A new cracking model for concrete ties reinforced with bars having different diameters and bond laws

This paper presents a model to predict the cracking behavior of concrete ties, reinforced with ribbed and plain bars having different diameters, subjected to a statically applied axial force. The model is based on linear elastic stress-strain (σ-ε) laws for both types of bars as well as for concrete and takes into account the effects of curing on concrete mechanical properties, as well as the effects of tensile creep and concrete restrained shrinkage strains. Different slip-bond relationships for ribbed and plain bars are considered. The non-linear differential equilibrium equations of the ties are solved numerically. Model accuracy has been checked for predictions of the crack widths and spacings, considering 52 experimental data. The proposed model is then applied to the concrete footing of the NPS®Cls, in order to show the cracking behavior of this element at the start-up.