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7. Concluding remarks
This paper has presented a closed-form solution for the whole failure process of
FRP wraps in RC beams shear-strengthened with wraps. It has been developed based
on the assumptions of a linear critical shear crack shape and the full-range behaviour
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closed-form solution has been validated by comparing its predictions with finite
element predictions. The solution is also applicable to configurations of FRP
side-strips or U-strips when a reliable anchorage system is deployed at the FRP ends
such that FRP rupture (instead of FRP debonding) dominates the final failure.
The closed-form solution is a powerful tool for understanding the behaviour of
FRP wraps. One of the major benefits is that it explicitly describes the development of
shear contribution of externally bonded FRP shear reinforcement to the shear
resistance of the RC beam as the critical shear crack widens. It may further be used
directly to evaluate the effect of the possible shear interaction between external FRP
shear reinforcement, concrete and internal steel stirrups on the shear strength of RC
beams shear-strengthened with FRP.
For RC beams shear-strengthened with FRP wraps or well-anchored FRP U- or
side strips where adverse shear interaction exists mainly between the external FRP (Vf )
and concrete (Vc) as aforementioned, a new shear strength model considering the
shear interaction between FRP and concrete can be developed based on the solution
presented in this paper. As the direct relationship between effective FRP strain and
maximum width of the critical shear crack can be established (e.g. Eqs (15) and (35)),
it can be further used to develop a new criterion of FRP strain limit by specifying a
reasonable crack width for serviceability consideration and to avoid a significant
degradation of the concrete shear resistance. A salient feature of the shear strength
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automatically considered. Such a shear strength model is being developed and will be
published in due course.
Acknowledgements
The authors acknowledge the financial support received from the National Natural
Science Foundation of China (Project Nos. 51108097, 51378130, 51578423) and
Guangdong Natural Science Foundation (Project No. S2013010013293). The authors
are also grateful for the financial support received from the Department of Education
of Guangdong Province for Excellent Young College Teacher of Guangdong Province
(Project No. Yq2013056). The first author would like to thank the China Scholarship
Council (CSC) for the scholarship awarded to him as a visiting scholar (File No.
201408440320) in the Department of Civil and Environmental Engineering,
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References
ACI-440.2R, 2008. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures. American Concrete Institute, Farmington Hills, Michigan, USA.
Ali, M.S.M., Oehlers, D.J., Seracino, R., 2006. Vertical shear interaction model between external FRP transverse plates and internal steel stirrups. Eng. Struct. 28, 381-389.
Bank, L.C., 2006. Composites for Construction: Structural Design with FRP Materials. John Wiley and Sons, Chichester, West Sussex, UK.
Bousselham, A., Chaallal, O., 2004. Shear strengthening reinforced concrete beams with fiber-reinforced polymer: Assessment of influencing parameters and required research. ACI Struct. J. 101, 219-227.
Bousselham, A., Chaallal, O., 2006a. Behavior of reinforced concrete T-beams strengthened in shear with carbon fiber-reinforced polymer - An experimental study. ACI Struct. J. 103, 339-347.
Bousselham, A., Chaallal, O., 2006b. Effect of transverse steel and shear span on the performance of RC beams strengthened in shear with CFRP. Compos. Pt. B-Eng. 37, 37-46.
Bousselham, A., Chaallal, O., 2008. Mechanisms of shear resistance of concrete beams strengthened in shear with externally bonded FRP. J. Compos. Constr. 12, 499-512.
Bousselham, A., Chaallal, O., 2009. Maximum Shear Strength of RC Beams Retrofitted in Shear with FRP Composites. J. Compos. Constr. 13, 302-314.
Cao, S.Y., Chen, J.F., Teng, J.G., Hao, Z., Chen, J., 2005. Debonding in RC beams shear strengthened with complete FRP wraps. J. Compos. Constr. 9, 417-428.
Carolin, A., Taljsten, B., 2005a. Experimental study of strengthening for increased shear bearing capacity. J. Compos. Constr. 9, 488-496.
Carolin, A., Taljsten, B., 2005b. Theoretical study of strengthening for increased shear bearing capacity. J. Compos. Constr. 9, 497-506.
CEB-FIP, 1993. CEB-FIP Model Code 1990. Thomas Telford, London, UK.
Chaallal, O., Nollet, M.-J., Perraton, D., 1998. Strengthening of RC beams by externally bonded side CFRP strips. J. Compos. Constr. 2, 111-113.
Chajes, M.J., Januszka, T.F., Mertz, D.R., Thomson, T.A.J., Finch, W.W.J., 1995. Shear strengthening of reinforced concrete beams using externally applied composite fabrics. ACI Struct. J. 92, 295-303.
Chen, G.M., 2010. Shear Behaviour and Strength of RC Beams Shear-Strengthened with Externally Bonded FRP Reinforcement, Department of Civil and Structural Engineering The Hong Kong Polytechnic University, Hong Kong, China.
