The Second Stage of the Stress-Strain State of Reinforced Concrete Constructions under the Action of Torsion with Bending (Theory)

Authors proposed a new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Authors have formulated three theorems. The first one relates the accumulation of tangential stresses (increments) from the edges to the middle of a rectangular cross-section with the formula for determining tangental stresses for round cross-sections. The second theorem allows us to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows us to remove the need to use special tables for the calculation not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.