International Journal of Fracture

, Volume 146, Issue 4, pp 213–231 | Cite as

Minimum reinforcement in concrete structures and material/structural instability

  • Giuseppe Ferro
  • Alberto Carpinteri
  • Giulio Ventura
Original Paper


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.


Minimum reinforcement Scale effects Reinforced concrete beams Transitional failure phenomena Brittleness number Fiber reinforced concrete Concrete crushing 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Giuseppe Ferro
    • 1
  • Alberto Carpinteri
    • 1
  • Giulio Ventura
    • 1
  1. 1.Department of Structural and Geotechnical EngineeringPolitecnico di TorinoTorinoItaly

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