Advances in concrete construction

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Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation

  • Guenaneche, B. (Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Benyoucef, S. (Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Tounsi, A. (Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Adda Bedia, E.A. (Centre of Excellence for Advanced Materials Research, King Abdulaziz University)
  • Received : 2018.07.04
  • Accepted : 2019.02.24
  • Published : 2019.05.25
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Abstract

This paper introduces a new efficient analytical method, based on shear deformations obtained with 2D elasticity theory approach, to perform an explicit closed-form solution for calculation the interfacial shear and normal stresses in plated RC beam. The materials of plate, necessary for the reinforcement of the beam, are in general made with fiber reinforced polymers (Carbon or Glass) or steel. The experimental tests showed that at the ends of the plate, high shear and normal stresses are developed, consequently a debonding phenomenon at this position produce a sudden failure of the soffit plate. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. In order to efficiently model the calculation of the interfacial stresses we have integrated the effect of shear deformations using the equilibrium equations of the elasticity. The approach of this method includes stress-strain and strain-displacement relationships for the adhesive and adherends. The use of the stresses continuity conditions at interfaces between the adhesive and adherents, results pair of second-order and fourth-order coupled ordinary differential equations. The analytical solution for this coupled differential equations give new explicit closed-form solution including shear deformations effects. This new solution is indented for applications of all plated beam. Finally, numerical results obtained with this method are in agreement of the existing solutions and the experimental results.

