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1.
International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), pp. 305-321 IJCIET © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2012): 3.1861 (Calculated by GISI) IAEME www.jifactor.com SEISMIC RESPONSE OF FRP STRENGTHENED RC FRAME Shaikh Zahoor Khalid 1 S.B. Shinde2 1 2 P.G. Student Dept. of Civil Associate Professor Dept. of Civil Engineering, J.N.E.C., Aurangabad Engineering, J.N.E.C., Aurangabad (M.S.) India. (M.S.) India. E-mail : szahoor555@gmail.com E-mail : sb_shinde@yahoo.co.in ABSTRACT The use of fiber-reinforced plastic (FRP) materials is becoming attractive solution to retrofitting, strengthening and constructing column-like structural systems. The method is considered superior to conventional concrete and steel jacketing methods in terms of confinement strength; post-retrofit ductility, sectional area, weight, corrosion resistance; application ease and overall project costs. Axial strength and ductility increase of concrete columns is needed whenever repair and strengthening are involved. Repair may be required when columns are damaged under excessive external loads or due to erosion in exposed environments. Strengthening may be required when there is a change of structural use or removal of some adjacent load bearing structural members. Concrete jacketing, though has a lower cost, simply adds weight and cross sectional area to the original structure and may be undesirable. On the contrary, FRP composites, initially developed for aerospace and automobile applications, are found to be a very promising material for civil engineering applications because of their high strength/weight ratio, high corrosion resistance, ease of installation, and relatively low cost of maintenance. The aim of the present research was to recover the structural properties that the Frame had before the seismic action by providing both column and beams cracks with FRP laminate and to prove that FRP can be used for retrofitting for cracked sections. The driving principals in the design and the outcomes of the study are presented in the paper. Comparisons between original and repaired structures are discussed in terms of global and local performances. In addition to the validation of the proposed technique, the results will represent a reference database for the development of design criteria for the seismic repair of RC frames using FRP. Keywords: Fiber reinforced plastic (FRP), Axial Strength, Concrete Jacketing, Retrofitting, 305
2.
International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME 1. INTRODUCTION Fiber-reinforced plastic (FRP) confined concrete under static axial, flexural and cyclic or seismic lateral loads have been under investigation to develop retrofit technologies and new construction methods. Over the past twenty years, a few models were developed for FRP confined concrete. No one model can be applied directly for design with confidence. Moreover, all models for the prediction of ultimate strength of the hybrid column are developed based on the first confinement model that is developed by Richart et al. in 1927. The only changes were the difference in constant coefficient and the power coefficient corresponding to the confining pressure. They are all developed from regression analysis of the researchers’ experimental data. A few stress-strain relationships were also developed so as to model the load-deformation behavior of the confined concrete. These models mainly relied on previously developed models for concrete or soil behaviors under triaxial stresses or confinement stresses. Subsequent modifications were made to fit in the use of FRP confinement.[1-7] Finally, it should be pointed out that all these models are only valid, if accurate, for the use of FRP encased concrete construction method, but not for retrofitting or strengthening of concrete. The reason is that from the preceding experiments, FRP were used to wrap on sound concrete instead of cracked concrete, which can have a very different behavior upon initial loading. The FRP materials were also wrapped on initially unstressed concrete specimens. When the specimens were prepared and loaded, both concrete and FRP were stressed together from scratch. In reality, for the case of strengthening or retrofitting, concrete columns are already under stress. The FRP is used to wrap around stressed columns afterwards. The strength increase by FRP confinement may or may not be the as much as predicted because the Poisson’s ratio of damaged concrete is much larger than that of concrete stressed in the elastic region, hence activating the FRP confinement much earlier than one might expect due to substantial radial dilation. Plastic zone of concrete is entered not long after additional loading after wrap. Ultimate strain will definitely be different in this case. [9-12] Amirr M Malik, Hamid Saadatmanesh[8] presented analytical models to calculate the stresses in the strengthened beams, and the shear force resisted by the composite plates before cracking and after formation of flexural cracks. The anisotropic (orthotropic) behavior of the composite plates or fabric has been considered in the analytical model. The companion paper extends this discussion into post cracking behavior at the ultimate load, where the diagonal shear cracks are formed. The method has been developed assuming perfect bond between FRP and concrete (i.e. no slip), and using compatibility of the strains in the FRP and the concrete beam. Amer M. Ibrahim, Mohammed Sh. Mahmood[13] presented an analysis model for reinforced concrete beams externally reinforced with fiber reinforced polymer (FRP) laminates using finite elements method adopted by ANSYS. The finite element models are developed using a smeared cracking approach for concrete and three dimensional layered elements for the FRP composites. The results obtained from the ANSYS finite element analysis are compared with the experimental data for six beams with different conditions from researches (all beams are deficient shear reinforcement). The comparisons are made for load-deflection curves at mid-span; and failure load. The results from finite element analysis were calculated at the same location as the experimental test of the beams. Baris Binici, Guney Ozcebe, Ramazan Ozcelik[14] Proposed that an urgent need to retrofit deficient mid-rise reinforced concrete (RC) frame buildings in Turkey. For this purpose, an efficient FRP retrofit scheme has been developed previously, in which hollow clay brick infill walls can be utilized as lateral load resisting elements after retrofitting. The 306
3.
