Steel stresses and shear forces in reinforcing bars due to dowel action

Reinforcing bars in structural concrete are typically designed to carry axial forces. Nevertheless, due to their bending stiffness, the bars can also carry transverse forces, that are associated with the localized bending mechanism (dowel action) resulting from the relative displacements (or slip) wherever a crack interface or a discontinuity interface (between two concrete parts cast at different times) intercept the bar. Such localized bending induces stress concentrations in both the bars and the concrete. The relative displacement can occur at interfaces either perpendicular to the bar or inclined with respect to its axis. Thanks to steel ductility, the bending stresses in the bars due to dowel action do not impair the sectional capacity at the ultimate limit state. Fatigue verifications, however, require an accurate evaluation of these stresses under imposed transverse displacements or shear forces. As well known, dowel action can be described by means of the traditional unidimensional Winkler's model (beam on an elastic foundation), where the bearing stiffness of the concrete embedment is typically introduced through a couple of parameters, namely the bar diameter and the concrete strength in compression. The actual behavior of a dowel, however, is definitely more complex and for such a reason, improvements are needed for the Winkler's model to introduce other parameters typical of actual structures. Hence, a new formulation is introduced in this study for the bearing stiffness, that is calibrated based on mechanical considerations and measurements with optical fibers. The proposed formulation also accounts for the following parameters: angle between the crack and the bar, concrete-cover thickness, number of load cycles and the softening effect caused by the local secondary cracks radiating from bar ribs during the pull-out process. The predictions of the model-implemented with the proposed bearing stiffness-fit fairly well the test results under both monotonic and cyclic loads, in terms of shear force-transverse displacement response and peak stress in the reinforcing bars.