New Model for the Analysis of Size-Scale Effects on the Ductility of Reinforced Concrete Elements in Bending

The well-known cohesive crack model describes strain localization with a softening stress variation in concrete members subjected to tension. An analogous behavior is also observed in compression, when strain localization takes place in a damaged zone and the stress reaches the compression strength with surface energy dissipation. In the present paper, we propose the new concept of overlapping crack model, which is analogous to the cohesive one and permits us to simulate material interpenetration due to crushing. The two aforementioned elementary models are merged into a more complex algorithm able to describe both cracking and crushing growths during loading processes in reinforced concrete members. A numerical procedure based on elastic coefficients is developed, taking into account the proposed constitutive laws in tension and compression. With this algorithm, it is possible to effectively capture the flexural behavior of reinforced concrete beams by varying the reinforcement percentage and/or the beam depth.

[1]  Rune Brincker,et al.  FRACTURE ENERGY OF HIGH-STRENGTH CONCRETE IN COMPRESSION. FRACTURE OF CONCRETE AND ROCK: RECENT DEVELOPMENTS. PAPERS PRESENTED AT THE INTERNATIONAL CONFERENCE, UNIVERSITY OF WALES, COLLEGE OF CARDIFF, SCHOOL OF ENGINEERING, SEPTEMBER 20-22, 1989 , 1989 .

[2]  Alberto Carpinteri,et al.  Scale-independent constitutive law for concrete in compression , 2008 .

[3]  A. Hillerborg.  Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams , 1990 .

[4]  A. Carpinteri.  Minimum Reinforcement in Concrete Members , 1999 .

[5]  Alberto Carpinteri,et al.  Size Effects on Strength, Toughness, and Ductility , 1989 .

[6]  J. P. Ulfkjær,et al.  Rotational Capacity of Reinforced Concrete Beams , 1995 .

[7]  A W Beeby,et al.  CONCISE EUROCODE FOR THE DESIGN OF CONCRETE BUILDINGS. BASED ON BSI PUBLICATION DD ENV 1992-1-1: 1992. EUROCODE 2: DESIGN OF CONCRETE STRUCTURES. PART 1: GENERAL RULES AND RULES FOR BUILDINGS , 1993 .

[8]  Surendra P. Shah,et al.  Effect of Length on Compressive Strain Softening of Concrete , 1997 .

[9]  Alessandro Pasquale Fantilli,et al.  Size effect of compressed concrete in four point bending RC beams , 2004 .

[10]  Alberto Carpinteri.  A fracture mechanics model for reinforced concrete collapse , 1981 .

[11]  Mitsuyoshi Akiyama,et al.  CONCENTRIC LOADING TEST OF RC COLUMNS WITH NORMAL- AND HIGH-STRENGTH MATERIALS AND STRESS-STRAIN MODEL FOR CONFINED CONCRETE CONSIDERING COMPRESSIVE FRACTURE ENERGY , 2005 .

[12]  A. Hillerborg,et al.  Sensitivity in Shear Strength of Longitudinally Reinforced Concrete Beams to Fracture Energy of Concrete , 1988 .

[13]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[14]  R. Eligehausen,et al.  Rotation capacity of plastic hinges and allowable degree of moment redistribution , 1987 .

[15]  Alberto Carpinteri,et al.  Influence of material parameters and geometry on cohesive crack propagation , 1985 .

[16]  M.R.A. van Vliet,et al.  Experimental investigation of concrete fracture under uniaxial compression , 1996 .

[17]  Gabriel O. Ribeiro,et al.  Analysis Of Reinforced Concrete Structures Using Ansys , 2022 .

[18]  Alberto Carpinteri,et al.  Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium , 1985 .

[19]  Alberto Carpinteri,et al.  Stability of Fracturing Process in RC Beams , 1984 .

[20]  Crescentino Bosco,et al.  Experimental investigation on the ultimate rotational capacity of r.c. beams , 1992 .

[22]  Juan José López Cela,et al.  Material Identification Procedure for Elastoplastic Drucker–Prager Model , 2002 .

[23]  Surendra P. Shah,et al.  Shear Resistance of Reinforced Concrete Beams--A Fracture Mechanics Approach , 1990, SP-118: Fracture Mechanics: Application to Concrete.

[24]  Z. Bažant,et al.  Size effect in shear failure of longitudinally reinforced beams , 1984 .

[25]  David Darwin,et al.  Fracture Energy of High-Strength Concrete , 2001 .

[26]  A. Carpinteri,et al.  Softening and Snap-Through Behavior of Reinforced Elements , 1992 .

[27]  J. R. Carmona,et al.  Flexural to shear and crushing failure transitions in RC beams by the bridged crack model , 2007 .

[28]  W. Corley.  Rotational Capacity of Reinforced Concrete Beams , 1966 .

[29]  Alberto Carpinteri,et al.  Minimum reinforcement in high strength concrete , 1990 .