Skip to main content
Log in

Minimum reinforcement in concrete structures and material/structural instability

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The problem of the assessment of minimum reinforcement in concrete members has been examined both theoretically and experimentally by the bridged crack model. The model has been demonstrated to be an efficient numerical tool for investigating the behavior of structural elements in bending, and allowed to show the minimum reinforcement percentage depends on the structural element size, and decreases with increasing beam depths. In the model, Linear Elastic Fracture Mechanics concepts are used to determine the equilibrium and the compatibility equations of a beam segment subjected to bending in presence of a mode I crack. Recently, the model has been extended to include the presence of closing stresses as a function of the crack opening in addition to steel reinforcement closing traction. This allows to characterize the mechanical behavior of fiber reinforced structural elements. A criterion for accounting for crushing in compression has been introduced as well, to bound from below (minimum reinforcement) and from above (maximum reinforcement) a region of stable and ductile mechanical behavior as a function of the mechanical properties as well as of the size of the structural element. Some experimental results are commented under this light.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abdalla HM, Karihaloo BL (2003) Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests. Mag Concrete Res 55: 133–141

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bosco C, Carpinteri A, Debernardi PG (1992) Scale effect on plastic rotational capacity of r.c. beams. In: Bažant ZP(eds) Fracture mechanics of concrete structures. Elsevier, London, pp 735–740

    Google Scholar 

  • Carpinteri A (1981a) A fracture mechanics model for reinforced concrete collapse. In: Proceedings of the I.A.B.S.E. colloquium on advanced mechanics of reinforced concrete. Delft, pp 17–30

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Carpinteri A, Massabó R (1997a) Continuous vs discontinuous bridged-crack model for fiber-reinforced materials in flexure. Int J Solids Struct 34: 2321–2338

    Article  Google Scholar 

  • Carpinteri A, Massabó R (1997b) Reversal in failure scaling transition of fibrous composites. J Eng Mech (ASCE) 123: 107–114

    Article  Google Scholar 

  • Carpinteri A, Ferro G, Bosco C, Elkatieb M (1999) Scale effects and transitional failure phenomena of reinforced concrete beams in flexure. In: Carpinteri A (ed) Minimum reinforcement in concrete members, vol 24. ESIS Publications, Elsevier Science Ltd, pp 1–30

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

    Article  Google Scholar 

  • Ferro G (2002) Multilevel bridged crack model for high-performance concretes. Theor Appl Fract Mech 38: 177–190

    Article  CAS  Google Scholar 

  • Hawkins N, Hjorsetet K (1992) Minimum reinforcement requirement for concrete flexural members. In: Carpinteri A(eds) Applications of fracture mechanics to reinforced concrete. Elsevier, London, pp 37–412

    Google Scholar 

  • 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 

  • Hillerborg A, Moder M, Petersson P (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6: 773–782

    Article  Google Scholar 

  • Jenq YS, Shah SP (1986) Crack propagation in fiber-reinforced concrete. J Eng Mech (ASCE) 112: 19–34

    Google Scholar 

  • Karihaloo BL (1995) Fracture mechanics and structural concrete. Addison-Wesley, Longman

    Google Scholar 

  • Karihaloo BL, Wang J (2000) Mechanics of fibre-reinforced cementitious composites. Comput Struct 76: 19–34

    Article  Google Scholar 

  • Karihaloo BL, Abdalla HM, Imjai T (2003) A simple method for determining the true specific fracture energy of concrete. Mag Concrete Res 55: 471–481

    Article  Google Scholar 

  • Li VC, Wang Y, Backer S (1991) A micromechanical model of tension-softening and bridging toughening of short random fiber reinforced brittle matrix composites. J Mech Phys Solids 39: 607–625

    Article  Google Scholar 

  • Noghabai K (2000) Beams of fibrous concrete in shear and bending: experiment and model. J Struct Eng (ASCE) 126: 243–251

    Article  Google Scholar 

  • RILEM TC50 (1985) Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Mater Struct 18:287–290

    Google Scholar 

  • RILEM TC89 (1990) Determination of fracture parameters of plain concrete using three-point bend tests. Mater Struct 23:457–460

    Google Scholar 

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

    Article  Google Scholar 

  • Ruiz G, Elices M, Planas J (1998) Experimental study on fracture of reinforced concrete beams. Mater Struct 31: 683–691

    Article  CAS  Google Scholar 

  • Swamy RN, Al-Ta’an SA (1981) Deformation and ultimate strength in flexure of reinforced beams made with steel fiber concrete. ACI J Proc 5: 395–405

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferro, G., Carpinteri, A. & Ventura, G. Minimum reinforcement in concrete structures and material/structural instability. Int J Fract 146, 213–231 (2007). https://doi.org/10.1007/s10704-007-9162-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-007-9162-6

Keywords

Navigation