International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME main premise of this practical retrofit scheme was to limit inter-storey deformations by FRP strengthened infill walls that are integrated to the boundary frame members by means of FRP anchors. Based on the analytical model that was previously verified extensively by comparison with test results, a simplified model was proposed for use in displacement based design of FRPs for deficient RC frame buildings. Researchers have been going on in the last two decades in the United States, Canada, Japan, Singapore, and some other countries. Significant contributions were mainly founded in the past ten years in the US and Japan. Besides the above mentioned studies there have been several studies on FRP, all these studies are based on testing columns under different load conditions or testing beams under different load conditions. Experimental testing and analytical models have been studied but differently for beams and columns and not as a single unit i.e RC frame. Hence there is a gap in knowledge of the behaviour of FRP wrapped RC frame when studied as a unit [15-16]. 2. PRESENT STUDY This paper presents findings of a programme where RC frame has been analysed using finite element analysis in STAAD PRO software. Different number of models with different thicknesses of FRP has been made and results have been compared for various location of cracks. 2.1 Design Parameters Considered:- Beam cross Section: 300mmx500mm Column Cross Section: 300mmx500mm Beam length: 5m Column Length: 4m (Floor to Floor) Diameter of Steel Bar: 20mm Thickness of FRP Sheet: 1mm 2.2 Material Constants :- a. Concrete: Density= 25kn/m3 Elasticity= 2.5x107kn/m2 Poisson’s Ratio=0.15 b. Steel: Density= 78.5kn/m3 Elasticity= 2.1x108 kn/m2 Poisson’s Ratio=0.15 c. FRP: Density= 16kn/m3 (As per ACI 440.2R-02) Elasticity= 3.6 x107kn/m2 Poisson’s Ratio=0.17 2.3 Method of Analysis:- Different frame models namely 2bay 3storey and 3 bay 5 storey are made using STAAD.PRO.V8i software and are analysed for different crack locations and various thicknesses of FRP. Line models of 2bay 3storey and 3bay 5storey can be seen in fig 1 and fig 2 respectively. For analysis purpose each frame model i.e. 3bay 5Storey and 2bay 3storey is distinguished into three groups namely Model I, Model II and MODELIII depending upon the different crack patterns. Each group consists of • Sound RC Frame 307
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME • RC Frame Cracked During Earthquake Load • RC Frame Retrofitted Using FRP Laminate Fig. 1: 2 Bay 3 Storey line Model Fig. 2: 3 Bay 5 Storey line Model 2.4 3Bay 5Storey:- In order to validate the numerical representation of the reinforced concrete beams and columns strengthening with Fiber Reinforced Plastic (FRP), lateral loading is considered for each storey for the analysis of Frame. Results and comparisons are based on this analysis. For the present paper the analysis is done at different crack location and the thickness of FRP used for wrapping the cracked section is 1mm. Three different frame models with different crack location will be analysed using the proposed STAAD PRO finite element analysis. Model I A) Sound RC frame: This is a solid RC frame which is subjected to design lateral loads on each storey. The analysis of the behaviour of this frame for the stresses developed and storey displacement due to the applied lateral load is observed. Refer Fig. 3 Fig. 3 : Sound RC Frame B) RC frame cracked due to earthquake load: This frame consists of three different cracks developed due to lateral load. The first crack at an integration point is shown with a red circle outline, the second crack with a green outline and the third crack with a pink outline.(refer fig4).The analysis of the behaviour of this frame for the stresses developed and storey displacement due to the applied lateral load is observed. This frame consists of three different cracks developed due to lateral load. The first crack at an integration point is shown with a red circle outline, the second crack with a green outline and the third crack with a pink outline.(refer fig4).The analysis of the Fig. 4 : R.C. Frame Cracked behaviour of this frame for the stresses developed and storey During Earthquake Load displacement due to the applied lateral load is observed. (Pattern I) 308
