Skip to main content
SpringerLink
Log in

Failure mode transitions in RC beams: A cohesive/overlapping crack model application

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

The analysis of reinforced concrete beams in flexure taking into account the nonlinear behaviour of concrete is addressed by a numerical approach based on the Cohesive-Overlapping Crack Model. An extensive experimental research has been proposed by Bosco and Carpinteri (Scale effects and transitional phenomena of reinforced concrete beams in flexure. ESIS Technical Committée 9 Round Robin proposal, 1993), Bosco et al. (Scale effects and transitional failure phenomena of reinforced concrete beams in flexure. Report to ESIS Technical Committée 9, 1996) and El-Khatieb (Transizione di scala duttile-fragile per le travi in calcestruzzo armato. PhD Thesis, 1997) in order to obtain a rational explanation for failure transitional phenomena of RC beams by varying steel percentage and/or beam slenderness and/or beam size-scale. In the present paper, collapse mechanisms due to concrete tensile cracking, concrete compressive crushing and steel yielding and/or slippage are analysed and a numerical vs. experimental comparison is presented in order to validate the proposed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Baluch M, Azad A, Ashmawi W (1992) Fracture mechanics application to reinforced concrete members in flexure. In: Carpinteri A (ed) Applications of fracture mechanics to reinforced concrete. Elsevier, London, pp 413–436

    Google Scholar 

  2. Bažant ZP (1989) Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization. Cem Concr Res 19:973–977

    Article  Google Scholar 

  3. Bazant ZP, Beisel S (1994) Smeared-tip superposition method for cohesive fracture with rate effect and creep. Int J Fract 65:277–290

    Google Scholar 

  4. Bosco C, Carpinteri A (1992) Softening and snap-through behavior of reinforced elements. J Eng Mech 118:1564–1577

    Article  Google Scholar 

  5. Bosco C, Carpinteri A (1992) Fracture mechanics evaluation of minimum reinforcement in concrete structures. In: Carpinteri A (ed) Applications of fracture mechanics to reinforced concrete. Elsevier, London, pp 347–377

    Google Scholar 

  6. Bosco C, Carpinteri A (1993) Scale effects and transitional phenomena of reinforced concrete beams in flexure. ESIS Technical Committée 9 Round Robin proposal, Department of Structural Engineering of Politecnico di Torino, Italy

  7. Bosco C, Carpinteri A (1995) Discontinuous constitutive response of brittle matrix fibrous composites. J Mech Phys Solids 43:261–274

    Article  ADS  MATH  Google Scholar 

  8. Bosco C, Carpinteri A, Debernardi PG (1990) Minimum reinforcement in high-strength concrete. J Struct Eng 116:427–437

    Article  Google Scholar 

  9. Bosco C, Carpinteri A, Ferro G, El-Khatieb M (1996) Scale effects and transitional failure phenomena of reinforced concrete beams in flexure. Report to ESIS Technical Committée 9, Dipartimento di Ingegneria Strutturale, Politecnico di Torino

  10. Brincker R, Henriksen MS, Christensen FA, Heshe G (1999) Size effects on the bending behaviour of reinforced concrete beams. In: Carpinteri A (ed) Minimum reinforcement in concrete members. Elsevier, Oxford, pp 127–180

    Chapter  Google Scholar 

  11. Carpinteri A (1980) Size effect in fracture toughness testing: a dimensional analysis approach. In: Sih GC, Mirabile M (eds) Analytical and experimental fracture mechanics. Sijthoff & Noordhoff, Alphen an den Rijn, pp 785–797

    Google Scholar 

  12. Carpinteri A (1981) A fracture mechanics model for reinforced concrete collapse. In: Advanced mechanics of reinforced concrete, Proc IABSE colloquium. Delft University Press, Delft, pp 17–30

    Google Scholar 

  13. Carpinteri A (1981) Static and energetic fracture parameters for rocks and concretes. Mater Struct 14:151–162

    Google Scholar 

  14. Carpinteri A (1982) Notch sensitivity in fracture testing of aggregative materials. Eng Fract Mech 16:467–481

    Article  Google Scholar 

  15. Carpinteri A (1984) Stability of fracturing process in RC beams. J Struct Eng 110:544–558

    Article  Google Scholar 

  16. Carpinteri A (1985) Interpretation of the Griffith instability as a bifurcation of the global equilibrium. In: Shah SP (ed) Application of fracture mechanics to cementitious composites. Nijhoff, Dordrecht, pp 287–316

    Chapter  Google Scholar 

  17. Carpinteri A, Massabò R (1996) Bridged versus cohesive crack in the flexural behaviour of brittle-matrix composites. Int J Fract 81:125–145

    Article  Google Scholar 

  18. Carpinteri A, Colombo G, Ferrara G, Giuseppetti G (1989) Numerical simulation of concrete fracture through a bilinear softening stress-crack opening displacement law. In: Shah SP, Swartz SE (eds) Fracture of concrete and rock. Springer, New York, pp 131–141

    Chapter  Google Scholar 

  19. Carpinteri A, Ferro G, Ventura G (2003) Size effects on flexural response of reinforced concrete elements with nonlinear matrix. Eng Fract Mech 70:995–1013

