# Strength and ductility of fiber reinforced polymer plated RC beams.

IntroductionFRP plating is a versatile technique which can be applied equally well for existing RC beams and new ones. Plating of FRP laminates results in the increase of composite moment of inertia of the section, thus making it behave with more stiffness after plating. The present study is aimed at investigating the effect of FRP plate thickness and area of steel reinforcement on the performance of FRP plated RC beams.

Saadatmanesh and Ehsani (1991) experimentally investigated the static strength of RC beams upgraded by gluing GFRP plates to their tension flanges. The results indicated that the flexural strength can be significantly increased by bonding GFRP plates to the tension face of RC beams; the gain in ultimate strength was more significant in beams with lower steel reinforcement ratios; plating reduced crack size at all load levels.

Neelamegam et al. (1992) studied the strength and stiffness characteristics of various types of composite laminates such as FRP, ferrocement, polymer impregnated glass fibre reinforced mortar, glass impregnated glass fibre reinforced resin mortar and polymer impregnated glass fibre reinforced ferrocement. Highly reinforced ferrocement exhibited high strength and ductility followed closely by FRP. Dattatreya et al. (1993) investigated the applicability of externally bonded plates/laminates towards strengthening RC beams in distress. The beams subjected to varying degrees of initial distress were strengthened with ferrous as well as non-ferrous plates/laminates and tested to destruction. The performance of the beams was evaluated in terms of strength, stiffness, failure modes, ductility and cracking behaviour. The results showed that distressed beams, strengthened with steel plates exhibited marked improvement in strength capacity when compared to unrepaired plated beams but with loss in ductility; distressed beams strengthened with composite laminates exhibited the same or slightly lower flexural capacity when compared with unrepaired plated beams but with considerable improvement in ductility.

Ganga Rao and Vijay (1998) evaluated the increase in flexural strength of RC beams with CFRP wrapping. They reported that beams strengthened with CFRP wrapping carried higher applied load; no de-bonding was observed at failure; CFRP wrapping resulted in a gradual plastic strain increase in steel bars; increase in ultimate strength was higher for beams with a lower percentage of steel reinforcement.

Shahawy and Beitelman (1999) presented an experimental and analytical study involving the static and fatigue performance of reinforced concrete beams strengthened with externally bonded carbon fibre reinforced plastic (CFRP) sheets. They compared with the standard section and equivalent sections with two and three layers of CFRP involving the improvements in fatigue behaviour, stiffness, and capacity. The results from the fatigue study indicated that fatigue life of reinforced concrete beams could be significantly extended through the use of externally bonded CFRP laminates.

Aprile, Limkatanyu and Spacone (2001) investigated the stiffness, the load capacity and the failure modes of RC members strengthened in bending with bonded steel or CFRP thin plates. They predicted the behaviour of the strengthened beams, a displacement-based fiber beam model including bond slip. The authors proposed a model to confirm and investigate distinct failure modes observed in experimental investigations. They also studied the role of bond slip and bond failure in RC shallow beams strengthened with either steel or CFRP thin plates.

Alagusundaramoorthy et al. (2002) investigated the effectiveness of externally bonded CFRP sheets and fabrics in enhancing the flexural and shear strength of concrete beams. They concluded that appreciable enhancement in flexural strength and shear strength can be achieved using externally epoxy bonded CFRP sheets and fabric. They also presented an analytical procedure for predicting the flexural behaviour of CFRP strengthened concrete beams and compared them with the experimental results.

Pham and Al-Mahaidi (2004) investigated the effectiveness of available prediction models for the strength of FRP retrofitted RC beams. They predicated the mechanism of flexural failure, debonding at ends or midspan. The authors compared the results with experimental database of RC beams from literature survey and concluded that beam theory can be used to predict the full composite action of beams strengthened with FRP.

Islam et al. (2005) studied the shear strengthening of RC deep beams using externally bonded FRP systems. They carried out strengthening process only in the shear span across the potential failure plane. The parameters investigated were the size of the grid bars and orientation of the grid system and the method of bonding. They predicted that the growth of diagonal crack widths depends upon the reinforcement ratio, orientation of placement and on bond characteristics.