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME C) RC frame retrofitted by FRP laminate: In this frame the cracked sections mentioned in the above frame are wrapped using 1mm thick FRP laminate. The cracked sections are wrapped as a single unit long the periphery. Again the analysis of the behaviour of this frame for the stresses developed and storey displacement due to the applied lateral load is observed. Refer Fig. 5 Fig. 5: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern I) The stress pattern and storey displacement obtained from the analysis of RC frame cracked due to earthquake load and RC frame retrofitted by FRP laminate are compared with the stress pattern and storey displacement obtained from the analysis of Sound RC frame. As the frames of Model I are analysed and compared, similar analysis and comparison is done for Model II and Model III frames for different crack locations. The Sound RC frame is same as mentioned above in Model I for both Model II and Model III. RC frame cracked due to earthquake load and RC frame retrofitted by FRP laminate for Model II is shown in fig 6a and 6b respectively, similarly RC frame cracked due to earthquake load and RC frame retrofitted by FRP laminate for Model III is shown in fig 7a and 7b respectively. Fig. 6a : R.C. Frame Cracked During Earthquake Load (Pattern II) Fig. 6b: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern II) 309
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 7a : R.C. Frame Cracked During Fig. 7b: R.C. Frame Retrofitted (Wrapped) by F.R.P. Earthquake Load (Pattern III) Laminate (Pattern III) 3. RESULT AND COMPARISON Results obtained from the different frame models for stresses and storey displacements are compared. For different crack locations, the cracks developed are in beam as well as in columns. So foe better comparison of the results the beam stresses and the column stresses are compared individually Model I 3.1 Beam Stress Pattern Comparison Fig. 8a: Sound R.C. Frame Fig.8b: R.C. Frame Cracked During Earthquake Load (Pattern I) 310
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 8c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern I) It can be seen from the beam stress pattern developed in the sound RC frame due to lateral loads (fig. 8a), these stresses are disturbed when the cracks are developed due to earthquake load (fig. 8b), and the variations in the stress pattern can be observed near the crack locations. But when the same frame i.e. RC frame cracked due to effect of earthquake load is retrofitted with FRP laminate of 1mm thickness, the original stress pattern and strength as that of the sound RC frame is regained (fig. 8c). 3.2 Column Stress Pattern Comparison Fig.9b: R.C. Frame Cracked During Earthquake Load Fig. 9a: Sound R.C. Frame (Pattern I) 311
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 9c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern I) It can be seen from the column stress pattern developed in the sound RC frame due to lateral loads (fig. 9a), these stresses are disturbed when the cracks are developed due to earthquake load (fig. 9b), and the variations in the stress pattern can be observed near the crack locations. But when the same frame i.e. RC frame cracked due to effect of earthquake load is retrofitted with FRP laminate of 1mm thickness, the original stress pattern and strength as that of the sound RC frame is regained (fig. 9c). 3.3 Storey Displacement In the table given below the storey displacement in x-direction of Sound RC frame, RC frame cracked due to earthquake load and RC frame retrofitted (wrapped) by FRP laminate are compared. z Table I: Comparison for storey displacement in x-direction for Model I Storey Displacement in x-direction (mm) Storey RC frame cracked RC frame retrofitted Sound RC frame during earthquake load by FRP laminate 0 5.281 5.283 5.281 1 36.072 36.105 36.077 2 66.764 66.848 66.777 3 92.466 93.043 92.536 4 111.369 114.533 111.711 5 122.464 134.453 123.485 From the table above it can be observed that when the lateral load is acted upon the RC frame cracked due to earthquake load, the storey displacement varies as compared to the sound RC frame. The variations of the storey displacement can be seen on the storeys where the cracks are developed in the beams or columns. In the above case the cracks are located on the 4th and 5th storey, but when the crack frame is retrofitted with FRP laminate the original 312