    Article  Google Scholar 

  20. Carpinteri A, Ruiz Carmona J, Ventura G (2007) Propagation of flexural and shear cracks through reinforced concrete beams by the bridged crack model. Mag Concr Res 59:743–756

    Article  Google Scholar 

  21. Carpinteri A, Corrado M, Paggi M, Mancini G (2007) Cohesive versus overlapping crack model for a size effect analysis of RC elements in bending. In: Carpinteri A, Gambarova P, Ferro G, Plizzari G (eds) Fracture mechanics of concrete and concrete structures. Taylor & Francis, Leiden, pp 655–663

    Google Scholar 

  22. Carpinteri A, Corrado M, Paggi M, Mancini G (2009) New model for the analysis of size-scale effects on the ductility of reinforced concrete elements in bending. J Eng Mech 135:221–229

    Article  Google Scholar 

  23. Comité Euro-International du Béton C (1993) CEB-FIP Model Code 1990, Bulletin No. 213/214. Telford, Lausanne

    Google Scholar 

  24. Corrado M, Cadamuro E, Carpinteri A (2011) Dimensional analysis approach to study snap back-to-softening-to-ductile transitions in lightly reinforced quasi-brittle materials. Int J Fract 172:53–63

    Article  Google Scholar 

  25. El-Khatieb M (1997) Transizione di scala duttile-fragile per le travi in calcestruzzo armato. PhD Thesis, Dipartimento di Ingegneria Strutturale, Politecnico di Torino

  26. Eurocode 2 (2004) Design of concrete structures, Part 1-1: General rules and rules for buildings. p 230

    Google Scholar 

  27. Gustafsson PJ (1985) Fracture mechanics studies of non-yielding materials like concrete. Report TVBM-1007, Div Bldg Mater Lund Inst Tech, Sweden

  28. Gustafsson PJ, Hillerborg A (1988) Sensitivity in shear strength of longitudinally reinforced concrete beams to fracture energy of concrete. ACI Struct J 85:286–294

    Google Scholar 

  29. Hawkins NM, Hjorsetet K (1992) Minimum reinforcement requirement for concrete flexural members. Elsevier, London, pp 379–412

    Google Scholar 

  30. Hillerborg A (1990) Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams. Eng Fract Mech 35:233–240

    Article  Google Scholar 

  31. Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–782

    Article  Google Scholar 

  32. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364

    Google Scholar 

  33. Jansen DC, Shah SP (1997) Effect of length on compressive strain softening of concrete. J Eng Mech 123:25–35

    Article  Google Scholar 

  34. Jenq YS, Shah SP (1989) Shear resistance of reinforced concrete beams—a fracture mechanics approach. In: Li VC, Bazant ZP (eds) Fracture mechanics: application to concrete (Special Report ACI SP-118). Am Concrete Institute, Detroit, pp 327–358

    Google Scholar 

  35. Markeset G, Hillerborg A (1995) Softening of concrete in compression localization and size effects. Cem Concr Res 25:702–708

    Article  Google Scholar 

  36. Palmquist SM, Jansen DC (2001) Postpeak strain-stress relationship for concrete in compression. ACI Mater J 98:213–219

    Google Scholar 

  37. Planas J, Elices M (1992) Asymptotic analysis of a cohesive crack: 1. Theoretical background. Int J Fract 55:153–177

    Article  ADS  Google Scholar 

  38. RILEM TCS (1985) Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Draft Recommendation. Materials and Structures, vol 18

    Google Scholar 

  39. Ruiz G (2001) Propagation of a cohesive crack crossing a reinforcement layer. Int J Fract 111:265–282

    Article  Google Scholar 

  40. Ruiz G, Elices M, Planas J (1999) Size effects and bond-slip dependence of lightly reinforced concrete beams. In: Carpinteri A (ed) Minimum reinforcement in concrete members. Elsevier, Oxford, pp 127–180

    Google Scholar 

  41. So KO, Karihaloo BL (1993) Shear capacity of longitudinally reinforced beams—a fracture mechanics approach. J ACI 90:591–600

    Google Scholar 

  42. Suzuki M, Akiyama M, Matsuzaki H, Dang TH (2006) Concentric loading test of RC columns with normal- and high-strength materials and averaged stress-strain model for confined concrete considering compressive fracture energy. In: Proc 2nd fib congress, Naples, Italy

    Google Scholar 

  43. UNI 6556 Determinazione del modulo elastico secante a compressione

  44. van Vliet M, van Mier J (1996) Experimental investigation of concrete fracture under uniaxial compression. Mech Cohes-Frict Mater 1(1):115–127

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    A. Carpinteri & E. Cadamuro

  2. Civil Engineering Department, Isra University, P.O. Box 22, Amman, Jordan

    M. El-Khatieb

Authors
  1. A. Carpinteri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. El-Khatieb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Cadamuro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Cadamuro.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carpinteri, A., El-Khatieb, M. & Cadamuro, E. Failure mode transitions in RC beams: A cohesive/overlapping crack model application. Meccanica 48, 2349–2366 (2013). https://doi.org/10.1007/s11012-013-9753-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-013-9753-4

Keywords

Search

Navigation