Structural Engineering and Mechanics

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Curvature-based analysis of concrete beams reinforced with steel bars and fibres

  • Kaklauskas, Gintaris (Department of Reinforced Concrete Structures and Geotechnics, Vilnius Gediminas Technical University) ;
  • Sokolov, Aleksandr (Laboratory of Innovative Building Structures, Vilnius Gediminas Technical University) ;
  • Shakeri, Ashkan (Department of Reinforced Concrete Structures and Geotechnics, Vilnius Gediminas Technical University) ;
  • Ng, Pui-Lam (Institute of Building Materials, Vilnius Gediminas Technical University) ;
  • Barros, Joaquim A.O. (Institute for Sustainability and Innovation in Structural Engineering, University of Minho)
  • Received : 2020.04.29
  • Accepted : 2021.11.19
  • Published : 2022.02.10
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Abstract

Steel fibre-reinforced concrete (SFRC) is an emerging class of composite for construction. However, a reliable method to assess the flexural behaviour of SFRC structural member is in lack. An analytical technique is proposed for determining the moment-curvature response of concrete beams reinforced with steel fibres and longitudinal bars (R/SFRC members). The behaviour of the tensile zone of such members is highly complex due to the interaction between the residual (tension softening) stresses of SFRC and the tension stiffening stresses. The current study suggests a transparent and mechanically sound method to combine these two stress concepts. Tension stiffening is modelled by the reinforcement-related approach assuming that the corresponding stresses act in the area of tensile reinforcement. The effect is quantified based on the analogy between the R/SFRC member and the equivalent RC member having identical geometry and materials except fibres. It is assumed that the resultant tension stiffening force for the R/SFRC member can be calculated as for the equivalent RC member providing that the reinforcement strain in the cracked section of these members is the same. The resultant tension stiffening force can be defined from the moment-curvature relation of the equivalent RC member using an inverse technique. The residual stress is calculated using an existing model that eliminates the need for dedicated mechanical testing. The proposed analytical technique was validated against test data of R/SFRC beams and slabs.

Keywords

Acknowledgement

This project has received funding from European Social Fund (Project No. 09.3.3-LMT-K-712-01-0145) under a grant agreement with the Research Council of Lithuania (LMTLT).

