Browse > Article
http://dx.doi.org/10.12989/sem.2022.81.3.349

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)
Publication Information
Structural Engineering and Mechanics / v.81, no.3, 2022 , pp. 349-365 More about this Journal
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
deformation; moment-curvature; steel fibre-reinforced concrete; tension stiffening;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 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.   DOI
2 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.
3 ASTM C496-17 (2017), Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, American Society for Testing and Material.
4 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.
5 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.   DOI
6 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.   DOI
7 DAfStb (2012), Deutscher Ausschuss fur Stahlbeton, Deutscher Ausschuss Fur Stahlbeton, Budapester Strasse 31, D-10787 Berlin.
8 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.
9 Broberg, K.B. (1999), Cracks and Fracture, Elsevier.
10 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.   DOI
11 Cunha, V.M.C.F. (2010), "Steel fibre reinforced self-compacting concrete (from micro-mechanics to composite behaviour)", Doctoral Thesis, University of Minho.
12 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.   DOI
13 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.   DOI
14 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.   DOI
15 EN 14651 (2005), Test Method for Metallic Fibered Concrete-Measuring the Flexural Tensile Strength (Limit of Proportionality (Lop), Residual), European Committee for Standardization.
16 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).   DOI
17 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.   DOI
18 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.   DOI
19 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.
20 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.   DOI
21 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).   DOI
22 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.   DOI
23 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.   DOI
24 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.
25 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.   DOI
26 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.
27 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).   DOI
28 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.   DOI
29 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.   DOI
30 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).   DOI
31 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.   DOI
32 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.   DOI
33 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.   DOI
34 Shi, Z. (2009), Crack Analysis in Structural Concrete, Burlington, USA, Butterworth-Heinemann Elsevier.
35 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.   DOI
36 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).   DOI
37 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.   DOI
38 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.   DOI
39 Harvinder, S. (2020), "Closed-form solution for shear strength of steel fiber-reinforced concrete beams", ACI Struct. J., 117(3), 261-269.
40 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.
41 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.   DOI
42 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.   DOI
43 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.   DOI
44 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.   DOI
45 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.   DOI
46 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.   DOI
47 Stahli, P. (2008), "Ultra-fluid, oriented hybrid-fibre-concrete", Doctoral Thesis, Diss. ETH No. 17996, ETH Zurich.
48 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.   DOI
49 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.   DOI
50 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).   DOI
51 Comite Euro-International du Beton (CEB) (2013), CEB-FIP Model Code 2010: Model Code for Concrete Structures, Ernst & Sohn, Wiley, Berlin, Germany.
52 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.
53 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.
54 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.   DOI
55 Craig, R.J. (1987), "Flexural behavior and design of reinforced fiber concrete members", ACI Spec. Publ., 105, 517-564.
56 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.   DOI
57 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.   DOI
58 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.   DOI
59 ACI 544.4R-88 (1988), Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Michigan.
60 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.   DOI
61 Alsayed, S.H. (1993), "Flexural deflection of reinforced fibrous concrete beams", ACI Struct. J., 90, 72-76.
62 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.   DOI
63 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.   DOI
64 Neumark, S. (1965), Solution of Cubic and Quartic Equations, Pergamon Press, Headington Hall, Oxford.
65 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.   DOI
66 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.   DOI
67 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.   DOI
68 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).   DOI
69 Ashour, S.A. and Wafa, F.F. (1993), "Flexural behavior of high-strength fiber reinforced concrete beams", ACI Struct. J., 90, 279-287.