Keywords

References

  1. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  2. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
  3. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B, 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043
  4. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A: Mater. Sci. Proc., 123(4), 296. https://doi.org/10.1007/s00339-017-0854-0
  5. Alfredsson, K.S. and Hoberg, J.L. (2008), "A closed-form solution to statically indeterminate adhesive joint problems exemplified on ELS-specimens", Int. J. Adhes. Adhesiv., 28, 350-361. https://doi.org/10.1016/j.ijadhadh.2007.10.002
  6. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
  7. Antes, H. (2003), "Fundamental solution and integral equations for Timoshenko beams", Comput. Struct., 81(6), 383-396. https://doi.org/10.1016/S0045-7949(02)00452-2
  8. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  9. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/SEM.2018.65.4.453
  10. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  11. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/WAS.2018.27.5.311
  12. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/EAS.2018.14.2.103
  13. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  14. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  15. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  16. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/SEM.2018.65.1.019
  17. Bensaid, I. and Kerboua, B. (2017), "Interfacial stress analysis of functionally graded beams strengthened with a bonded hygrothermal aged composite plate", Compos. Interf., 24(2), 149-169. https://doi.org/10.1080/09276440.2016.1196333
  18. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  19. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/SEM.2018.66.1.061
  20. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  21. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  22. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  23. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  24. Cowper, G.R. (1966). "The shear coefficient in Timoshenko's beam theory", J. Appl. Mech., ASCE, 33(2), 335-340. https://doi.org/10.1115/1.3625046
  25. Daouadji, T., Chedad, A. and Adim, B. (2016), "Interfacial stresses in RC beam bonded with a functionally graded material plate", Struct. Eng. Mech., 60(4), 693-705. https://doi.org/10.12989/sem.2016.60.4.693
  26. Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Des., 2(1), 57-69. https://doi.org/10.12989/ACD.2017.2.1.057
  27. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  28. Edalati, M. and Fereidoon, I. (2012),"Interfacial stresses in RC beams strengthened by externally bonded FRP/steel plates with effects of shear deformation", J. Compos. Constr., ASCE, 16(1), 60-73. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000238
  29. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  30. Etman, E.E. and Beeby, A.W. (2000), "Experimental programme and analytical study of bond stress distributions on a composite plate bonded to a reinforced concrete beam", Cement Concrete Compos., 22(4), 281-91. https://doi.org/10.1016/S0958-9465(00)00030-5
  31. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  32. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036
  33. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  34. Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/CAC.2018.21.4.431
  35. Guenaneche, B., Tounsi, A. and Adda Bedia, E.A. (2014), "Effect of shear deformation on interfacial stress analysis in plated beams under arbitrary loading", Int. J. Adhes. Adhesiv., 48, 1-13. https://doi.org/10.1016/j.ijadhadh.2013.09.016
  36. Guilbeau, L. (1930), "The history of the solution of the cubic equation", Math. News Lett., 5(4), 8-12. https://doi.10.2307/3027812.
  37. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030
  38. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018d), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004
  39. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018b), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002
  40. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
  41. Hollaway, L.C. and Leeming, M.B. (1999), Strengthening of Reinforced Concrete Structures using Externally-Bonded FRP Composites in Structural and Civil Engineering. Cambridge, Woodhead Publishing Ltd., UK
  42. Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E: Lowdimens. Syst. Nanostr., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037
  43. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/SEM.2018.65.5.621
  44. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  45. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90, 479-492. https://doi.org/10.1007/s11071-017-3676-x
  46. Kolahchi, R. and Moniri Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  47. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  48. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017c), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 1099636217731071. https://doi.org/10.1177/1099636217731071.
  49. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  50. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FG-CNTreinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  51. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  52. Kreja, I. (2011), "A literature review on computational models for laminated composite and sandwich panels", Cent. Eur. J. Eng., 1(1), 59-80. https://doi.org/10.2478/s13531-011-0005-x
  53. Kurtz, S., Balaguru, P. and Helm, J. (2008), "Experimental study of interfacial shear stresses in FRP-strengthened RC beams", J. Compos. Constr., 12(3), 312-322. https://doi.org/10.1061/(ASCE)1090-0268(2008)12:3(312).
  54. Maalej, M. and Bian, Y. (2001), "Interfacial shear stress concentration in FRP strengthened beams", Compos. Struct., 54(4), 417-426. https://doi.org/10.1016/S0263-8223(01)00078-2