References

  1. Abrishambaf, A., Barros, J.A.O. and Cunha, V. (2015), "Tensile stress-crack width law for steel fibre reinforced self-compacting concrete obtained from indirect (splitting) tensile tests", Cement Concrete Compos., 57, 153-165. https://doi.org/10.1016/j.cemconcomp.2014.12.010.
  2. ACI 544.4R-88 (1988), Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Michigan.
  3. Alsayed, S.H. (1993), "Flexural deflection of reinforced fibrous concrete beams", ACI Struct. J., 90, 72-76.
  4. Amin, A. and Gilbert, R.I. (2018), "Instantaneous crack width calculation for steel fiber reinforced concrete flexural members", ACI Struct. J., 115(2), 535-543. https://doi.org/10.14359/51701116
  5. Amin, A., Foster, S.J. and Kaufmann, W. (2017), "Instantaneous deflection calculation for steel fiber reinforced concrete one way members", Eng. Struct., 131, 438-445. http://dx.doi.org/10.1016/j.engstruct.2016.10.041.
  6. Amin, A., Foster, S.J. and Muttoni, A. (2015), "Derivation of the σ-w relationship for SFRC from prism bending tests", Struct. Concrete, 16(1), 93-105. https://doi.org/10.1002/suco.201400018.
  7. Amin, A., Foster, S.J. and Watts, M. (2016), "Modelling the tension stiffening effect in SFR-RC", Mag Concrete Res., 68(7), 339-352. https://doi.org/10.1680/macr.15.00188.
  8. Amin, A., Foster, S.J., Gilbert, R.I. and Kaufmann, W. (2017), "Material characterisation of macro synthetic fibre reinforced concrete", Cement Concrete Compos., 84, 124-133. https://doi.org/10.1016/j.cemconcomp.2017.08.018.
  9. Ashour, S.A. and Wafa, F.F. (1993), "Flexural behavior of high-strength fiber reinforced concrete beams", ACI Struct. J., 90, 279-287.
  10. ASTM C1609/C1609M-12 (2012), Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam with Third-Point Loading), American Society for Testing and Materials.
  11. ASTM C496-17 (2017), Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, American Society for Testing and Material.
  12. Barros, J.A.O. and Figueiras, J. (1999), "Flexural behavior of SFRC: testing and modeling", J. Mater. Civil Eng., ASCE, 11(4), 331-339. https://doi.org/10.1061/(ASCE)0899-1561(1999)11:4(331).
  13. Barros, J.A.O., Santos, S.P.F., Lourenco, L.A.P. and Goncalves, D. (2008), "Flexural behaviour of steel fibre reinforced selfcompacting concrete laminar structures", Proceedings, 1st Spanish Congress on Self-Compacting Concrete, Valencia, Spain, February.
  14. Barros, J.A.O., Taheri, M. and Salehian, H. (2017), "A model to predict the crack width of FRC members reinforced with longitudinal bars", ACI Spec. Publ., SP-319, 2.1-2.16.
  15. Broberg, K.B. (1999), Cracks and Fracture, Elsevier.
  16. Campione, G. (2008), "Simplified flexural response of steel fiber-reinforced concrete beams", J. Mater. Civil Eng., ASCE, 20(4), 283-293. https://doi.org/10.1061/(ASCE)0899-1561(2008)20:4(283).
  17. Campione, G., La Mendola, L. and Papia, M. (2006), "Shear strength of fiber reinforced beams with stirrups", Struct. Eng. Mech., 24(1), 107-136. https://doi.org/10.12989/sem.2006.24.1.107.
  18. Chu S.H. and Kwan A.K.H. (2021), "Crack mitigation utilizing enhanced bond of rebars in SFRC", Struct., 33, 4141-4147. https://doi.org/10.1016/j.istruc.2021.06.095.
  19. Comite Euro-International du Beton (CEB) (2013), CEB-FIP Model Code 2010: Model Code for Concrete Structures, Ernst & Sohn, Wiley, Berlin, Germany.
  20. Craig, R.J. (1987), "Flexural behavior and design of reinforced fiber concrete members", ACI Spec. Publ., 105, 517-564.
  21. Cunha, V.M.C.F. (2010), "Steel fibre reinforced self-compacting concrete (from micro-mechanics to composite behaviour)", Doctoral Thesis, University of Minho.
  22. Cunha, V.M.C.F., Barros, J.A.O. and Sena-Cruz, J.M. (2010), "Pullout behaviour of steel fibres in self-compacting concrete", J. Mater. Civil Eng., ASCE, 22(1), 1-9. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000001.
  23. DAfStb (2012), Deutscher Ausschuss fur Stahlbeton, Deutscher Ausschuss Fur Stahlbeton, Budapester Strasse 31, D-10787 Berlin.
  24. de Montaignac, R., Massicotte, B. and Charron, J.P. (2012), "Design of SFRC structural elements: flexural behaviour prediction", Mater. Struct., 45(4), 623-636. https://doi.org/10.1617/s11527-011-9785-y.
  25. Deluce, J.R. and Vecchio, F.J. (2013), "Cracking behavior of steel fiber reinforced concrete members containing conventional reinforcement", ACI Struct. J., 110(3), 481-490.
  26. Domski, J. and Zakrzewski, M. (2020), "Deflection of steel fiber reinforced concrete beams based on waste sand", Mater., 13(2), 392. https://doi.org/10.3390/ma13020392.
