Analysis of Crack Spacing in Reinforced Concrete by a Lattice Model

A new numerical method is proposed for prediction of crack spacing in reinforced concrete. It is assumed that the deformation pattern of crack spacing consumes the least energy among all kinematically admissible deformations, and the energy minimization approach is applied to predict crack spacing. To simplify the problem, a lattice model is used, in which the cracking process is represented by softening of the concrete bar elements. The crack spacing due to tension and bending is investigated. The results confirm that crack spacing can be predicted by energy minimization. To account for the influence of the bond slip between the concrete and the reinforcing steel, the traditional bond-link element is employed. The influence of the bond slip on the cracking pattern is studied through numerical examples. The results show that without considering bond-slip, the damage near the reinforcement is distributed rather than localized, whereas considering bond-slip, the damage near the reinforcement is localized. The influence of bond slip on crack spacing is significant.

[1]  Yew-Chaye Loo,et al.  A New Formula for Prediction of Crack Widths in Reinforced and Partially Prestressed Concrete Beams , 2001 .

[2]  D. Borst,et al.  Failure in plain and reinforced concrete : an analysis of crack width and crack spacing , 1996 .

[3]  Characteristics and Computational Procedure in Softening Plasticity , 1989 .

[4]  W. Press,et al.  Numerical Recipes in Fortran: The Art of Scientific Computing.@@@Numerical Recipes in C: The Art of Scientific Computing. , 1994 .

[5]  J. Pamin,et al.  Simulation of crack spacing using a reinforced concrete model with an internal length parameter , 1998 .

[6]  Sami H. Rizkalla,et al.  Crack Prediction for Members in Uniaxial Tension , 1984 .

[7]  Byung Hwan Oh,et al.  New Formulas for Maximum Crack Width and Crack Spacing in Reinforced Concrete Flexural Members , 1987 .

[8]  D. Ngo,et al.  Finite Element Analysis of Reinforced Concrete Beams , 1967 .

[9]  M. M. Giammatteo,et al.  Local bond stress-slip relationships of glass fibre reinforced plastic bars embedded in concrete , 1995 .

[10]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[11]  Arthur H. Nilson,et al.  INTERNAL MEASUREMENT OF BOND SLIP , 1972 .

[13]  Antoine E. Naaman,et al.  Bond Stress-Slip Response of Reinforcing Bars Embedded in FRC Matrices under Monotonic and Cyclic Loading , 1997 .

[14]  C. R. Braam.  Control of crack width in deep reinforced concrete beams , 1990 .

[15]  Graham Baker,et al.  Influence of bond slip on crack spacing in numerical modeling of reinforced concrete , 2003 .

[16]  J. Blaauwendraad,et al.  Crack Models for Concrete, Discrete or Smeared? Fixed, Multi-Directional or Rotating? , 1989 .

[17]  Manfred Keuser,et al.  Finite Element Models for Bond Problems , 1987 .

[18]  M. S. Elgarf,et al.  Bond characteristics of corrding reinforcement in concrete beams , 1999 .

[19]  Z. Bažant,et al.  Spacing of Cracks in Reinforced Concrete , 1983 .

[20]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[21]  G. Hunt,et al.  Computational approach to localization using global energy minimization , 2000 .