"Finite Element Analysis of Reinforced Concrete Structures Under Monotonic Loading"
by H.G. Kwak and F.C. Filippou

Abstract: This study deals with the finite element analysis of the monotonic behavior of reinforced concrete beams, slabs and beam-column joint subassemblages. It is assumed that the behavior of these members can be described by a plane stress field. Concrete and reinforcing steel are represented by separate material models which are combined together with a model of the interaction between reinforcing steel and concrete through bond-slip to describe the behavior of the composite reinforced concrete material. The material behavior of concrete is described by two failure surfaces in the biaxial stress space and one failure surface in the biaxial strain space. Concrete is assumed as a linear elastic material for stress states which lie inside the initial yield surface. For stresses outside this surface the behavior of concrete is described by a nonlinear orthotropic model, whose axes of orthotropy are parallel to the principal strain directions. The concrete stress-strain relation is derived from equivalent uniaxial relations in the axes of orthotropy. The behavior of cracked concrete is described by a system of orthogonal cracks, which follow the principal strain directions and are thus rotating during the load history. Crushing or cracking of concrete takes place when the strains lie outside the ultimate surface in the biaxial strain space.

A new smeared finite element model is proposed based on an improved cracking criterion, which is derived from fracture mechanics principles. This model retains objectivity of the results for very large finite elements, since it considers cracking to be concentrated over a small region around the integration point and not over the entire finite element, as do previous models.

A new reinforcing steel model which is embedded inside a concrete element, but accounts for the effect of bond-slip is developed. This model results in significant savings in the number of nodes needed to account for the effect of bond-slip, particularly, in three dimensional finite element models. A new nonlinear solution scheme is developed in connection with this model.

Finally, correlation studies between analytical and experimental results and several parameter studies are conducted with the objective to establish the validity of the proposed models and identify the significance of various effects on the local and global response of reinforced concrete members. These studies show that the effects of tension-stiffening and bond-slip are very important and should always be included in finite element models of the response of reinforced concrete members. On the other hand, parameters, such as the tensile strength of concrete and the value of the cracked shear constant, do not seem to affect the response of slender beams in bending.

If you are interested in a copy of this report, send e-mail to Professor Filippou 

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