The influence of the kinematics of rough surface engagement on the transfer of forces in cracked concrete

One of the most instrumental aspects governing the response of structural concrete at ultimate limit state refers to the possibility of developing smeared cracking patterns within a member (associated normally to the presence of sufficient reinforcement for control of cracking) or whether failures are associated to localization of strains in a single crack. In the former case, the strains are smeared. New cracks can develop at different orientations and stress redistributions occur in a controlled manner. These cases are governed by equilibrium and by material yield conditions and can thus be designed according to limit analysis. The response corresponding to crack localization is however associated to potentially brittle failures, occurring by a sudden opening and sliding of a critical crack, and does not normally allow for controlled redistributions of stresses. In this case, the shape and kinematics of the critical crack are governing for the strength of the member and design methods based on limit analysis are generally not applicable. In this paper, a discussion on the transfer of forces in cracked concrete is presented, allowing to consider in a consistent manner both cases where smeared or localized cracking occur. This is investigated by means of the stress state developed in the vicinity of a localized crack and accounting for equilibrium, kinematics and material damage conditions. The approach presented allows for a comprehensive view of the phenomenon of transfer of forces through cracked concrete and to describe cases governed by the material strength or by friction conditions depending on the crack kinematics. On this basis, the implications for shear design of concrete members are discussed.