Xiong et al. (2007) tried to device a way for preventing tension delamination of concrete cover in midspan of FRP strengthened beams by combining CFRP and GFRP sheets at midspan of a beam. They have concluded that the hybrid CF/GF reinforced polymer strengthening could not only prevent the tension delamination of the bottom concrete cover, but also lead to a significant increase of deformation capacity of the strengthened beams at a very low cost compared to CFRP strengthening.

Research Significance

Studies on the behaviour of FRP plated RC beams are very essential for arriving at effective rehabilitation, retrofit and strengthening strategies for the aging infrastructure of the world. The beams used in construction works have different steel reinforcement ratios and hence behave differently when strengthened with FRP plating. The study considered beams having different internal steel reinforcement ratios and would be helpful for anticipating/ predicting the performance of real world beams when strengthened with FRP plating. The regression equations would be helpful in quick estimation of the performance characteristics of FRP plated beams before installation of the FRP plating.

Experimental Investigation Materials

Cement concrete having characteristic compressive strength of 23.54 MPa was used for casting the beams. The longitudinal steel reinforcement was provided using Fe 415 grade steel rods and shear stirrups were provided using Fe 250 grade steel rods of 8 mm diameter. The tensile steel reinforcements were provided at three different levels of 0.419%, 0.603% and 0.905% of the gross cross sectional area of the beam.

The FRP plates were manufactured using Chopped Strand Mat (CSM) fibres (75 mm length and 16 micron diameter) and Woven Rovings fibres. The plate thicknesses were 3 mm and 5 mm. The properties of FRP used for the experimental work were tested in an independent laboratory and listed in Table 1.

Specimens

A total of fifteen reinforced concrete beams were cast with three different levels of longitudinal steel reinforcement. Beams provided 0.419%, 0.603% and 0.905% steel reinforcement were designated SR1, SR2 and SR3 beams respectively. Each type of beam had five specimens, one without plating and four with GFRP plating of 3 mm or 5 mm thickness. The specimen details are presented in Table 2. The reinforcement details for the beam sections are presented in Figs. 1 to 3.

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FRP Plating

The beams soffits were cleaned and GFRP plates were bonded using epoxy adhesive. The GFRP plates consisted of Woven Rovings and Chopped Strand Mat fibres and were 3 mm or 5 mm in thickness. Four beams from each steel ratio were bonded with FRP plates and the remaining were tested without any plating to serve as reference specimens. Fig. 4 shows the application of GFRP plate to beam soffit. The beams were cured for seven days to permit the epoxy adhesive to gain strength before testing.

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Testing of Beams

The beams were tested under four point bending by applying two equal loads dividing the span into three equal parts. Deflectometers were fixed at the mid span and below the loading points to measure the deflection. Two deflectometers were fixed on top of the beam near a support at a spacing of 100 mm in order to measure the curvature. A large dial deflection gauge was fixed beneath the centre point of the beam to measure the large deflections beyond yield stage. The load was applied through a hydraulic jack placed on top of a spreader beam. The test setup is shown in Fig. 5.

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The strains near top and bottom of the beam were measured using demec gauge with four measuring pins located at every 200 mm distance. The loading was applied monotonically at increments of 2500 N and all deflection readings were measured for each load increment. The extension at rebar level and compression at top of the beam were measured using the DEMEC gauge. The readings on the two dial gauges placed on top surface of the beam over support section were also taken.

The failure of reference beams without any GFRP plating was preceded by high levels of deformation after yield point. But, the failure of GFRP plated beams was observed to be due to one of the following reasons: delamination, ripping of cover concrete along with GFRP plate or fracture of laminate.

Results and Discussion

The load-deflection curves for the beams are shown in Figs. 6 to 8. In all the cases, the beams with GFRP plating reached higher load levels. The stiffness of the GFRP plated beams was higher than that of the unplated beams, resulting in higher load carrying capacity at lower deformation levels.

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The summary of salient load-deflection results is presented in Table 3. Specimens bonded with 3mm thick CSM GFRP showed first cracks at 17.17 kN, 26.96 kN and 22.07 kN (increase of 0.00%, 57.14% and 28.57% over the corresponding reference specimens) and those with 5 mm thick CSM GFRP laminate showed first cracks at 24.53 kN, 24.53 kN and 46.60 kN (increase of 42.85%, 42.85% and 90.00% over the corresponding reference specimens), where the three sets of data correspond to three steel reinforcement percentages of 0.419%, 0.603% and 0.905% respectively.

