Structural Engineering and Mechanics

  • 제53권5호
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  • Pages.997-1016
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  • 2015
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar

  • Torres, Lluis (Analysis and Advanced Materials for Structural Design (AMADE), Polytechnic School, University of Girona) ;
  • Barris, Cristina (Analysis and Advanced Materials for Structural Design (AMADE), Polytechnic School, University of Girona) ;
  • Kaklauskas, Gintaris (Department of Bridges and Special Structures, Vilnius Gediminas Technical University (VGTU)) ;
  • Gribniak, Viktor (Civil Engineering Research Centre, VGTU)
  • 투고 : 2013.11.06
  • 심사 : 2014.11.27
  • 발행 : 2015.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

The contribution of tensioned concrete between cracks (tension-stiffening) cannot be ignored when analysing deformation of reinforced concrete elements. The tension-stiffening effect is crucial when it comes to adequately estimating the load-deformation response of steel reinforced concrete and the more recently appeared fibre reinforced polymer (FRP) reinforced concrete. This paper presents a unified methodology for numerical modelling of the tension-stiffening effect in steel as well as FRP reinforced flexural members using the concept of equivalent deformation modulus and the smeared crack approach to obtain a modified stress-strain relation of the reinforcement. A closed-form solution for the equivalent secant modulus of deformation of the tensioned reinforcement is proposed for rectangular sections taking the Eurocode 2 curvature prediction technique as the reference. Using equations based on general principles of structural mechanics, the main influencing parameters are obtained. It is found that the ratio between the equivalent stiffness and the initial stiffness basically depends on the product of the modular ratio and reinforcement ratio ($n{\rho}$), the effective-to-total depth ratio (d/h), and the level of loading. The proposed methodology is adequate for numerical modelling of tension-stiffening for different FRP and steel reinforcement, under both service and ultimate conditions. Comparison of the predicted and experimental data obtained by the authors indicates that the proposed methodology is capable to adequately model the tension-stiffening effect in beams reinforced with FRP or steel bars within wide range of loading.

