Reinforcement impact on state of cracks in concrete slabs

In the present work the stress-strain state of a reinforced concrete slab with a transverse edge crack of constant depth is considered. There is investigated the effect of reinforcement upon the distribution of the fracture mechanics along the crack front. The uniformly or linearly distributed stresses at the slab ends are described as an external load. These loads correspond to pure tension and pure bending of the slab, respectively. For a case when the depth of the crack is less than the depth of the reinforcement rod, an analytical approach for an assessment of the crack state is proposed. As a characteristic of the crack state, the stress intensity factor (SIF) is used. Using the finite-element CalculiX package, the numerical results have been obtained, and adequacy of the analytical solution justified. The calculations have been performed for a wide range of variations in the geometrical parameters of the slab and the crack. For this purpose, a principle of replacing the external load with the pressure on the crack faces, well known in linear fracture mechanics, is generalized for the case of heterogeneous elastic bodies. The results of calculations show that the variation of the SIF value along the crack front is insignificant (up to 5% for practically realizable parameter values). On this basis it is concluded that the crack depth most likely is constant in the early stages of its fatigue development. For shallow cracks the SIF value will decrease near the reinforcing rod. It is interesting to note that for deep cracks the presence of reinforcement can lead to local increasing, not decreasing, of the SIF values. Considering this fact, the results presented in the paper may be useful in the design of reinforced concrete structures. It is especially important to take it into account in an individual design, in particular, in designing agricultural buildings where non-standard reinforced concrete structures are used.