In the case of 3mm thick WR GFRP plated beams, the first crack loads showed increase of 71.43%, 114.29% and 70.00% over the corresponding reference specimens. The increase was 100.00%, 185.71% and 120.00% for 5mm thick WR GFRP laminates, the triplet data representing steel reinforcement ratios of 0.419%, 0.603% and 0.905%. Increasing thickness of GFRP plating resulted in increase in the first crack load.

The beams SR1CSM3, SR2CSM3 and SR3CSM3, with 3 mm CSMGFRP plating, exhibited increase in yield loads by 28.57%, 21.43% and 40.00% compared to the beams SR1, SR2 and SR3 respectively. The 3 mm thick WRGFRP plated beams of SR1WR3, SR2WR3 and SR3WR3 showed increase in yield load by 57.14%, 42.86% and 103.33% respectively. The 5 mm CSMGFRP plated beams SR1CSM5, SR2CSM5 and SR3CSM5 increase in yield load was 128.57%, 28.57% and 60.00% compared to the beams SR1, SR2 and SR3 respectively. The 5 mm thick WRGFRP plated beams of SR1WR5, SR2WR5 and SR3WR5 showed increase in yield loads by 200.00%, 64.29% and 60.00% respectively. The application of GFRP plating resulted in higher yield load for all steel ratios. The effect of plating was very high on specimens with the lowest steel reinforcement ratio of 0.419%. The increase in yield load was higher for WR GFRP plated beams when compared to the CSM GFRP plated beams.

The yield deflection values exhibited higher reductions with increasing GFRP plate thickness. Plating with CSMGFRP laminates resulted in less deflection compared to plating with WRGFRP. This might not be taken as an indication of increase in stiffness value of CSMGFRP plated beams, since the yield loads attained by these beams are much lower than those attained by WRGFRP plated beams.

Thickness of GFRP is a major parameter influencing the ultimate strength of beams. Applying 3 mm thick GFRP laminate on specimens with steel reinforcement ratios of 0.419%, 0.603% and 0.905% resulted in 7.13%, 29.43% and 3.84% increase in strength for CSM plated beams and in 71.40%, 76.49% and 23.07% increase in strength for WR plated beams. Applying 5 mm thick GFRP on specimens with steel ratios of 0.419%, 0.603% and 0.905% resulted in 42.84%, 47.06% and 26.91% increase in strength for CSM plated beams and in 85.70%, 111.78% and 65.38% increase in strength for WR plated beams.

The results indicate that the application of GFRP provides effects similar to the provision of more percentage of internal steel reinforcement on strength. The percentage of increase in ultimate strength is more significant for beams having lower steel ratio than for those having higher steel ratio. The application of Woven Rovings fibre reinforced laminate resulted in higher ultimate strength values compared to Chopped Strand Mat (CSM) reinforced laminates. The results indicate that the distinction in fibre types is significant at lower steel ratios and lower thickness levels of laminate. As both tensile steel ratio and GFRP plate thickness increased, the differences arising out of laminate types vanished.

The results indicate that the increase in steel reinforcement leads to increase in strength. But the amount of increase is more pronounced for un-plated specimens. As the thickness of GFRP plate increased, the percentage increase in load carrying capacity achieved has exhibited significant reduction. Similarly, CSM laminated specimens showed more sensitivity to increase in steel reinforcement ratio compared to WR laminated specimens.

Table 4 shows the deflection and energy ductility values. In the case of unplated beams, increase in steel reinforcement ratio resulted in higher deflection ductility values. But, in the case of GFRP plated beams, the deflection ductility values showed a reduction or very meagre increase. Substantial increases in deflection ductility values are noted only for 3 mm thick CSMGFRP plated beams.

The beams SR1CSM3, SR1CSM5, SR1WR3 and SR1WR5 showed increase in deflection ductility by 50.57%, 56.01%, 4.86% and 64.49% respectively over the control beam SR1. The beams SR2CSM3, SR2CSM5, SR2WR3 and SR2WR5 with 0.603% steel reinforcement exhibited increase in deflection ductility values by 13.58%, 42.67%, 15.20% and 35.16% respectively over the control beam SR2. For the beams SR3CSM3, SR3CSM5, SR3WR3 and SR3WR5 having 0.905% steel reinforcement showed increase in deflection ductility by 12.39%, 30.30%, 16.77% and 52.24% respectively over the beam SR3.

