Cracking Analysis of Partially Prestressed Concrete Tie Under the Effect of Primary and Secondary Cracks

A mathematical model, named general model, for the cracking analysis of a concrete tie reinforced by ordinary and prestressing steels, subjected to a statically applied axial force, is proposed. The two types of steels do not have only different diameters, but also different bond properties, since in general the prestressing steel presents a lower bond quality with respect to the ordinary steel. The model is based on the assumptions of linear elastic σ-ε laws for both types of steels, as well as for the concrete, and on the bond law proposed in fib Model Code 2010. Both the crack formation stage and the stabilized cracking stage are analyzed. In particular, in the stabilized cracking stage, under the as-sumption that the crack spacing is maximum and equal to twice the transmis-sion length, the effect of primary and Goto cracks is taken into account. More-over, in the stabilized cracking stage two phases are distinguished, that means a first initial transitional phase where the transmission length of ordinary steel is smaller than the transmission length of prestressing steel, followed by a fully developed phase, where the two transmission lengths are equal to each other. Finally, the theoretical results of the maximum crack spacing and the maximum crack width, obtained with the general model, are compared to the experimental data available in the literature showing that the theoretical results are always on the safe side