Cracking analysis of partially prestressed concrete tie taking account of the effect of secondary cracks

A further extension of a general crack prediction model to the case of a concrete tie reinforced ...with two types of bars with different diameters and different bond characteristics, subjected to a statically applied axial force, is here presented. This applies to the case of a partially prestressed concrete tie reinforced simultaneously by ordinary and prestressing steels, since the bond behaviour of prestressing steel is different from the bond behaviour of reinforcing bars. 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 by 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 internal secondary cracks, or Goto cracks, is taken into account. The refined method allows the stress redistributions between prestressing and reinforcing steels to be considered. Finally, the theoretical results of the crack spacing and the crack width, obtained with the general model are compared to the experimental data available in the literature.