The effect of finite element mesh size in nonlinear analysis of reinforced concrete structures

Abstract A new approach is developed to the nonlinear analysis of reinforced concrete (R/C) structures subjected to a monotonically increasing load, i.e. from zero up to the ultimate load. Tensile cracking and the nonlinear stress-strain relationship for concrete and reinforcement are taken into account in the analysis. Concrete is assumed to be elastic in the tension region and elasto-hardening plastic in the compression region. The reinforcing bar is considered as a linear strain hardening material. The tension stiffening effect of concrete between cracks is also considered. The effect of finite element mesh sizes on the analysis of the behavior of the structure, which is the most significant among the effects such as load step, and integration orders, etc. is investigated and a new criterion to reduce the numerical error associated with the mesh sizes is developed. This newly developed criterion is based on the fracture energy concept and can be easily implemented into a numerical analysis procedure. In particular, this approach can be used effectively with relatively large finite element mesh sizes. The proposed criterion is tested by comparing the analytical results from this study with those of experimental studies and other previous numerical studies.