Chen, G.M., Teng, J.G., Chen, J.F., 2012. Process of debonding in RC beams shear-strengthened with FRP U-strips or side strips. International Journal of Solids and Structures 49, 1266-1282.
Chen, G.M., Teng, J.G., Chen, J.F., 2013. Shear strength model for FRP-strengthened RC beams with adverse FRP-steel Interaction. J. Compos. Constr. 17, 50-66.
ACCEPTED MANUSCRIPT
Chen, G.M., Teng, J.G., Chen, J.F., Rosenboom, O.A., 2010. Interaction between Steel Stirrups and Shear-Strengthening FRP Strips in RC Beams. J. Compos. Constr. 14, 498-509.
Chen, G.M., Zhang, Z., Li, Y.L., Li, X.Q., Zhou, C.Y., 2016. T-section RC beams shear-strengthened with anchored CFRP U-strips. Compos. Struct. 144, 57-79.
Chen, J.F., Teng, J.G., 2003a. Shear capacity of fiber-reinforced polymer-strengthened reinforced concrete beams: Fiber reinforced polymer rupture. Journal of Structural Engineering-Asce 129, 615-625.
Chen, J.F., Teng, J.G., 2003b. Shear capacity of FRP-strengthened RC beams: FRP debonding. Constr. Build. Mater. 17, 27-41.
Chen, J.F., Yuan, H., Teng, J.G., 2007. Debonding failure along a softening FRP-to-concrete interface between two adjacent cracks in concrete members. Eng. Struct. 29, 259-270.
CNR-DT-200R1, 2013. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures. Advisory Committee on Technical Recommendations for Construction, National Research Council, Rome, Italy.
Concrete-Society, 2012. Design Guidance for Strengthening Concrete Structures Using Fiber Composite Materials, TR55, 3nd editon. The Concrete Society, Camberley, Surrey, UK.
Denton, S.R., Shave, J.D., Poter, A.D., 2004. Shear strengthening of reinforced concrete structures using FRP composites, in: L.C. Hollaway, M.K., Chryssanthopoulos, and S.S. J. Moy (Ed.), Proceedings, Second International Conference on Advanced Polymer Composites for Structural Applications in Construction (ACIC 2004). Woodhead Publishing Limited, Cambridge, England, University of Surrey, pp. 134-143.
fib, 2001. Externally Bonded FRP Reinforcement for RC Structures. Federation Internationale du Beton (fib), Lausanne, Switzerland.
GB50608-2010, 2010. Technical code for infrastructure application of FRP composites. Ministry of Housing and Urban-Rural Development, P.R. China, Beijing. HB305, 2008. Design Handbook for RC Structures Retrofitted with FRP and Metal Plates: Beams and Slabs. Standards Australia, GPO Box 476, Sydney, NSW, Australia.
Hollaway, L.C., Teng, J.G., 2008. Strengthening and Rehabilitation of Civil Infrastructures Using Fibre-reinforced Polymer (FRP) Composites. Woodhead Publishing Limited, Cambridge England.
Islam, M.R., Mansur, M.A., Maalej, M., 2005. Shear strengthening of RC deep beams using externally bonded FRP systems. Cem. Concr. Compos. 27, 413-420.
Jirawattanasomkul, T., Dai, J.G., Zhang, D.W., Senda, M., Ueda, T., 2013. Experimental Study on Shear Behavior of Reinforced-Concrete Members Fully Wrapped with Large Rupture-Strain FRP Composites. J. Compos. Constr. 18, 12. JSCE, 2001. Recommendations for Upgrading of Concrete Structures with Use of Continuous Fiber sheets, Concrete Engineering Series 41. Japan Society of Civil Engineers, Tokyo, Japan.
ACCEPTED MANUSCRIPT
Khalifa, A., Gold, W.J., Nanni, A., Abel-Aziz, M.I., 1998. Contribution of externally bonded FRP to shear capacity of RC flexural members. J. Compos. Constr. 2, 195-202.
Khalifa, A., Nanni, A., 2000. Improving shear capacity of existing RC T-section beams using CFRP composites. Cem. Concr. Compos. 22, 165-174.
Khalifa, A., Nanni, A., 2002. Rehabilitation of rectangular simply supported RC beams with shear deficiencies using CFRP composites. Constr. Build. Mater. 16, 135-146.
Kim, Y., Quinn, K., Ghannoum, W.M., Jirsa, J.O., 2014. Strengthening of Reinforced Concrete T-Beams Using Anchored CFRP Materials. ACI Struct. J. 111, 1027-1035. Leung, C.K.Y., Chen, Z.F., Lee, S., Ng, M., Xu, M., Tang, J.M., 2007. Effect of size on the failure of geometrically similar concrete beams strengthened in shear with FRP strips. J. Compos. Constr. 11, 487-496.