  27. Dundar, C., Tanrikulu, A.K. and Frosch, R.J. (2015), "Prediction of load-deflection behaviour of multi-span FRP and steel reinforced concrete beams", Compos. Struct., 132, 680-693. https://doi.org/10.1016/j.compstruct.2015.06.018.
  28. EN 14651 (2005), Test Method for Metallic Fibered Concrete-Measuring the Flexural Tensile Strength (Limit of Proportionality (Lop), Residual), European Committee for Standardization.
  29. Ezeldin, A.S. and Shiah, T.W. (1995), "Analytical immediate and long-term deflections of fiber-reinforced concrete beams", J. Struct. Eng., 121, 727-738. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:4(727).
  30. Gilbert, R.I. and Warner, R.F. (1978), "Tension stiffening in reinforced concrete slabs", J. Struct. D., ASCE, 104(12), 1885-1900. https://doi.org/10.1061/JSDEAG.0005054.
  31. Gribniak, V., Kaklauskas, G., Kwan, A.K.H., Bacinskas, D. and Ulbinas, D. (2012), "Deriving stress-strain relationships for steel fibre concrete in tension from tests of beams with ordinary reinforcement", Eng. Struct., 42, 387-395. https://doi.org/10.1016/j.engstruct.2012.04.032.
  32. Harvinder, S. (2020), "Closed-form solution for shear strength of steel fiber-reinforced concrete beams", ACI Struct. J., 117(3), 261-269.
  33. Hsu, C.T.T., He, R.L. and Ezeldin, S. (1992), "Load-deformation behavior of steel fiber reinforced concrete beams", ACI Struct. J., 89, 650-657.
  34. JSCE (1984), Method of Tests for Flexural Strength and Flexural Toughness of Steel Fiber Reinforced Concrete. Part III-2 Method of Tests for Steel Fiber Reinforced Concrete, SF4 - The Japan Society of Civil Engineers, 3, 58-61.
  35. Kaklauskas, G. (2017), "Crack model for RC members based on compatibility of stress-transfer and mean-strain approaches", J. Struct. Eng., ASCE, 143(9), 04017105. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001842.
  36. Kaklauskas, G. and Ghaboussi, J. (2001), "Stress-strain relations for cracked tensile concrete from RC beam tests", J. Struct. Eng., ASCE, 127(1), 64-73. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(64).
  37. Kaklauskas, G. and Gribniak, V. (2011), "Eliminating shrinkage effect from moment-curvature and tension-stiffening relationships of reinforced concrete members", J. Struct. Eng., ASCE, 137(12), 1460-1469. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000395.
  38. Kaklauskas, G. and Gribniak, V. (2016), "Hybrid tension stiffening approach for decoupling shrinkage effect in cracked reinforced concrete members", J. Eng. Mech., ASCE, 142(11), 04016085. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001148.
  39. Kaklauskas, G. and Sokolov, A. (2021), "A peculiar value of M to Mcr ratio: Reconsidering assumptions of curvature analysis of reinforced concrete beams", J. Appl. Eng. Sci., 7, 100053. https://doi.org/10.1016/j.apples.2021.100053.
  40. Kaklauskas, G., Gribniak, V., Meskenas, A., Bacinskas, D., Juozapaitis, A., Sokolov, A. and Ulbinas, D. (2014), "Experimental investigation of the deformation behavior of SFRC beams with an ordinary reinforcement", Mech. Compos. Mater., 50(4), 417-426. https://doi.org/10.1007/s11029-014-9428-9.
  41. Kaklauskas, G., Gribniak, V., Salys, D., Sokolov, A. and Meskenas, A. (2011), "Tension-stiffening model attributed to tensile reinforcement for concrete flexural members", Procedia Eng., 14, 1433-1438. https://doi.org/10.1016/j.proeng.2011.07.180.
  42. Kaklauskas, G., Ramanauskas, R. and Jakubovskis R. (2017), "Mean crack spacing modelling for RC tension elements", Eng. Struct., 150(1), 843-851. https://doi.org/10.1016/j.engstruct.2017.07.090.
  43. Lackner, R. and Mang, H.A. (2003), "Scale transition in steel-concrete interaction. Part I: Model", J. Eng. Mech., ASCE, 129(4), 393-402. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:4(393).
  44. Lehmann, M. and Glodkowska, W. (2021), "Shear capacity and behaviour of bending reinforced concrete beams made of steel fibre-reinforced waste sand concrete", Mater., 14(11), 2996. https://doi.org/10.3390/ma14112996.
  45. Lim, T., Paramasivam, P. and Lee, S. (1987), "Behavior of reinforced steel-fiber-concrete beams in flexure", J. Struct. Eng., 113, 2439-2458. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:12(2439).
  46. Marti, P., Alvarez, M., Kaufmann, W. and Sigrist V. (1998), "Tension chord model for structural concrete", Struct. Eng. Int., 8(4), 287-298. https://doi.org/10.2749/101686698780488875.
  47. Mazaheripour, H., Barros, J.A.O. and Sena-Cruz, J.M. (2016), "Tension-stiffening model for FRC reinforced by hybrid FRP and steel bars", Compos. Part B J., 88, 162-181. http://dx.doi.org/10.1016/j.compositesb.2015.10.042.
  48. Mazaheripour, H., Barros, J.A.O., Soltanzadeh, F. and Sena-Cruz J. (2016), "Deflection and cracking behavior of SFRSCC beams reinforced with hybrid prestressed GFRP and steel reinforcements", Eng. Struct., 125, 546-565. https://doi.org/10.1016/j.engstruct.2016.07.026.
