Deformation Model and Algorithm for Calculation of Reinforced Concrete Structures of Round Cross-section Under Torsion with Bending

Despite a fairly long period of research and a significant number of publications around the world on the problem of the complex resistance of reinforced concrete, the existing calculation models still remain far from perfect. This is especially true for structures with a non-rectangular cross section. The article presents a version of the model and an algorithm for the analytical calculation of reinforced concrete structures of a circular cross section in torsion with bending, which most fully reflects the specifics of the power resistance of such structures. The model takes into account all the components of external forces in a rod element of a circular cross section, the spatial nature of cracks, with the combined action of moments, various cases of the location of the compressed concrete zone, depending on the ratio of the acting forces in the calculated structure. For a spatial crack, calculated sections are taken in the form of diagonal large and small ellipses and a spatial surface bounded by concave and convex spatial parabolas. In compressed and stretched concrete, a broken section of three sections is considered, two in the form of longitudinal trapezoid and the third, middle section in the form of a small ellipse rotated at an angle to the longitudinal axis of the structure. The obtained analytical dependencies allow one to determine interconnected design parameters, such as stresses in the concrete of the compressed zone, the height of the compressed concrete, stresses in the longitudinal and transverse reinforcement, deformations in concrete and reinforcement, the length of the projection of a spatial inclined crack, and others. The deformation model and algorithm can be used in the design of reinforced concrete structures of circular and annular cross-section, working in bending with torsion.