An analytical solution of the elastic concrete ring under restrained shrinkage, considering an interlayer slip

Restrained shrinkage is a common cause of cracking in concrete structures. It is often investigated by the ring test, which consists of a concrete ring restrained by an inner steel ring. Due to the imposed restraint, cracks can form in the concrete ring over time. In this paper, a new analytical method for the concrete ring under restrained shrinkage is presented. The method is based on the geometrically exact Reissner beam theory. It considers creep strains in addition to autogenous and drying shrinkage strains. A model of adhesive contact between the steel ring and the concrete ring is assumed. The method provides exact solutions for the deformation of the concrete ring, the induced stresses due to shrinkage and creep of concrete and the contact tractions. The new analytical method is applied for the case of a flexible and a rigid steel ring, and for two concrete mixes, differing in strength and stiffness parameters. The obtained results, which are in agreement with the experimental findings reported in the literature, show that the stiffer and stronger concrete leads to a longer time to crack formation. The first crack forms earlier, and the magnitude of the extensional strain is smaller when the steel ring is stiffer. Large magnitudes of creep strain result in later cracking. It is also shown that the contact stiffness affects the extensional strain of concrete and the time of crack formation. The components of the contact traction change with location and time.