키워드

과제정보

연구 과제 주관 기관 : Ministerio de Ciencia e Innovacion

참고문헌

  1. Aiello, M.A. and Ombres, L. (2000), "Cracking analysis of FRP-reinforced concrete flexural members", Mech. Compos. Mater., 36(5), 389-394. https://doi.org/10.1023/A:1026699101440
  2. Al-Sunna, R.A.S., Pilakoutas, K., Hajirasouliha, I. and Guadagnini, M. (2012), "Deflection behaviour of FRP reinforced concrete beams and slabs: an experimental investigation", Compo.s Part: Eng., 43(5), 2125-34. https://doi.org/10.1016/j.compositesb.2012.03.007
  3. Balazs, G.L., Bisch, P., Borosnyoi, A., Burdet, O., Burns, C., Ceroni, F., Cervenka, V., Chiorino, M.A., Debernardi, P., Eckfeldt, L., El-Badry, M., Fehling, E., Foster, S.J., Ghali, A., Gribniak, V., Guiglia, M., Kaklauskas, G., Lark, R.J., Lenkei, P., Lorrain, M., Mari, A., Ozbolt, J., Pecce, M., Caldentey, A.P., Taliano, M., Tkatcic, D., Torrenti, J.M., Torres, L., Toutlemonde, F., Ueda, T., Vitek, J.L. and Vrablík, L. (2013), "Design for SLS according to fib Model Code 2010", Struct. Concrete, 14(2), 99-123. https://doi.org/10.1002/suco.201200060
  4. Barris, C., Torres, L., Turon, A., Baena, M. and Catalan, A. (2009), "An experimental study of the flexural behaviour of GFRP RC beams and comparison with prediction models", Compos. Struct., 91(3), 286-295. https://doi.org/10.1016/j.compstruct.2009.05.005
  5. Barris, C. and Torres, L. (2011), Fibre reinforced polymer reinforced concrete beams, Serviceability behaviour: testing and analysis, LAP LAMBERT Academic Publishing GmbH & Co.
  6. Barris, C., Torres, L., Comas, J. and Mias, C. (2013), "Cracking and deflections in GFRP RC beams: an experimental study", Compos. Part: Eng., 55, 580-590. https://doi.org/10.1016/j.compositesb.2013.07.019
  7. Bischoff, P.H. (2005), "Reevaluation of deflection predictions for concrete beams reinforced with steel and fiber reinforced polymer bars", J. Struct. Eng., 131(5), 752-762. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752)
  8. Bischoff, P.H. (2007a), "Rational model for calculating deflections of reinforced concrete beams and slabs", Can. J. Civil Eng., 34(8), 992-1002. https://doi.org/10.1139/l07-020
  9. Bischoff, P.H. (2007b), "Deflection calculation of FRP reinforced concrete beams based on modifications to the existing Branson equation", J. Compos. Constr., 11(1), 4-14. https://doi.org/10.1061/(ASCE)1090-0268(2007)11:1(4)
  10. CEN (2004), "Eurocode 2: design of concrete structures - Part 1.1: General rules and rules for buildings (EN 1992-1-1:2004), Comite Europeen de Normalisation, Brussels.
  11. Choi, C.K. and Cheung, S.H. (1994), "A simplified model for predicting the shear response of reinforced concrete membranes", Thin Wall. Struct., 19, 37-60. https://doi.org/10.1016/0263-8231(94)90004-3
  12. Choi, C.K. and Cheung, S.H. (1996), "Tension stiffening model for planar reinforced concrete members", Comput. Struct., 59(1), 179-190. https://doi.org/10.1016/0045-7949(95)00146-8
  13. Dede, T. and Ayvaz, Y. (2009), "Nonlinear analysis of reinforced concrete beam with/without tension stiffening effect", Mater. Des., 30(9), 3846-3851. https://doi.org/10.1016/j.matdes.2009.02.003
  14. fib (2010), Model Code 2010. First complete draft, Federation International du Beton, fib Bulletin 56.
  15. Floegl, H. and Mang, A. (1982), "Tension stiffening concept based on bond slip", J Struct Div, 108(12), 2681-2701.
  16. Gilbert, R.I. and Warner, R.F. (1978), "Tension stiffening in reinforced concrete slabs", J. Compos. Constr., 104(12), 1885-1900.
  17. Gilbert, R.I. (1983), "Deflection calculations for reinforced concrete beams", Civil Engineering Transactions, Institution of Engineers, 128-134.
  18. Gilbert, R.I. (2007), "Tension-stiffening in lightly reinforced concrete slabs", J. Struct. Eng., 133(6), 899-903. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(899)
  19. Gribniak, V., Kaklauskas, G., Torres, L., Daniunas, A., Timinskas, E. and Gudonis, E. (2013), "Comparative analysis of deformations and tension-stiffening in concrete beams reinforced with GFRP or steel bars and fibers", Compos. Part: Eng., 50, 158-170. https://doi.org/10.1016/j.compositesb.2013.02.003
