Cracking analysis of concrete tie reinforced with two diameter bars accounting for the effect of secondary cracks

The paper presents an extension of a general crack prediction model, that has recently been proposed in co authorship with Debernardi, to the case of a concrete tie reinforced with two types of bars with different diameters, but with the same bond characteristics, subjected to a statically applied axial force. The model, which is based on the assumptions of linear elastic "sigma-epsilon" laws for both types of bars, as well as for the concrete, and on the bond law proposed in fib Model Code 2010, is used to study both the crack formation stage and the stabilized cracking stage considering the effect of internal secondary cracks. Some case studies are examined to show the influence of the diameters and of the reinforcement ratios on the cracking behaviour, even though they have not been verified experimentally because of a lack of available test results in the literature. Moreover, a parametric analysis is conducted to compare the theoretical results obtained using the general model and the calculation methods proposed in fib Model Code 2010 and Eurocode 2, and it emerges that both standards underestimate the maximum crack spacing and the maximum crack width obtained with the general model. A modified version of the fib Model Code 2010 calculation method, here called Simplified Method, which is based on an improved assessment of the average bond stress that takes into account the effect of internal secondary cracks, is also proposed for the stabilised cracking stage