Material model for the analysis of reinforced concrete surface structures

A material model for the analysis of reinforced concrete surface structures is developed. The constitutive model employs the smeared crack concept, i.e. only average stresses are considered at an integration point. While uncracked concrete is modelled with a plasticity approach, the paper focuses on the numerical treatment of cracked reinforced concrete in a state of plane stress. Special attention is given to the modelling of the tension stiffening effect, the re-orientation of the principal tensile strain direction and the compressive strength of cracked concrete. The material model has been implemented in the finite element program SEGNID and tested extensively. Here the comparisons of calculated and experimentally measured results on reinforced concrete surface structures-several panels, a plate subjected to torsion and a free-formed shell-are presented.List of symbols d bar diameter - D stiffness matrix - D_c stiffness matrix of concrete - D_s stiffness matrix of reinforcement - D rotational stiffness matrix - f stress - f_c stresses in concrete - f_c1 tensile stress in concrete - f_c2 compressive stress in concrete - f_c2,min concrete compressive strength - f_c cylinder crushing strength - f_s stresses in reinforcement - f_t concrete tensile strength - f_y yield strength of reinforcement - f₁ applied principal tensile stress - f₂ applied principal compressive stress - F tension force - F_y yield force - l length - M moment - Q dowel resistance - r_xy vector of unbalanced stresses - s applied load - s applied stress vector - T₁, T₂ transformation matrices - w crack width - x, y reference coordinate system - 1, 2 crack oriented coordinate system - curvature - _xy incremental strain in the reference coordinate systemExtended version of the contribution Two-dimensional FE-analysis of reinforced concrete membrane elements to the International Conference on Computational Engineering Science, Atlanta, April 10–14, 1988, presented by the second named author