DOI QR코드

DOI QR Code

Importance of a rigorous evaluation of the cracking moment in RC beams and slabs

  • Lopes, A.V. (Department of Civil Engineering, University of Coimbra, CEMUC) ;
  • Lopes, S.M.R. (Department of Civil Engineering, University of Coimbra, CEMUC)
  • 투고 : 2010.10.17
  • 심사 : 2011.06.22
  • 발행 : 2012.04.25

초록

The service loads are often decisive in the design of concrete structures. The evaluation of the cracking moment, $M_{cr}$, is an important issue to predict the performance of the structure, such as, the deflections of the reinforced concrete beams and slabs. To neglect the steel bars of the section is a simplification that is normally used in the computation of the cracking moment. Such simplification leads to small errors in the value of this moment (typically less than 20%). However, these small errors can conduce to significant errors when the values of deflections need to be computed from $M_{cr}$. The article shows that an error of 10% on the evaluation of $M_{cr}$ can lead to errors over 100% in the deformation values. When the deformation of the structure is the decisive design parameter, the exact computing of the cracking moment is obviously very important. Such rigorous computing might lead to important savings in the cost of the structure. With this article the authors wish to draw the attention of the technical community to this fact. A simple equation to evaluate the cracking moment, $M_{cr}$, is proposed for a rectangular cross-section. This equation leads to cracking moments higher than those obtained by neglecting the reinforcement bars and is a simple rule that can be included in Eurocode 2. To verify the accuracy of the developed model, the results of the proposed equation was compared with a rigorous computational procedure. The proposed equation corresponds to a good agreement when compared with the previous approach and, therefore, this model can be used as a practical aid for calculating an accurate value of the cracking moment.

