The Limit State of a Multilayered Physically Nonlinear Concrete Rods

The paper considers the problem of longitudinal and transverse bending of the multilayered concrete rods of constant cross section under the quasi-static loads. It is assumed that concretes are deformed linearly at deformations below the elastic limit, and nonlinearly quasi-elastically above it. In the area of nonlinear deformation, the correlations between strain and deformation are taken in the form of the second-order polynomials with different coefficients for different grades of concrete. It is supposed that there is a uniaxial strain condition, and in the compression area all layers of the rod are elastically deformed, while in the tension area the layers can be in the areas of elastic, nonlinear quasi-elastic deformation and include the boundary of these two areas. The presented analytical correlations are obtained to determine the distribution of displacements, deformations, forces, and the position of the neutral line in the case of a statically determinable problem of transverse bending of a hinged rod. An algorithm to determine the possible external loads is given for each of the possible deformation configurations in the rod layers.