  20. Gupta, A.K. and Maestrini, S.R. (1990), "Tension-stiffness model for reinforced concrete bars", J. Struct. Eng., 116(3), 769-790. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(769)
  21. Kaklauskas, G. and Ghaboussi, J. (2001), "Stress-strain relations for cracked tensile concrete from RC beam tests", .J Struct. Eng., 127(1), 64-73. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(64)
  22. Kaklauskas, G. (2004), "Flexural layered deformational model of reinforced concrete members", Mag. Concrete Res., 56(10), 575-584. https://doi.org/10.1680/macr.2004.56.10.575
  23. Kaklauskas, G., Gribniak, V. and Girdzius, R. (2011a), "Average stress-average strain tension-stiffening relationships based on provisions of design codes", J Zhejiang University: Science A, 12(10), 731-736. https://doi.org/10.1631/jzus.A1100029
  24. Kaklauskas, G., Gribniak, V., Salys, D., Sokolov, A. and Meskenas, A. (2011b), "Tension-stiffening model attributed to tensile reinforcement for concrete flexural members", Proc. Eng., 14, 1433-1438. https://doi.org/10.1016/j.proeng.2011.07.180
  25. Lin, C.S. and Scordelis, A.C. (1975), "Non linear analysis of RC shells of general form", J. Struct. Div., 101(3), 523-538.
  26. Massicote, B., Elwi, A.E. and MacGregor, J.G. (1990), "Tension-stiffening model for planar reinforced concrete members", J. Struct. Eng., 106(11), 3039-3058.
  27. Moosecker, E. and Grasser, W. (1981), "Evaluation of tension stiffening effects in reinforced concrete linear members", Proc. Adv. Mech. Reinf. Concrete, IABSE, 541-550.
  28. Murashev, V.N., Sigalov, V.I. and Baikov, E.E. (1971), Design of reinforced concrete structures, Zhelezobetonnye konstruktsii, MIR Publishers, Moscow.
  29. Pilakoutas, K., Guadagnini, M., Neocleous, K. and Matthys, S. (2011) "Design guidelines for FRP reinforced concrete structures" Proc. Inst. Civil Eng. Struct. Build., 4, 255-263.
  30. Prakhya, G.K.V. and Morley, C.T. (1990), "Tension-stiffening and moment-curvature relations of reinforced concrete elements", ACI Struct. J., 87(5), 597-605.
  31. Russo, G. and Romano, F. (1992), "Cracking response of RC members subjected to uniaxial tension", J. Struct. Eng., 118(5), 1172-1190. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:5(1172)
  32. Sarkar, P., Govind, M. and Menon, D. (2009), "Estimation of short-term deflection in two-way RC slab", Struct. Eng. Mech., 31(2), 237-240. https://doi.org/10.12989/sem.2009.31.2.237
  33. Scanlon, A. and Murray, D.W. (1974), "Time-dependent reinforced concrete slab deflections", J. Struct. Div., 100(9), 1911-1924.
  34. Stramandinoli, R.S.B. and La Rovere, H.L. (2008), "An efficient tension-stiffening model for nonlinear analysis of reinforced concrete members", Eng. Struct., 30(7), 2069-2080. https://doi.org/10.1016/j.engstruct.2007.12.022
  35. Torres, L., Lopez-Almansa, F. and Bozzo, L.M. (2004), "Tension-stiffening model for cracked flexural concrete members", J. Struct. Eng., 130(8), 1242-1251. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:8(1242)
  36. Wu, Z., Yoshikawa, H. and Tanabe, T. (1991), "Tension stiffness model for cracked reinforced concrete", J. Struct. Eng., 117(3), 715-732. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:3(715)
  37. Wu, H.Q. and Gilbert, R.I. (2009), "Modelling short-term tension stiffening in reinforced concrete prisms using a continuum based finite element model", Eng. Struct., 31(10), 2380-2391. https://doi.org/10.1016/j.engstruct.2009.05.012

피인용 문헌

  1. An Improved Approach for Measuring Cracking and Decompression Moments in Prestressed Concrete Members vol.28, pp.1, 2018, https://doi.org/10.1080/10168664.2018.1431431
  2. Analysis of Residual Flexural Stiffness of Steel Fiber-Reinforced Concrete Beams with Steel Reinforcement vol.13, pp.12, 2015, https://doi.org/10.3390/ma13122698
  3. COMPARATIVE ANALYSIS OF FLEXURAL STIFFNESS OF CONCRETE ELEMENTS WITH DIFFERENT TYPES OF COMPOSITE REINFORCEMENT SYSTEMS vol.13, pp.None, 2015, https://doi.org/10.3846/mla.2021.13713
  4. Residual stress - strain relations inversely derived from experimental moment - curvature response of RC beams with fibres compared to the recommendations of design codes vol.34, pp.None, 2015, https://doi.org/10.1016/j.istruc.2021.09.070