CALCULATION MODEL OF A COMPLEX-STRESSED REINFORCED CONCRETE ELEMENT UNDER TORSION WITH BENDING

Abstract

The article presents the methodology and principles of creating calculation models for reinforced concrete structures operating in conditions of complex resistance. A block calculation model of reinforced concrete bar structures in torsion with bending is presented. This model consists of a support block formed by a spatial crack and a compressed zone of concrete closed on it and a second block formed by a vertical section running perpendicular to the longitudinal axis of a reinforced concrete element along the edge of the compressed zone closing the spatial spiral. Cases are considered when the torque effec has the greatest influenceon the stress-strain state of structures. In this case, the following forces are taken into account as the calculated forces in the spatial section: normal and tangential forces in the concrete of the compressed zone; components of axial and shear forces in the reinforcement crossed by a spatial crack. A feature of the proposed calculation model is that it considers independently of each other the strength of an element in spatial sections passing along a spatial crack, and the strength of an element between spatial cracks. The spatial section is formed by a crack located on three sides of the element and a compressed zone located on the fourth side and closing the ends of the spiral crack. In this case, the compressed zone, depending on the ratio of the bending and torque moments, can be located along the horizontal and vertical (lateral) edges of the element. The governing equations are written in the form of static equations for the adopted calculation cross-sections and a closed-loop system that unites them, written as a function of many variables with Lagrange multipliers λ_i. On the basis of the constructed function for all the variables included in it, an additional non-decaying system of equations has been compiled, from which follows a dependence that allows finding the projecton of a dangerous spatial crack.