  55. Maalej, M. and Leong, K.S. (2005), "Effect of beam size and FRP thickness on interfacial shear stress concentration and failure mode of FRP strengthened beams", Compos. Sci. Technol., 65(7-8), 1148-1158. https://doi.org/10.1016/j.compscitech.2004.11.010
  56. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  57. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  58. Malek, A.M., Saadatmanesh, H. and Ehsani, M.R. (1998), "Prediction of failure load of R/C beams strengthened with FRP plate due to stress concentration at the plate end", ACI Struct. J., 95(1), 142-52.
  59. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw . Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443
  60. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  61. Narayanamurthy, V., Chen, J.F. and Cairns, J. (2016), "Improved model for interfacial stresses accounting for the effect of shear deformation in plated beams", Int. J. Adhes. Adhesiv., 64, 33-47. https://doi.org/10.1016/j.ijadhadh.2015.10.001
  62. Panjehpour, M., Ali, A.A.A. and Aznieta, F.N. (2014a), "Energy absorption of reinforced concrete deep beams strengthened with CFRP sheet", Steel Compos. Struct., 16(5), 481-489. https://doi.org/10.12989/scs.2014.16.5.481
  63. Panjehpour, M., Ali, A.A.A., Voo, Y.L. and Aznieta, F.N. (2014b), "Effective compressive strength of strut in CFRP-strengthened reinforced concrete deep beams following ACI 318-11", Comput. Concrete, 13(1), 135-165. https://doi.org/10.12989/cac.2014.13.1.135
  64. Rabahi, A., Adim, B., Chargui, S. and Hassaine Daouadji, T. (2015), "Interfacial Stresses in FRP-plated RC Beams: Effect of Adherend Shear Deformations", Multiphys. Model. Simul. Syst. Des. Monit., 2, 317-326.
  65. Rabinovitch, O. and Frostig, Y. (2000), "Closed-form high-order analysis of RC beams strengthened with FRP strips", J. Compos. Constr., ASCE, 4(2), 65-74. https://doi.org/10.1061/(ASCE)1090-0268(2000)4:2(65)
  66. Roberts, T.M. (1989), "Approximate analysis of shear and normal stress concentrations in the adhesive layer of plated RC beams", Struct. Eng., 67(12), 229-233.
  67. Roberts, T.M. and Haji-Kazemi, H. (1989), "Theoretical study of the behavior of reinforced concrete beams strengthened by externally bonded steel plates", Proc. Inst. Civil Eng., 87(2), 39-55.
  68. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2017), "Static, free vibration and transient response of laminated composite curved shallow panel-an experimental approach", Eur. J. Mech., A/Solid., 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  69. Shen, H.S., Teng, J.G. and Yang, J. (2001), "Interfacial stresses in beams and slabs bonded with thin plate", J. Eng. Mech., ASCE, 127(4), 399-406. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(399)
  70. Smith, S.T. and Teng, J.G. (2001), "Interfacial stresses in plated beams", Eng. Struct., 23(7), 857-871. https://doi.org/10.1016/S0141-0296(00)00090-0
  71. Stafford, S.B. and Coull, A. (1991), Tall Building Structures: Analysis and Design, Wiley, New York.
  72. Taljsten, B. (1997), "Strengthening of beams by plate bonding", J. Mater. Civil Eng., ASCE, 9(4), 206-212. https://doi.org/10.1061/(ASCE)0899-1561(1997)9:4(206)
  73. Teng, J.G., Cheng, J.F., Smith, S.T. and Lam, L. (2002a), FRPStrengthened RC Structures, West Sussex, Wiley.
  74. Teng, J.G., Cheng, J.F., Smith, S.T. and Lam, L. (2003), "Behavior and strength of FRP-strengthened RC structures: a state-of-theart review", Proc. Inst. Civil Eng., Struct. Build., 156(1), 51-62. https://doi.org/10.1680/stbu.2003.156.1.51
  75. Teng, J.G., Zhang, J.W. and Smith, S.T. (2002b), "Interfacial stresses in reinforced concrete beams bonded with a soffit plate: a finite element study", Constr. Build. Mater., 16(1), 1-14. https://doi.org/10.1016/S0950-0618(01)00029-0
  76. Timoshenko, S. and Gere, J.M. (1984), Mechanics of Materials, Van Nostrand Reinhold Co.
  77. Tounsi A. (2006), "Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate", Int. J. Solid. Struct., 43, 4154-74. https://doi.org/10.1016/j.ijsolstr.2005.03.074
  78. Tounsi, A., Hassaine, D.T., Benyoucef, S. and Adda, B.E.A. (2009), "Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations", Int. J. Adhes. Adhesiv., 29(4), 343-351. https://doi.org/10.1016/j.ijadhadh.2008.06.008
  79. Tsai, M.Y., Oplinger, D.W. and Morton, J. (1998), "Improved theoretical solutions for adhesive lap joints", Int. J. Solid. Struct., 35(12), 1163-1185. https://doi.org/10.1016/S0020-7683(97)00097-8
  80. Vilnay, O. (1988), "The analysis of reinforced concrete beams strengthened by epoxy bonded steel plates", Int. J. Cement Compos. Lightw. Concrete, 10(2), 73-78. https://doi.org/10.1016/0262-5075(88)90033-4
  81. Wu, Z.S., Yuan, H., Kojima, Y. and Ahmed, E. (2005), "Experimental and analytical studies on peeling and spalling resistance of unidirectional FRP sheets bonded to concrete", Compos. Sci. Technol., 65(7-8), 1088-1097. https://doi.org/10.1016/j.compscitech.2004.11.018
  82. Yang, J. and Wu, Y.F. (2007), "Interfacial stresses of FRP strengthened concrete beams: Effect of shear deformation", Compos. Struct., 80(3), 343-351. https://doi.org/10.1016/j.compstruct.2006.05.016
  83. Yang, Q.S., Peng, X.R. and Kwan, A.K.H. (2004), "Finite element analysis of interfacial stresses in FRP-RC hybrid beams", Mech. Res. Commun., 31(3), 331-340. https://doi.org/10.1016/j.mechrescom.2003.11.011
  84. Ye, J.Q. (2001), "Interfacial shear stress transfer of RC beams strengthened by bonded composite plates", Cement Concrete Compos., 23(4-5), 411-417. https://doi.org/10.1016/S0958-9465(01)00015-4
  85. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  86. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  87. Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO2 nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009
  88. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/SCS.2018.26.2.125

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