In a reinforced concrete member, especially in a beam, mechanisms of shear transfer are as follows:1. The force created in shear bars after diagonal cracks, 2. The shear capacity of the concrete in a part of the compressive region of the concrete with no crack, 3. The forces from the aggregates interlock at both sides of the crack, 4. The force due to the dowel action of the flexural bars that connect both sides of the crack and create resistance against shear deformation of the crack. Dowel action can be defined as follows: the ability of the longitudinal bars to transfer the force perpendicular to their axis. The distance between the longitudinal axis of the non-deformed parts at both sides of the crack is considered as the deformation of the dowel bar.
To be able to analyze and design the reinforced concrete structure members correctly, their behavior must be evaluated under different loadings. The efficiency, accuracy, and speed of the structure analysis techniques depend on using suitable behavior models. In reinforced concrete structures, the concrete will be cracked under normal loadings due to its weakness in tension. Therefore, it is important to know the mechanisms of stress transfer in the cracked surfaces to evaluate the response of the reinforced concrete structures. In recent years, an extensive experimental and analytical study on the effect of longitudinal bars in shear transferring (dowel action) has done. Almost all the models presented the theory of Beam on Elastic Foundation (BEF) as the best way to simulate the behavior of the dowel action. In this model, the subgrade stiffness of concrete is the most important parameter. BEF model is a linear model because the dowel bar and its surrounding concrete are modeled by a uniaxial element on a row of springs. The advantage of the linear models is that they gather all features of the concrete and the interaction of the concrete-bar in a bearing stiffness coefficient. For this reason, a suitable formulation is required for it to model the beam behavior from the elastic stage to the failure. In the elastic state, the bearing stiffness can be presented as a constant like BEF traditional models. However, in the nonlinear state, the stiffness must be a function of displacement to model the failure due to the load.
 In the present research, an experimental program is followed on the beam-type specimens to identify the behavior of the cracked surfaces under the effect of the shear. Using the test specimens made of ultra-high performance concrete, the shear transferred through a longitudinal bar (dowel action) is measured. The shear response of the dowel bar, the subgrade stiffness, and the displacements are measured. Furthermore, suitable formulations are proposed for the UHPC subgrade stiffness.  Based on the results of the tests and using the studies of other researchers, a suitable model is presented for the shear mechanism through the bar in the cracked surfaces of ultra-high performance concrete. The results show the suitable precision of the proposed relations to estimate the dowel displacement-shear curve in the specimens with vertical and inclined cracks.

Keywords: Dowel action, Bearing stiffness, Ultra high performance concrete, steel bar

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