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

A mathematical 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 assumption that the crack spacing is maximum and equal to twice the transmission length, the effect of primary and secondary cracks is taken into account. This leads to distinguish, in the stabilized cracking stage, an initial transitional phase where the transfer length of ordinary steel is smaller than the transfer length of prestressing steel, followed by a fully developed phase, where the two transfer lengths are equal to each other. Finally, the theoretical results of the crack spacing and the crack width, obtained with this refined model are compared to the experimental data available in the literature.