Carrying capacity and optimization of three-layer reinforced concrete annular plate, supported on the internal contour

Within the model of an ideal rigid-plastic body the exact solution is obtained for the problem of bending of three-layer reinforced concrete annular plates having different angular structure reinforcement at the top and bottom layers. The middle layer of the plate is made of concrete. The plates are hinge supported along the annular contour located within the area of the plate. External and internal contours of the plates are free. The plates are under load uniformly distributed over the surface of the plate. The condition of plasticity for the main moments, based on a structural model of the composite, has the form of a rectangle of type Johansen condition. It is taken into account that the strength of concrete in tension is much less than in compression. It is shown that there are four schemes of limit deformation of the plate, depending on the location of the internal support. The conditions of implementation are defined for all schemes. The main moments and the velocities of the deflections of the plate are defined at different locations of the internal support. The simple analytic expressions are obtained for the limit load. The optimal location of support is determined. The optimal support is such a support, at which the plate has a maximum limit load. It is shown that the optimal position of the support corresponds to the formation of plastic hinge on it. The problem is solved to determine the optimal thickness of the top layer of the plate corresponding to the maximum limit load for a given total thickness of the reinforced layers. It is shown that the location of the support affects the optimal thickness ratio of the upper and lower layers. Numerical examples are given for different structures of reinforcement.