  49. Meskenas, A., Ramanauskas, R., Sokolov, A., Bacinskas, D. and Kaklauskas, G. (2021), "Residual stress-strain relations inversely derived from experimental moment-curvature response of RC beams with fibres compared to the recommendations of design codes", Struct., 34, 3363-3375. https://doi.org/10.1016/j.istruc.2021.09.070.
  50. Minelli, F. and Plizzari, G.A. (2015), "Derivation of a simplified stress-crack width law for fiber reinforced concrete through a revised round panel test", Cement Concrete Compos., 58, 95-104. https://doi.org/10.1016/j.cemconcomp.2015.01.005.
  51. Naaman, A.E. (2003), "Strain hardening and deflection hardening fiber reinforced cement composites", Proc. 4th Int. RILEM Workshop on High Performance Fiber Reinforced Cement Composites, Ann Abor, University of Michigan, 95-113.
  52. Neumark, S. (1965), Solution of Cubic and Quartic Equations, Pergamon Press, Headington Hall, Oxford.
  53. Ng, P.L., Lam, J.Y.K. and Kwan, A.K.H. (2010), "Tension stiffening in concrete beams. Part 1: FE analysis", Proc. Inst. Civil Eng.: Struct. Build., 163(1), 19-28. https://doi.org/10.1680/stbu.2009.163.1.19.
  54. RILEM TC 162-TDF (2000), "Test and design methods for steel fibre reinforced concrete: Recommendations", Mater. Struct., 33, 3-5. https://doi.org/10.1007/BF02481689.
  55. RILEM TC 162-TDF (2002), "Test and design methods for steel fibre reinforced concrete: Design of steel fibre reinforced concrete using the σ-w method: Principles and applications", Mater. Struct., 35, 262-278. https://doi.org/10.1007/BF02482132.
  56. RILEM TC 162-TDF (2003), "Test and design methods for steel fibre reinforced concrete: σ-ε-design method: Final recommendation", Mater. Struct., 36, 560-567. https://doi.org/10.1007/BF02480834.
  57. RILEM TC 162-TDF. (2001), "Test and design methods for steel fibre reinforced concrete: Uni-axial tension test for steel fibre reinforced concrete", Mater. Struct., 34, 3-6. https://doi.org/10.1007/BF02482193.
  58. Shi, Z. (2009), Crack Analysis in Structural Concrete, Burlington, USA, Butterworth-Heinemann Elsevier.
  59. Skocek, J. and Stang, H. (2008), "Inverse analysis of the wedge-splitting test", Eng. Fract. Mech., 75, 3173-3188. https://doi.org/10.1016/j.engfracmech.2007.12.003.
  60. Soltanzadeh, F., Cunha, V.M.C.F. and Barros, J.A.O. (2019), "Assessment of different methods for characterization and simulation of post-cracking behavior of self-compacting fiber reinforced concrete", Constr. Build. Mater., 227, 116704. https://doi.org/10.1016/j.conbuildmat.2019.116704.
  61. Stahli, P. (2008), "Ultra-fluid, oriented hybrid-fibre-concrete", Doctoral Thesis, Diss. ETH No. 17996, ETH Zurich.
  62. Taheri, M., Barros, J.A.O. and Salehian, H. (2012), "Parametric study of the use of strain softening/hardening FRC for RC elements failing in bending", J. Mater. Civil Eng., ASCE, 24(3), 259-274. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000373.
  63. Tan, K.H., Paramasivam, P. and Tan, K.C. (1994), "Instantaneous and long-term deflections of steel fiber reinforced concrete beams", ACI Struct. J., 91, 384-393.
  64. Tiberti, G., Minelli, F. and Plizzari, G.A. (2015), "Cracking behavior in reinforced concrete members with steel fibers: a comprehensive experimental study", Cement Concrete Res., 68, 24-34. https://doi.org/10.1016/j.cemconres.2014.10.011.
  65. Torres, L., Barris, C., Kaklauskas, G. and Gribniak, V. (2015), "Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar", Struct. Eng. Mech., 53(5), 997-1016. https://doi.org/10.12989/sem.2015.53.5.997.
  66. Torres, L., Lopez-Almansa, F. and Bozzo, L.M. (2004), "Tension-stiffening model for cracked flexural concrete members", J. Struct. Eng., ASCE, 130(8), 1242-1251. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:8(1242).
  67. UNI 11039 (2003), Steel Fiber Reinforced Concrete - Part I: Definitions, Classification Specification and Conformity - Part II: Test Method for Measuring First Crack Strength and Ductility Indexes, Italian Board for Standardization.
  68. Wu, H.Q. and Gilbert, R.I. (2009), "Modeling short-term tension stiffening in reinforced concrete prism using a continuum-based finite element model", Eng. Struct., 31(10), 2380-2391. https://doi.org/10.1016/j.engstruct.2009.05.012.
  69. Wu, K., Chen, F., Lin, J.F., Zhao, J.X. and Zheng, H.M. (2021), "Experimental study on the interfacial bond strength and energy dissipation capacity of steel and steel fibre reinforced concrete (SSFRC) structures", Eng. Struct., 235, 112094. https://doi.org/10.1016/j.engstruct.2021.112094.