Energy ductility was higher for beams with thicker GFRP plating. The beams SR1CSM3, SR1CSM5, SR1WR3 and SR1WR5 having steel ratio of 0.419% resulted in 73.47%, 116.55%, 29.02% and 110.37% increase in energy ductility compared to the beam SR1. For beams SR2CSM3, SR2CSM5, SR2WR3 and SR2WR5 with steel ratio of 0.603% exhibited 31.26%, 68.06%, 33.60% and 95.43% increase in energy ductility over the beam SR2. For the beams SR3CSM3, SR3CSM5, SR3WR3 and SR3WR5 having the highest level of steel reinforcement at 0.905%, the increase in energy ductility amounted to 38.79%, 51.46%, 38.61% and 141.63% over the beam SR3.

The results indicate that energy ductility is clearly influenced by the thickness of GFRP plating, exhibiting higher levels of increase for higher thickness of plating. This is contrary to the case of deflection ductility where the influence of plate thickness was not so categorically exhibited. This means that the application of GFRP plating contributes to the increase in strength as well as deflection capacities in combination. Yield ductility, which depends only on deflection values, does not show as much improvement as the energy ductility in response to applied thickness of GFRP plating.

Regression Modelling

Linear regression analysis was carried out for predicting the load and deflection values at service, yield and ultimate stages. The regression equation for ultimate load was modelled on the one proposed in section 9.6 of ACI 440.2R. Equations for other parameters were modelled with steel reinforcement ratio, type of FRP and thickness of FRP as parameters.

Regression Equation for Ultimate Load

The equation presented in ACI 440.2R for determination of nominal moment carrying capacity is:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

But, the equation proposed in this study considers a modification of the above equation by splitting it into two separate components, viz., contribution of steel for strength and contribution of FRP for strength. The reduction factor [psi].sub.f] is removed and two regression coefficients are introduced into the above equation to make the predictions more reflective of the experimental results. The equation for ultimate strength after regression analysis is,

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The constant [kappa], with value of 6/2.8x106), was introduced to convert the bending moment (in Nmm units) into load value (in kN unit) on a beam having 2.8m span under 2 point loading. The root mean squared error was 11.9 (18.64%) and fitness was 0.606. Fig. 9 and Table 5 show the experimental results against prediction of regression equation.

Regression Equations Parameters other than Ultimate Strength

Regression equations for parameters other than ultimate load carrying capacity were prepared with percentage steel ratio ([R.sub.s]), thickness of GFRP plate ([f.sub.t]) and type of GFRP ([F.sub.t]) as independent parameters. These equations are presented in Table 6 along with the fitness and RMS Error values. Figures 10.a to 10.m show the plots of the regression predictions against experimental values for the parameters under consideration.

These regression equations can be used for estimating performance parameters based on known input values.

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Conclusions

The performance of GFRP plated RC beams increased with regard to strength and deformation capacity. The following salient conclusions are drawn from the present investigation:

i. The ultimate load for 3 mm GFRP plated RC beams increased by a maximum of 40% for CSMGFRP plated beams and by 103% for WRGFRP plated beams, when compared to the reference beams.

ii. Thickness of GFRP had an influence on the performance of the GFRP plated RC beams. The ultimate load increased by a maximum of 76.49% and 111.78% for 3mm and 5mm thick WRGFRP plated beams.

iii. The steel reinforcement ratio affected the strength of beams by 85.07%, 80.00%, 33.33%, 65.00%, 65.38% for unplated, 3mm CSMGFRP plated, 3mm WRGFRP plated, 5mm CSMGFRP plated and 5mm WRGFRP plated beams.

iv. The type of GFRP influenced the performance of the GFRP plated beams. WRGFRP resulted in better performance when compared to CSMGFRP of the same thickness.

v. Deflection ductility values for beams with steel ratio of 0.419% showed increase up to 64.49% over the corresponding reference beams.

vi. Energy ductility values increased by up to 116.55%, 95.43% and 141.63% for 5 mm thick GFRP plated beams having steel ratios of 0.419%, 0.603% and 0.905% respectively.

vii. The regression equations proposed as part of this study will help estimate the performance of GFRP plated RC beams.

