Geodesic
Fracture mechanics as applied to plain and reinforced concrete with particular reference to scaling of experimental data
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 351-366.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Whereas in elasticity and plasticity geometrically similar structures behave in the same way, when strain-softening and strain-localization are taken into account the structural behaviour ranges from ductile to brittle merely by increasing size and keeping material properties and geometrical shape unchanged. The size-scale of plain and reinforced concrete elements has often revealed a fundamental influence on the global structural behaviour. This has been theoretically predicted and experimentally confirmed by the results obtained so far. As a consequence this is likely to influence several aspects concerning the design of large structures. The paper emphasizes how the size effects are also present in R.C. elements with a low content of steel and outlines the implications on the minimum steel percentage for these structures.
Mentre nel campo elastico e in quello plastico le strutture geometricamente simili hanno lo stesso comportamento, quando si considerano il ramo discendente della curva sforzi-deformazioni e la localizzazione delle deformazioni, il comportamento strutturale passa da duttile a fragile semplicemente modificando le dimensioni e lasciando inalterata la forma geometrica. Si riscontra quindi come l'effetto scala abbia una importanza fondamentale sul comportamento strutturale globale delle strutture di calcestruzzo semplice ed armato. Tale fenomeno, previsto teoricamente è confermato dai risultati sperimentali finora ottenuti dagli autori e può influenzare diversi aspetti riguardanti il progetto delle strutture. Il presente lavoro mette in evidenza come l'effetto scala sia presente anche nelle travi di calcestruzzo armato aventi basso contenuto di acciaio e ne delinea le implicazioni sulla percentuale minima di armatura per tali strutture. 
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Bosco, Crescentino; Carpinteri, Alberto. Fracture mechanics as applied to plain and reinforced concrete with particular reference to scaling of experimental data. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 351-366. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_4_a10/

[1] A. Carpinteri, Scale effects in fracture of plain and reinforced concrete structures. In: Fracture Mechanics of Concrete: Structural Application and Numerical Calculation. Martinus Nijhoff Publishers, Dordrecht-Boston-Lancaster 1985, 95-140.

[2] A. Carpinteri, Notch sensitivity in fracture testing of aggregative materials. Eng. Fracture Mech., 16, 1982, 467-481.

[3] Z. P. Bazant - L. Cedolin, Fracture mechanics of reinforced concrete. J. of Eng. Mech. Division (ASCE), 106, 1980, 1287-1306

[4] V. E. Saouma - A. R. Ingraffea, Fracture mechanics analysis of discrete cracking. IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft 1981, 413-436 (Final Report).

[5] P. E. Petersson - P. J. Gustavsson, A model for calculation of crack growth in concrete-like materials. In: D. R. J. OWEN - A. R. LUXMOORE (eds.), Numerical methods in Fracture Mechanics. Pineridge Press, 1980, 707-719.

[6] A. Hillerborg, Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams. Eng. Fracture Mech., vol. 35, No. 1/2/3, 1990, 233-240.

[7] A. Carpinteri, A fracture mechanics model for reinforced concrete collapse. IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft 1981, 17-30.

[8] L. ELFGREN (ed.), RILEM REPORT, Fracture Mechanics of Concrete Structures. From Theory to Applications. Chapman and Hall, 1989, 191-220.

[9] A. Carpinteri, Stability of fracturing process in RC beams. J. of Structural Eng. (ASCE), 110, 1984, 544-558.

[10] C. Bosco - A. Carpinteri - P. G. Debernardi, Fracture of reinforced concrete: scale effects and snap-back instability. Presented at the Int. Conf. on Fracture and Damage of Concrete and Rock (46/7/1988), Vienna (Austria); Eng. Fracture Mech., vol. 35, 4/5, 1990, 665-677.

[11] C. Bosco - A. Carpinteri - P. G. Debernardi, Size effect on the minimum steel percentage for reinforced concrete beams. Int. Conf. on Recent Developments on the Fracture of Concrete and Rock (20-22/9/1989), Cardiff, Wales, 1989, 672-681.

[12] A. Hillerborg - M. Modeer - P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of Fracture Mechanics and Finite Elements. Cement and Concrete Research, 6, 1976, 773-782.

[13] A. Carpinteri, Decrease of apparent tensile and bending strength with specimens size: two different explanations based on fracture mechanics. Int. J. of Solid and Structures, vol. 25, 4, 1989, 407-429.

[14] A. Carpinteri, Size effect in fracture toughness testing: a dimensional analysis approach. In: G. C. SMITH - M. MIRABLE (eds.), Proc. Int. Conf. on Analytical and Experim. Fracture Mechanics. Sijthoff and Noordhoff, 1981, 785-797.

[15] C. Bosco - A. Carpinteri - P. G. Debernardi, Minimum reinforcement in high-strength concrete. J. of Structural Eng. (ASCE), vol. 116, 2, 1990, 427-437.

[16] COMMISSION OF THE EUROPEAN COMMUNITIES, Industrial Processes - Building and Civil Engineering. Eurocode n. 2. Design of concrete structures. Part 1. General Rules and Rules for Buildings. October 1989.

[17] AMERICAN CONCRETE INSTITUTE, Building Code - Requirements for Reinforced Concrete (ACI 318-83), Detroit, Michigan, 1983.

[18] K. Szalai, Principle of dimensioning of slightly-reinforced concrete structures. Lectures presented at the 26th CEB Plenary Session, (20-23/9/1988), Dubrovnik 1988, 119-134.