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME storey displacement is observed as that of sound RC frame. Considering the storey displacement the graph is plotted (fig. 10). Fig10: Storey Displacement In X-Direction Model II 3.4 Beam Stress Pattern Comparison Fig. 11a: Sound R.C. Frame Fig.11b: R.C. Frame Cracked During Earthquake Load (Pattern II) 313
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 11c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern II) 3.5 Column Stress Pattern Comparison Fig.12b: R.C. Frame Cracked During Earthquake Load Fig. 12a: Sound R.C. Frame (Pattern II) 314
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 12c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern II) 3.6 Storey Displacement In the table given below the storey displacement in x-direction of Sound RC frame, RC frame cracked due to earthquake load and RC frame retrofitted (wrapped) by FRP laminate are compared. Table II: Comparison for storey displacement in x-direction for Model II Storey Displacement in x-direction (mm) Storey RC frame cracked RC frame retrofitted Sound RC frame during earthquake load by FRP laminate 0 5.281 5.283 5.281 1 36.072 36.037 36.071 2 66.764 66.836 66.774 3 92.466 91.482 92.468 4 111.369 118.739 112.056 5 122.464 130.529 123.237 315
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig23: Storey Displacement In X-Direction Model III 3.7 Beam Stress Pattern Comparison Fig. 13a: Sound R.C. Frame Fig.13b: R.C. Frame Cracked During Earthquake Load (Pattern III) 316
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 13c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern III) 3.8 Column Stress Pattern Comparison Fig.14b: R.C. Frame Cracked During Earthquake Load (Pattern III) Fig. 14a: Sound R.C. Frame 317
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig. 14c: R.C. Frame Retrofitted (Wrapped) by F.R.P. Laminate (Pattern III) 3.9 Storey Displacement In the table given below the storey displacement in x-direction of Sound RC frame, RC frame cracked due to earthquake load and RC frame retrofitted (wrapped) by FRP laminate are compared. Table III: Comparison for storey displacement in x-direction for Model III Storey Displacement in x-direction (mm) Storey RC frame cracked RC frame retrofitted Sound RC frame during earthquake load by FRP laminate 0 5.281 5.442 5.295 1 36.072 34.887 36.010 2 66.764 70.753 67.310 3 92.466 99.872 93.459 4 111.369 118.890 112.404 5 122.464 131.520 123.677 318
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Fig35: Storey Displacement In X-Direction As the stresses in beams, stresses in columns and storey displacement are obtained and compared for Model I, similar analysis and comparison is done for Model II (fig. 11a, 11b, 11c and Fig. 12a, 12b,12c) and Model III(fig.13a, 13b, 13c and 14a, 14b, 14c ). In all the models after retrofitting the RC frame cracked due to earthquake load, the stress pattern and the strength obtained is in good agreement with that of the original sound RC frame. Similarly, the storey displacement for Model II (table 2, fig. 14) and Model III (table 3, fig. 15) can be regained for the RC frame cracked due to earthquake load after retrofitting it with FRP laminate. 4. DISCUSSION AND CONCLUSION Different techniques have been developed in order to achieve local modification of structural components. Reinforced concrete jacketing, steel profile jacketing and steel encasement have been widely used in the past. All of them were characterised by disadvantaged related to constructability (i.e. difficulty of ensuring perfect bond and collaboration between new and old parts, loss of space, construction time and high impact on building function) and durability issues. Innovative techniques based on FRP material appear to be interesting alternatives to those solutions, along with high structural effectiveness. FRP is light and easy to install, their application does not imply loss of space and in some cases it can be performed without interrupting the use of structure. This numerical solution adopted to evaluate the ultimate shear strength of RC frame wrapped with FRP laminate is a simple, cheap and rapid way compared with experimental full scale set test. The results obtained demonstrate that the use of FRP laminate is far more effective and easy than reinforced concrete jacketing and steel profile jacketing in strengthening RC frame. The present models can be used in additional studies to develop design rules for strengthening RC frame using FRP laminates. The main outcomes of the present study can be summarised as follows: 319