Notations

[A.sub.f] - Area of FRP plate

A.sub.s - Area of steel reinforcement

c - Compressive stress in concrete

d - Effective depth of beam

[f.sub.f - Permissible stress in FRP plate

[f.sub.s] - Permissible stress in steel

[F.sub.t] - Type of GFRP; 1 for CSM; 2 for WR

h - Overall depth of beam

[M.sub.n] - Nominal bending moment

[P.sub.u] - Ultimate load on the beam

[R.sub.f] - Reinforcing steel ratio

[t.sub.f] - Thickness of GFRP

[[beta].sub.1] - Rectangular stress block parameter to describe actual non-linear stress distribution in concrete; (Section 10.2.7.3 of ACI 318-99)

[kappa] - Parameter which converts moment value (Nmm) into two point load (kN) on a beam having 2.8m length; (value is 6/2.8e6)

References

[1] ACI Committee 440 (1996), State-of-the-Art Report on Fibre Reinforced Plastic (FRP) Reinforcement for Concrete Structures, American Concrete Institute, Farmington Hills, Michingam, USA.

[2] Quantrill, R.J., Hollaway, L.C. and Throne, A.M. (1996), Experimental and Analytical Investigation of FRP Strengthened Beam Response: Part I, Magazine of Concrete Research, 48(177), 331-342

[3] Taheri. F, Shahin, K and Widiarsa, I, (2002), On the Parameters Influencing the Performance of Reinforced Concrete Beams Strengthened with FRP Plates, Composite Structures, 58, 217-226.

[4] Xiong, G.J., Jiang, X., Liu, J.W., and Chen, L., (February 2007), A way for preventing tension delamination of concrete cover in midspan of FRP strengthened beams, Journal of Construction and Building Materials, Volume 21 issue2, 402-408.

[5] Ashour, A.F, El-Refaie, S.A and Garrity, S.W, (2004), Flexural Strengthening of RC Continuous Beams using CFRP Laminates, Cement and Concrete Composites, 26, 765-775.

[6] Tavakkollzadeh, M. and Saadatmanesh, H., (2003), Strengthening of Steel-Concrete Composite Girders using Carbon Fiber Reinforced Polymer Sheets, Journal of Structural Engineering, ASCE, 129(1), 30-40.

[7] Alex Li, Jules Assih and Yves Delmas (2001), Shear Strengthening of RC Beams with Externally Bonded CFRP Sheets, Journal of Structural Engineer, ASCE, 127(4) 374-380.

[8] Alkhrdaji, T., Wideman, M.A., Belarbi, A. and Nanni, A., (2001), Shear Strength of GFRP RC Beams and Slabs, Proc., CCC 2001, Proceedings in Composites in Construction, Porto, Portugal, Oct. 10-12, 409-414.

[9] Khaled A. Soudki and Ted G. Sherwood, (2000), Behaviour of reinforced concrete beams strengthened with carbon fibre reinforced polymer laminates subjected to corrosion damage, Can. J. Civ. Eng./Rev. Can. Genie Civ., 27(5), 1005-1010.

[10] Alagusundaramoorthy, P., Harik, I.E. and Choo, C.E. (2002), Strengthening of Concrete Beams using CFRP Sheets and Fabrics, Proceedings of the International Conference on Reinforced Plastics, ITI Madras, Chennai, February, 139-145.

[11] Albrecht, P. (1987), Fatigue Strength of Adhesively Bonded Cover Plates, Journal of Structural Engineering, ASCE, Vol. 113, No. 6, June, 12361250.

Pannirselvam N.

Senior Lecturer, VIT University

Research Scholar, Department of Structural Engg.

Annamalai University, Annamalainagar--608002, India

E-mail: selvampannir@yahoo.com

Ragunath P.N. and Suguna K.

Professor, Department of Structural Engg.

