Generalized Deplanation Hypotheses for Linear and Angular Deformations in Reinforced Concrete Structures under Combined Torsion and Bending

Abstract

Statement of the problem. The analysis of the deplanation hypothesis for linear and angular deformations in reinforced concrete in bending with torsion has been carried out. Results. A simple new method from the method of grids has been developed for complex functions under the combined action of bending and torsion. Diagrams of linear and angular deformities and a new hypotheses have been analyzed. Complex functions have been found to determine the linear and angular deformations, bending and torque moments in the compressed area of concrete. The author has found the projection coefficients of linear and angular deformations using diagrams of compressed concrete and main reinforcement. Deplanations from a special geometric figure of deformations in a complex function have been found. There are vectors of several triangles and gradients where the proportions of a hypotenuse, cathetuses and vectors have been derived. Conclusions. It is also important that similar relative values can be obtained for any vectors. A field of small squares have been plotted and jumps from lateral, normal and other cracks appear have been determined. Fillings of the deformation (stress) diagrams have been obtained for the analysis of the moments in bending with torsion using simple expressions or in a full form. The research on the complex function of linear and angular deformations and the approximation of a function from Timoshenko-Goodyear have been carried out. The error of the deformations value of using the complex function at the points under study is 2% and is 7% at any points of the cross section.