키워드

참고문헌

  1. Bazant, Z.P. and Oh, B.H. (1983), "Spacing of cracks in reinforced-concrete", J. Struct. Eng.-ASCE, 109(9), 2066-2085. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:9(2066)
  2. Beeby, A. and Narayanan, R. (1995), Designers' Handbook to Eurocode 2. Part 1.1: Design of concrete structures, Thomas Telford, London.
  3. Bernardo, L.F.A. and Lopes, S.M.R. (2004), "Neutral axis depth versus flexural ductility in high strength concrete beams", J. Struct. Eng.-ASCE, 130(3), 452-459. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(452)
  4. Bernardo, L.F.A. and Lopes, S.M.R. (2008), "Behaviour of concrete beams under torsion - NSC plain and hollow beams", Mater. Struct., 41(6), 1143-1167. https://doi.org/10.1617/s11527-007-9315-0
  5. Bernardo, L.F.A. and Lopes, S.M.R. (2009a), "Plastic analysis of HSC beams in flexure", Mater. Struct., 42(1), 51-69. https://doi.org/10.1617/s11527-008-9366-x
  6. Bernardo, L.F.A. and Lopes, S.M.R. (2009b), "Torsion in HSC hollow beams: strength and ductility analysis", ACI Struct. J., 106(1) 39-48.
  7. Carmo, R.N.F. and Lopes, S.M.R. (2005), "Ductility and linear analysis with moment redistribution in reinforced high strength concrete beams", Can. J. Civil Eng., 32(1), 194-203. https://doi.org/10.1139/l04-080
  8. Carmo, R.N.F. and Lopes, S.M.R. (2008), "Available plastic rotation in continuous high-strength concrete beams", Can. J. Civil Eng., 35(10), 1152-1162. https://doi.org/10.1139/L08-064
  9. CEB (1985), Design manual on cracking and deformations, Comite Euro-International du Beton, Lausanne, Switzerland.
  10. CEB-FIP (1993), Model Code 1990, Comite Euro-Internacional du Beton - Federation Internationale de la Precontrainte, Thomas Telford, Lausanne, Switzerland.
  11. CEN (2002), EN 1990 Eurocode 0: Basis of Design, European Committee for Standardization, Brussels, Belgium.
  12. CEN (2004), EN 1992.1.1 Eurocode 2: Design of Concrete Structures; Part 1-1: General rules and rules for buildings, European Committee for Standardization, Brussels, Belgium.
  13. Cohn, M.Z. and Riva, P. (1992), "Yield safety, cracking control, and moment redistribution", J. Struct. Eng., 118(2), 447-468. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:2(447)
  14. Desayi, P. and Rao, K.B. (1987), "Probabilistic analysis of the cracking of RC beams", Mater. Struct., 20(6), 408-417. https://doi.org/10.1007/BF02472491
  15. Dufour, F., Pijaudier-Cabot, G., Choinska, M. and Huerta, A. (2008), "Extraction of a crack opening from a continuous approach using regularized damage models", Comput. Concrete, 5(4), 375-388. https://doi.org/10.12989/cac.2008.5.4.375
  16. Dujc, J., Brank, B., Ibrahimbegovic, A. and Brancherie, D. (2010), "An embedded crack model for failure analysis of concrete solids", Comput. Concrete, 7(4), 331-346. https://doi.org/10.12989/cac.2010.7.4.331
  17. FIB (1999), Structural Concrete - Textbook on Behaviour, Design and Performance, Federation Internationale du Beton, Vols. 1 and 2, Lausanne, Switzerland.
  18. Gutierrez, J. and Ochoa, J. (2007), "Short and long-term deflections in reinforced, prestressed, and composite concrete beams", J. Struct. Eng., 133(4), 495-506. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:4(495)
  19. Hutchinson, T.C. and Wang, T. (2009), "Evaluation of crack spacing in reinforced concrete shear walls", J. Struct. Eng., 135(5), 499-508. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:5(499)
  20. Kidder, F.E. (1984), Architects and Builders Pocket Book, John Wiley and Sons Inc.
  21. Lopes, A. (2005), "Simulacao numerica 2D da rotura de uma viga de betao armado", Proceedings do Simposio Ibero-Americano "O Betao nas Estruturas - SIABE05", Coimbra, 391-398 (in Portuguese).
  22. Lopes, S.M.R. and Bernardo, L.F.A. (2003), "Plastic rotation capacity of high-strength concrete beams", Mater. Struct., 36(255), 22-31. https://doi.org/10.1007/BF02481567
  23. Lopes, S.M.R. and Bernardo, L.F.A. (2009), "Twist behaviour of high-strength concrete hollow beams-formation of plastic hinges along the length", Eng. Struct., 31(1), 138-149. https://doi.org/10.1016/j.engstruct.2008.08.003
  24. Makhlouf, H.M. and Malhas, F.A. (1996), "The effect of thick concrete cover on the maximum flexural crack width under service load", ACI Struct. J., 93(3), 257-265.
  25. Marzouk, H., Hossin, M. and Hussein, A. (2010), "Crack width estimation for concrete plates", ACI Struct. J., 107(3), 282-290.
  26. Mayer, H. and Rusch, H.R. (1967), Bauschaden als folge der Durchbiegung von Stahlbeton-bauteilen, Deutscher Ausschuss fur Stahlbeton, heft 193 (in German).
  27. Oh, B.H., ASCE, M. and Kim, S.H. (2007), "Advanced crack width analysis of reinforced concrete beams under repeated loads", J. Struct. Eng., 133(3), 411-420. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:3(411)
  28. Popovics, S. (1970), "A review of stress-strain relationships for concrete", ACI J. Proc., 67(6), 243-248.
  29. Popovics, S. (1973), "Numerical approach to the complete stress-strain relation for concrete", Cement Concrete Res., 3(5), 583-599. https://doi.org/10.1016/0008-8846(73)90096-3
  30. Yoon, Y.S., Cook, W.D. and Mitchell, D. (1996), "Minimum shear reinforcement in normal medium, and highstrength concrete beams", ACI Struct. J., 93(5), 257-265.
  31. Zanuy, C. (2010), "Investigating the negative tension stiffening effect of reinforced concrete", Struct. Eng. Mech., 34(2), 199-211.
  32. Zanuy, C., Fuente, P. and Albajar, L. (2010), "Estimation of parameters defining negative tension stiffening", Eng, Struct,, 32(10), 3355-3362. https://doi.org/10.1016/j.engstruct.2010.07.009

피인용 문헌

  1. A finite element model to simulate long-term behavior of prestressed concrete girders vol.81, 2014, https://doi.org/10.1016/j.finel.2013.11.007
  2. Analysis and prediction of ultimate strength of high-strength SFRC plates under in-plane and transverse loads vol.52, pp.6, 2014, https://doi.org/10.12989/sem.2014.52.6.1273
  3. Finite element analysis of reinforced concrete spandrel beams under combined loading vol.13, pp.2, 2014, https://doi.org/10.12989/cac.2014.13.2.291
  4. Influence of the Composition of the Activator on Mechanical Characteristics of a Geopolymer vol.10, pp.10, 2020, https://doi.org/10.3390/app10103349
  5. Experimental Study on the Flexural Behavior of Alkali Activated Fly Ash Mortar Beams vol.10, pp.12, 2012, https://doi.org/10.3390/app10124379
  6. Long-term deflection prediction in steel-concrete composite beams vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.021