Annamalai University, Annamalainagar--608002, India

E-mail: Pnr_ks@yahoo.com

Table 1: Properties of GFRP Laminates Sl. Type of Fibre in Thickness Tensile No. GFRP (mm) Strength (MPa) 1. Chopped Strand Mat 3 126.20 2. Chopped Strand Mat 5 156.00 3. Woven Rovings 3 147.40 4. Woven Rovings 5 178.09 Sl. Type of Fibre in Ultimate Elasticity No. GFRP Elongation (%) Modulus (MPa) 1. Chopped Strand Mat 1.69 7467.46 2. Chopped Strand Mat 1.37 11386.86 3. Woven Rovings 2.15 6855.81 4. Woven Rovings 1.98 8994.44 Table 2: Specimen Specification Sl. Beam % Steel Type of Thickness of No. Designation Reinforcement GFRP GFRP 1. SR1 0.419 -- -- 2. SR1CSM3 0.419 CSM 3 3. SR1CSM5 0.419 CSM 5 4. SR1WR3 0.419 WR 3 5. SR1WR5 0.419 WR 5 6. SR2 0.603 -- -- 7. SR2CSM3 0.603 CSM 3 8. SR2CSM5 0.603 CSM 5 9. SR2WR3 0.603 WR 3 10. SR2WR5 0.603 WR 5 11. SR3 0.905 -- -- 12. SR3CSM3 0.905 CSM 3 13. SR3CSM5 0.905 CSM 5 14. SR3WR3 0.905 WR 3 15. SR3WR5 0.905 WR 5 Sl. Beam Composite Ratio No. Designation (Area of FRP / Area of Steel) 1. SR1 -- 2. SR1CSM3 2.387 3. SR1CSM5 3.979 4. SR1WR3 2.387 5. SR1WR5 3.979 6. SR2 -- 7. SR2CSM3 1.562 8. SR2CSM5 2.653 9. SR2WR3 1.592 10. SR2WR5 2.653 11. SR3 -- 12. SR3CSM3 1.231 13. SR3CSM5 2.051 14. SR3WR3 1.231 15. SR3WR5 2.051 Note: CSM--Chopped Strand Mat; WR--Woven Rovings Table 3: Loads, Deflections and Crack Width at Salient Stages Sl. Specimen First Yield Ultimate Deflectio No. Designation Crack Load Load n at First Load (kN) (kN) Crack (kN) (mm) 1. SR1 17.17 17.17 34.34 4.52 2. SR2 17.17 34.34 41.69 3.29 3. SR3 24.53 36.79 63.77 3.75 4. SR1CSM3 17.17 22.07 36.79 3.38 5. SR2CSM3 26.98 41.69 53.96 5.09 6. SR3CSM3 22.07 51.50 66.22 4.52 7. SR1CSM5 24.53 39.24 49.05 6.55 8. SR2CSM5 24.53 44.15 61.31 3.89 9. SR3CSM5 46.60 58.86 80.93 7.51 10. SR1WR3 29.43 44.15 58.86 7.77 11. SR2WR3 36.79 49.05 73.58 6.32 12. SR3WR3 41.69 74.80 78.48 7.47 13. SR1WR5 34.34 51.50 63.77 7.39 14. SR2WR5 49.05 56.41 88.29 11.72 15. SR3WR5 53.96 58.86 105.46 9.2 Sl. Specimen Yield Ultimate Crack Maximu No. Designation Deflection Deflection Width m Width (mm) (mm) at (mm) Yield (mm) 1. SR1 11.17 30.20 0.12 1.20 2. SR2 10.91 33.70 0.36 1.04 3. SR3 10.40 33.89 0.12 0.90 4. SR1CSM3 8.04 32.73 0.14 1.00 5. SR2CSM3 9.64 33.82 0.16 0.64 6. SR3CSM3 9.57 35.05 0.20 0.40 7. SR1CSM5 8.44 35.60 0.18 0.60 8. SR2CSM5 8.43 37.15 0.28 0.52 9. SR3CSM5 9.11 38.68 0.10 0.54 10. SR1WR3 11.58 32.83 0.36 0.82 11. SR2WR3 9.85 35.05 0.12 0.66 12. SR3WR3 9.86 37.52 0.30 0.54 13. SR1WR5 7.98 35.49 0.24 0.62 14. SR2WR5 10.63 44.38 0.06 0.58 15. SR3WR5 9.20 45.64 0.08 0.52 Table 4: Deflection and Energy Ductility Values Sl. No. Specimen Deflection Energy Deflection Designation Ductility Ductility Ductility Ratio 1. SR1 17.17 17.17 34.34 2. SR2 17.17 34.34 41.69 