Abstract
This paper proposes a new planar reinforced concrete (RC) formulation capable of modeling geometric and material nonlinearity. A new co-rotational sub-parametric formulation consisting of a four-noded element with quadratic hierarchic shape functions is presented. The novelty of this large-displacement-small strain element lies in the choice of the local coordinate system and the local degrees of freedom, which is mainly responsible for its simplicity and computational efficiency. For material nonlinearity, the Kotsovos and Pavlovic concrete model is used, with the addition of some numerical modifications including: (1) an accurate tangent stiffness for the nonlinear behavior of uncracked concrete; (2) a nonlinear uniaxial constitutive relationship for cracked concrete; and (3) exact cracking stress evaluation. Assuming perfect-bond, two layers of steel with only axial stiffness are smeared over the element according to their angles of orientation. Verification studies are presented to highlight the significance, limitations, and applicability of the proposed element in large displacement analysis of planar structures.
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