Deplanation hypotheses for angulardeformations in reinforced concrete structures under combined torsion and bending

The article analyzes the hypothesis of deplanation of angular deformations in reinforced concrete structures during bending with torsion. A simple method from the field of the grid methods for approximating the deformations of complex functions under the 3D stress state is considered. Diagrams of angular and linear deformations in such structures were built and analyzed to find these deformations, bending and torques perceived by the concrete of the compressed area using the accepted hypotheses and coefficients for projecting normal and shear stresses (strains) through diagrams of compressed concrete and working reinforcement. Approximating the calculated section by small squares, a spatial surface of deformations was constructed. This is with the corresponding gradients of these deformations in the section with a crack, and on this basis, expressions were written for the total longitudinal deformations in the section and shear deformations in the section of the element during bending with torsion. Using the membrane analogy of the Timoshenko-Goodyear stress functions and the proposed version of new complex functions from the field of the grid method, an analysis was made of its error, when we find the value of complex functions at the considered characteristic points (2%) and at any points of the cross section (7%).
The use of the proposed hypotheses and the given version of complex functions makes it possible considering the warping of the 3D stressed section of a reinforced concrete element with cracks undergoing bending with torsion.

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