THEORETICAL SOLUTION OF THE EQUATIONS OF EQUILIBRIUM FOR REINFORCED CONCRETE ELEMENTS OF CIRCULAR CROSS SECTION

Abstract

The article is devoted to the theoretical determination of the parameters of the stress-strain state of reinforced concrete elements of round cross section.

In modern buildings and constructions, structures of circular cross section, including columns, supports, piles, pylons and many other elements are quite widespread. There exist approximate methods of calculation of such reinforced concrete elements. The theoretical solution of the equations of equilibrium for reinforced concrete elements of circular cross section allows increasing the accuracy of calculations, contributes to further progress in the development of a comprehensive theory of reinforced concrete.

The purpose of the study is the theoretical solution of integral equations of equilibrium for reinforced concrete elements of circular cross section for the possibility of determining their stress-strain state.

In equilibrium equations, the specified integral characterizes the work of compressed concrete. For an element of circular cross section, it can be geometrically represented for a compressed cross section in the form of a body with a base limited by a circle or circle and its chord, the height of which is described by a fifth order polynomial. In this case, the bending moment perceived by the compressed concrete is found through the multiplication of the resultant force applied in the geometric center of the given body by distance h from the force to the extreme compressed fiber in the cross section.

Based on the recurrence formula for the integral of the differential binomial, there has been obtained a theoretical solution of the equilibrium equations of a normal circular cross section for reinforced concrete structures within the generally accepted assumptions. In the case when the circular cross section of the concrete structure does not have a stretched zone, an accurate laconic solution of the equilibrium equations of the stress-strain state is obtained after conducting mathematical transformations.

The article presents a theoretical solution of equilibrium equations for a normal circular cross section of reinforced concrete structures within generally accepted preconditions, which allows determining analytically the stress-strain state of reinforced concrete elements in a possible range of changes in the properties of concrete and reinforcement steel for any stage of structural load.