3. SR3 24.53 36.79 63.77 4. SR1CSM3 17.17 22.07 36.79 5. SR2CSM3 26.98 41.69 53.96 6. SR3CSM3 22.07 51.50 66.22 7. SR1CSM5 24.53 39.24 49.05 8. SR2CSM5 24.53 44.15 61.31 9. SR3CSM5 46.60 58.86 80.93 10. SR1WR3 29.43 44.15 58.86 11. SR2WR3 36.79 49.05 73.58 12. SR3WR3 41.69 74.80 78.48 13. SR1WR5 34.34 51.50 63.77 14. SR2WR5 49.05 56.41 88.29 15. SR3WR5 53.96 58.86 105.46 Sl. No. Specimen Energy Ductility Designation Ratio 1. SR1 4.52 2. SR2 3.29 3. SR3 3.75 4. SR1CSM3 3.38 5. SR2CSM3 5.09 6. SR3CSM3 4.52 7. SR1CSM5 6.55 8. SR2CSM5 3.89 9. SR3CSM5 7.51 10. SR1WR3 7.77 11. SR2WR3 6.32 12. SR3WR3 7.47 13. SR1WR5 7.39 14. SR2WR5 11.72 15. SR3WR5 9.2 Table 5: Experimental Results and Regression Predictions for Ultimate Load Beam Designation Experimental Regression Results (kN) Predictions (kN) SR1 34.34 30.09 SR2 41.69 52.31 SR3 63.77 67.38 SR1CSM3 36.79 46.13 SR2CSM3 53.96 62.41 SR3CSM3 66.22 74.32 SR1CSM5 49.05 66.23 SR2CSM5 61.31 77.24 SR3CSM5 80.93 85.79 SR1WR3 58.86 44.85 SR2WR3 73.58 61.53 SR3WR3 78.48 73.68 SR1WR5 63.77 60.06 SR2WR5 88.29 72.49 SR3WR5 105.46 82.00 Table 6: Regression equations for Prediction Parameters S.N Prediction Parameter Equation 1 First Crack 16.96 + 10.4319[R.sub.s] + Load (kN) 4.6333[F.sub.t] + 1.3450[t.sub.f] 2 First Crack 1.206 + 2.0513[R.sub.s] + Deflection (MM) 1.6822[F.sub.t] + 0.4687[t.sub.f] 3 Service Load (kN) 15.39 + 5.2144[R.sub.s] + 1.7256[F.sub.t] + 0.5379[t.sub.f] 4 Service Deflection (mm) 1.352 +1.0918[R.sub.s] + 0.4700[F.sub.t] + 0.0918[t.sub.f] 5 Yield Load (kN) 16.9 + 20.0165[R.sub.s] + 8.8544[F.sub.t] + 1.9733[t.sub.f] 6 Yield Deflection (mm) 11.98 -0.4621[R.sub.s] - 0.8867 [F.sub.t] - 0.2557[t.sub.f] 7 Crack Width at Yield 0.07057 + 0.0524[R.sub.s] + Load (mm) 0.0333[F.sub.t] + 0.0034t 8 Ultimate Deflection (mm) 130.37 2.4706[R.sub.s] 1.4433 [F.sub.t] 0.3610t 9 Maximum Crack Width 1.137 - 0.2312[R.sub.s] - 0.1289[F.sub.t] - 0.0365 [t.sub.f] 10 Deflection Ductility 2.348 + 0.3823[R.sub.s] + 0.4722 [F.sub.t] + 0.1297 [t.sub.f] 11 Energy Ductility 2.935 + 1.4903[R.sub.s] + 1.2067 [F.sub.t] + 0.3072[t.sub.f] 12 Deflection Ductility 0.7294 + 0.0618[R.sub.s] + 0.1989 Ratio [F.sub.t] + 0.0557 [t.sub.f] 13 Energy Ductility Ratio 0.5881+0.1418[R.sub.s] +0.3344 [F.sub.t]+0.0941 [t.sub.f] S.N Prediction Parameter Fitness RMS Error 1 First Crack 0.344 5.75 Load (kN) 2 First Crack 0.71 0.86 Deflection (MM) 3 Service Load (kN) 0.21 3.39 4 Service Deflection (mm) 0.47 0.40 5 Yield Load (kN) 0.49 7.32 6 Yield Deflection (mm) 0.68 0.48 7 Crack Width at Yield 0.79 0.071 Load (mm) 7.32 8 Ultimate Deflection (mm) 0.63 0.88 9 Maximum Crack Width 0.50 0.11 10 Deflection Ductility 0.73 0.22 11 Energy Ductility 0.77 0.51 12 Deflection Ductility 0.61 0.12 Ratio 13 Energy Ductility Ratio 0.66 0.19