Li, A., Diagana, C., Delmas, Y., 2001. CRFP contribution to shear capacity of strengthened RC beams. Eng. Struct. 23, 1212-1220.
Li, A., Diagana, C., Delmas, Y., 2002. Shear strengthening effect by bonded composite fabrics on RC beams. Compos. Pt. B-Eng. 33, 225-239.
Li, S.W., 2015. Shear strength models of RC beams shear strengthened with complete FRP wrap or FRP U-strips with end anchorage, School of Civil and Transportation Engineering. Guangdong University of Technology, Guangzhou.
Liotta, M.A., 2006. FRP Shear Strengthening in Shear Tests and Design Equations, Department of Struct Engineering & Geotechnology. University Roma La Sapienza, Rome.
Lu, X.Z., Teng, J.G., Ye, L.P., Jiang, J.J., 2005. Bond-slip models for FRP sheets/plates bonded to concrete. Eng. Struct. 27, 920-937.
Matthys, S., 2000. Structural Behaviour and Design of Concrete Members Strengthened with Externally Bonded FRP Reinforcement, Department of Structural Engineering. University of Ghent, Belgium, Ghent.
Mofidi, A., Chaallal, O., 2011. Shear Strengthening of RC Beams with EB FRP: Influencing Factors and Conceptual Debonding Model. J. Compos. Constr. 15, 62-74. Mofidi, A., Chaallal, O., Benmokrane, B., Neale, K., 2012. Performance of End-Anchorage Systems for RC Beams Strengthened in Shear with Epoxy-Bonded FRP. J. Compos. Constr. 16, 322-331.
Monti, G., Liotta, M., 2007. Tests and design equations for FRP-strengthening in shear. Constr. Build. Mater. 21, 799-809.
Monti, G., Santinelli, F., Liotta, M.A., 2004. Mechanics of FRP shear strengthening of RC beams, 11th European Conference on Composite Materials (ECCM 11), Rhodes, Greece.
Oehlers, D.J., Seracino, R., 2004. Design of FRP and Steel Plated RC structures: Retrofitting Beams and Slabs for Strength, Stiffness and Ductility. Elsevier, UK. Park, S.Y., Namaan, A.E., Lopez, M.M., Till, R.D., 2001. Shear strengthening effect of RC beams using glued CFRP sheets, in: Teng, J.G. (Ed.), The International Conference on FRP Composites in Civil Engineering, Hong Kong, pp. 669-676.
ACCEPTED MANUSCRIPT
Pellegrino, C., Modena, C., 2002. Fiber reinforced polymer shear strengthening of reinforced concrete beams with transverse steel reinforcement. J. Compos. Constr. 6, 104-111.
Pellegrino, C., Modena, C., 2006. Fiber-reinforced polymer shear strengthening of reinforced concrete beams: Experimental study and analytical modeling. ACI Struct. J. 103, 720-728.
Pellegrino, C., Modena, C., 2008. An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams. Mech. Compos. Mater. 44, 231-244.
Priestley, M., Seible, F., Calvi, G., 1996. Seismic Design and Retrofit of Bridges. John Wiley and Sons, New York
Priestley, M.J.N., Seible, F., 1995. Design of seismic retrofit measures for concrete and masonry structures. Constr. Build. Mater. 9, 365-377.
Taljsten, B., 2003. Strengthening concrete beams for shear with CFRP sheets. Constr. Build. Mater. 17, 15-26.
Teng, J.G., Chen, G.M., Chen, J.F., Rosenboom, O.A., Lam, L., 2009. Behavior of RC Beams Shear Strengthened with Bonded or Unbonded FRP Wraps. J. Compos. Constr. 13, 394-404.
Teng, J.G., Chen, J.F., 2009. Mechanics of debonding in FRP-plated RC beams. Proc. Inst. Civil Eng.-Struct. Build. 162, 335-345.
Teng, J.G., Chen, J.F., Smith, S.T., Lam, L., 2002. FRP-Strengthened RC Structures. John Wiley and Sons, Chichester, West Sussex, UK.
Teng, J.G., Lam, L., Chen, J.F., 2004. Shear strengthening of RC beams using FRP composites. Progress in Structural Engineering and Materials 6, 173-184.
Teng, J.G., Yuan, H., Chen, J.F., 2006. FRP-to-concrete interfaces between two adjacent cracks: Theoretical model for debonding failure. International Journal of Solids and Structures 43, 5750-5778.
Triantafillou, T.C., 1998. Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites. ACI Struct. J. 95, 107-115.
Triantafillou, T.C., Antonopoulos, C.P., 2000. Design of concrete flexural members strengthened in shear with FRP. J. Compos. Constr. 4, 198-205.
Ye, L.P., Lu, X.Z., Chen, J.F., 2005. Design proposals for the debonding strengths of FRP strengthened RC beams in the Chinese design code. Iifc Secretariat, Hong Kong.