Fracture Mechanics of Reinforced Concrete

by Zdeněk P. Bažant, (F.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
Luigi Cedolin, (M.ASCE), Assoc. Prof.; Politecnico di Milano, Milano, Italy; formerly, Visiting Scholar, Northwestern Univ., Evanston, Ill.,

Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 6, Pg. 1287-1306

Document Type: Journal Paper


The propagation of an element-wide blunt smeared crack band in a finite element mesh is analyzed. The results strongly depend on element size; e.g., a four times reduction in element size causes a 3.5 times reduction in the load to cause further crack propagation in a reinforced concrete planel. An energy criterion for crack band extension in concrete with a dense regular reinforcing grid is formulated and it is shown to be objective, i.e., the results for greatly different element sizes cioncide. This is achieved, however, only if bound slip near the crack band is also taken into account. An approximate formula for the lenght of bond slip of the bars crossing the crack band is derived, and for implementation in finite element programs an expression for an equivalent lenght of free bond slip (slip without bond stresses) is determined. The energy criterion is also generalized for nonlinear material behavior numerical results are given.

Subject Headings: Reinforced concrete | Finite element method | Bonding | Material properties | Cracking | Mesh generation | Load factors | Grid systems

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