Minimum reinforcement for crack width control in restrained concrete members considering the deformation compatibility

The current design code EC2 [1] regulates the minimum reinforcement for crack width control in restrained concrete members by taking up the cracking force of the cross section. Although this concept gives straightforward results, its consistent application can lead to high reinforcement amounts with increasing member thickness. The reason is the simplifying assumption of an infinite member length neglecting the deformation compatibility.
The cracking force approach was therefore empirically modified to reflect practical experience, see [2]. However, the main modification of a limited tensile strength seems particularly dubious, as the primarily affected thick members have already a strong developed tensile strength before any risk of cracking occurs at all.
Finally, this circumstance leaves the structural designer with the dilemma of being either uneconomic or having no mechanical proof in a possible case of damage.
However, the mechanically consistent estimation of the minimum reinforcement for crack width control can be achieved by considering the deformation compatibility of the restrained member, see [3]. With the introduction of [4], this deformation-based design concept became state of the art for mass concrete members of hydraulic structures.
This contribution presents the general application of the deformation-based design concept due the findings of [5]. The reliability and the practicability of this approach will then be illustrated by the deformation-based minimum reinforcement design of a trough structure.