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International Journal of
Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME • The results confirmed that FRP laminate allowed the RC frame retrofitted, to withstand the lateral loads as the original RC frame. • RC frame retrofitted with FRP laminates showed a large displacement capacity without exhibiting any loss of strength and was able to provide energy dissipation very similar to that of the original sound RC frame. • The cyclic behaviour of RC frame retrofitted with FRP laminates was stable and no significant effect of cumulative damage was observed on the strengthened elements • FRP laminates are a better option for retrofitting because the can withstand the seismic loads. ACKNOWLEDGEMENT The authors wish to thank the Management, Principal, Head of Civil Engineering Department and staff of Jawaharlal Nehru engineering College, Aurangabad and Authorities of Dr. Babasaheb Ambedkar Marathwada University for their support. The authors express their deep and sincere thanks to Mr. Karim M. Pathan (Consulting Structural Engineer, Aurangabad) for his tremendous support and valuable guidance from time to time. REFERENCES [1] Yousef A. Al-Salloum, Hussein M. Elsanadedy, Aref A. Abadel (2011), “Behavior of FRP-confined concrete after high temperature exposure”, Construction and Building Materials, Vol.25, pp. 838-850. [2] Prof. Björn Täljsten (2007) “ Use of FRP in Construction in Scandinavia – Experiences and a Verification test”, Composites & Polycon. [3] Tim Ibell, Antony Darby, Steve Denton (2009), “Research issues related to the appropriate use of FRP in concrete structures”, Construction and Building Materials Vol.23, pp.1521-1528. [4] R.V.Balendran, T.M Rana, T.Masood and W.G.Tang (2002), “Application of FRP bars an reinforcement in civil engineering structures”, Structural Survey Vol.20, pp.62-72. [5] Khaled Soudki; Ehab El-Salakawy and Brent Craig 2007, “Behavior of CFRP Strengthened Reinforced Concrete Beams in Corrosive Environment”, Journal of Composites for Construction, Vol.11, No. 3, pp. 291-298. [6] H.W. Zhang, S.T. Smith, (2011) “FRP-to-concrete joint assemblages anchored with multiple FRP anchors”, Composite Structures, pp. 1-12. [7] L.C. Hollaway (2010), “A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties”, Construction and Building Materials Vol.24, pp. 2419–2445. [8] Amirr M Malik, Hamid Saadatmanesh (1998), “Analytical study Of Reinforced Concrete Beams With Web-Bonded Fiber Reinforced Plastic Plates or Fabrics”, ACI Structural Journal, Vol.95, No3. [9] Stephen J. Foster (1999), “Design and Detailing of High Strength Concrete Columns”, UNICIV Report No. R375, ISBN: 85841 342 6, [10] Supaviriyakit, T., Pornpongsaroj, P. and Pimanmas. (2004), “A. Finite element analysis of FRP-strengthened RC beams”, Songklanakarin J. Sci. Technol., 26(4) : pp.497-507 [11] Meisam Safari Gorji. (2009), “Analysis of FRP Strengthened Reinforced Concrete Beams Using Energy Variation Method”, World Applied Sciences Journal 6 (1), pp.105-111. 320
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Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME [12] Tavio T. Tata A. (2009), “ Predicting Nonlinear Behavior and Stress-Strain Relationship of Rectangular Confined Reinforced Concrete Columns with ANSYS”; Civil Engineering Dimension, Vol.11, No. 1, pp. 23-31. [13] Amer M. Ibrahim, Mohammed Sh. Mahmood. (2009), “Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates”, European Journal of Scientific Research, Vol.30 No.4, pp.526-541. [14] Baris Binici, Guney Ozcebe, Ramazan Ozcelik. (2007) , “Analysis and design of FRP composites for seismic retrofit of infill walls in reinforced concrete frames”, Composites: Part B 38 pp. 575–583 [15] J.G. Teng, H. Yuan, J.F. Chen. (2006), “FRP-to-concrete interfaces between two adjacent cracks: Theoretical model for de-bonding failure”, International Journal of Solids and Structures 43 pp.5750–5778. [16] C. Faella, E. Martinelli, E. Nigro. (2008), “Formulation and validation of a theoretical model for intermediate de-bonding in FRP-strengthened RC beams”, Composites: Part B 39 pp. 645–655. 321
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