Integral Method for Determining the Stress State of an Anisotropic Reinforced Concrete Shell

Abstract

The article deals with the issue of estimating the strength and stress-strain state of a reinforced concrete shell by the method of membrane theory and the theory of infinitesimal bending. A brief description of the methodology consists in the fact that the ground stress state of the shell is allocated to an independent problem, when, without introducing boundary effects, two of the four boundary conditions of the general moment theory are distinguished, which, together with the equations of the momentless theory, determine the ground stress state, and then boundary effects are superimposed. The equilibrium equations of the moment theory in forces and moments, geometric equations, components of tangential deformation and displacement, and the physical equations of state connecting them, expressing forces and moments through the components of deformation, are presented, since the characteristics of the stress-strain state of the shell depend not only on the variability of external influences and forces, but also on the length of the structure. The provisions laid down in the article shall be retained in the case of casings made of anisotropic material, provided that the presented elastic ratio is met. A system of equations of the generalized semi-membrane (semi-bending) state of an arbitrary shell of zero curvature, which determines the accuracy of this approach, is solved. The equations of the semi-torque theory for a circular cylindrical shell are presented, as well as describing the semi-membrane stress state of a long shell of zero curvature. The most important result of the study is the method of constructing integrals of the ground stress state of the shell based on the method of simple iterations, which expands the possibilities of the reliability theory, which makes it possible to build the foundations for the practical calculation of reinforced concrete shells according to the membrane theory and the theory of infinitesimal bending.

Keywords

• reinforced concrete shell
• moment theory
• membrane theory
• displacements
• deformations of concrete
• equilibrium equations