To the approximation of rectangular and complex cross-sections of reinforced concrete structures under the action torsion with bending

Abstract

Special analytical method for determining tangential tension stresses in reinforced concrete structures operating in conditions of complex resistance –torsion with bending is proposed in this paper. Its peculiarity consists in the approximation of rectangular and any complicated cross-sections of reinforced concrete structures with the help of their division into squares with the circles inscribed there in, connected together into a single monolithic figure. The dependence of tangential torsion stresses becomes valid on the distance to the centre of the circle under consideration within each j-th circle. The further the circle from the centre of the rectangle is located, the greater its moment of inertia becomes and the maximum stresses are reached in the middle of the rectangle the long sides. Such model makes it possible to remove the question of the necessity using of special tables also for their calculation in the elastic stage. Also it makes possible to separate the stress-strain state in a whole set of circular sections from the additional field associated with the deformation of the rectangular section. The authors corrected and significantly supplemented the dependencies for taking into account the deplanation of a rectangular cross-section rod. Attention is focused on the physical essence of longitudinal displacements caused by deplanation, an analogy with elementary movements caused by shearing forces is carried out. In the study, the classification of spatial cracks for reinforced concrete rod structures under the action torsion with bending was generalized; while the process of spatial cracks formation of the first, second, and third types is tied to the proposed method for determining tangential stresses (angular deformations) for complex cross-sections. The proposed dependencies allow us to search for the values of the model design parameters at of the stress-strain state stages of the reinforced concrete rod structure, including in the plastic and in the limiting stages. The components of the torsion stress (angular deformations) are again synthesized and separated by the proposed method for the convenience of analysis in principal stresses tensors (main strains). Transformational transitions from a cylindrical to a Cartesian coordinate system and the attraction of local coordinate systems made it possible to simplify the equations as much as possible. Moreover, the equations are constructed in such a way that the resolving system does not turn into a decaying system. The physical interpretation of the solution obtained, with respect to the problem of crack resistance, is that it allows us to search for the minimum generalized load that corresponds to the formation of the first, second or third spatial crack types and the coordinates of their formation point. As a result, the effectiveness of the proposed method is shown with approximating rectangular and complex cross sections of reinforced concrete structures under the action torsion with bending and taking into account physical nonlinearity, deplanation of cross-sections, pre stressing in longitudinal and transverse reinforcement and the influence of local stress fields.