.06       24.90    1900.00   390.00

S8CSM5     570       1.07         0.10       32.26    3566.67   677.33

S16CSM5    660       1.95         0.09       37.35    3250.00   609.60

S24CSM5    555       2.26         0.07       31.41    2511.11   457.20

S32CSM5    530       2.88         0.07       29.99    2400.00   453.00

Table 4: Results at Ultimate Point.

Specimen   Ultimate   Ultimate     Ultimate    Ultimate
Desig-     Load       Deflection   Lateral     Stress
nation     (kN)       (mm)         Expansion   (MPa)

S8R0        510         2.60         0.45      28.86

S16R0       470         3.40         0.31      26.60

S24R0       435         4.20         0.26      24.62

S32R0       405         3.70         0.21      22.92

S8CSM3      850         5.54         1.71      48.10

S16CSM3     800         8.62         1.34      45.27

S24CSM3     705        11.36         1.26      39.89

S32CSM3     680        13.64         1.11      38.48

S8CSM5     1100         9.82         3.10      62.25

S16CSM5     940        18.64         2.99      53.19

S24CSM5     860        20.49         2.15      48.67

S32CSM5     790        26.69         2.11      44.70

Specimen   Ultimate   Ultimate
Desig-     Axial      Lateral
nation     (Micro-    Micro-
           Strain     Strain

S8R0        8666.67     2997.2

S16R0       5666.67    2048.93

S24R0       4666.67    1744.13

S32R0       3083.33    1420.00

S8CSM3     18466.67   11430.00

S16CSM3    14366.67    8923.87

S24CSM3    12622.22    8398.93

S32CSM3    11366.67    7418.00

S8CSM5     32733.33   20692.53

S16CSM5    31066.67   19930.53

S24CSM5    22766.67   14342.53

S32CSM5    22241.67   14055.00

Table 5: Data Used for Regression Analysis.

           Compressive   Inverse of    Confinement
           Stress        Slenderness   Coefficient   Compressive
Specimen   from          Ratio         [2E.sub.f]    Strength from
Desig-     Mander        1             [fu.sub.nt]   Experiment
nation     et al                       []D   (minus
           (1988)                                    strength
           Model                                     of steel)

S8R0       30.32         0.134771        0.00           21.78
S16R0      30.32         0.067431        0.00           19.52
S24R0      30.32         0.044944        0.00           17.54
S32R0      30.32         0.033704        0.00           15.84
S8CSM3     37.53         0.135685        0.21           41.02
S16CSM3    37.53         0.067889        0.21           38.19
S24CSM3    37.53         0.045249        0.21           32.81
S32CSM3    37.53         0.033944        0.21           31.40
S8CSM5     46.28         0.137363        0.44           55.17
S16CSM5    46.28         0.068681        0.44           46.11
S24CSM5    46.28         0.045767        0.44           41.59
S32CSM5    46.28         0.034329        0.44           37.62

Table 6: Values of Regression Coefficients.

S1. No.   Coefficient   Value

1.          [a.sub.0]   -35.9863
2.          [a.sub.1]     1.6278
3.          [a.sub.2]   102.7220
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Author:Nagaradjane, V.; Raghunath, P.N.; Suguna, K.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Apr 1, 2009
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