The development of methods for calculating the stiffness of reinforced concrete structures with cracks at the limit states is an urgent task. The proposed method implies that the spatial cracks develop on special bilinear surfaces. It involves dividing a rectangular section into a series of squares, which are subsequently replaced by the circles inscribed in them. This approach requires the introduction of the concept of “equivalence” between the torsional stiffness characteristics of a rectangular section and the circumscribed circle. The equation for determining the tangential torsional stresses (taking into account the deplanation) at any point of the cross section is written in a cylindrical and Cartesian coordinate system. Two variants of modelling a real crack are proposed: in the form of stepwise located three-dimensional finite elements that are detached in common nodes, or using an imaginary crack along which pairs of finite elements are picked out. So, we use a special double cantilever model for the calculation. Having a picture of the applied force and deformation loads (crack opening) in the console nodes, it is possible to determine the values of the work in the state: “before detach” and “after detach” of the double-element model.

The physical essence of the “nagel effect” for main reinforcement in a spatial crack of reinforced concrete structures under the action of bending and torsion for the model of reinforced concrete structures deformation involves the formation of the first block and the second block of a spatial crack. The second block is located on the upper surface of the longitudinal reinforcement to the surface of normal stresses and the resultant force from crushing concrete and a special adhesion force to the surface of the reinforcement (and the additional effect of breaking the continuity) in the eccentricity to its center of the axis of the reinforcement for distributed variable bending moment (through the calculation of statically indefinable systems for the force method). It is important to allocate a special area of the left side for the longitudinal reinforcement in the first block of separation and the formation of a new longitudinal crack, which removes surface normal and tangential of stress adhesion. Consider the scheme-a beam with two fixed ends: to calculate it, take the main system obtained as a result of making a cut in the middle of the beam for given unit diagrams of bending moments: under the action of a vertical load; with linear displacements of the fixed ends (normal to the beam axis); with rotations of the fixed ends in construction mechanics.

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.

The physical essence of the “nagel effect” for main reinforcement in an inclined crack of reinforced concrete structures for the model of deformation of reinforced concrete structures includes formation of the first block and the second block of an inclined crack. This effect is considered is constructions under the action of vertical load, with linear displacements (normal to the axis of the beam) and rotations of the fixed end. We can find the unknown τad from the canonical equations for structural mechanics. When we multiply the single diagrams of bending moments caused by displacements Δ1 and Δ2 and displacement caused by longitudal force Ns (x) and increment ΔNs . In this case, for the “nagel effect”, we take into account the presence of several forces and displacements: the force P1 for the surface for the second block; adhesion to the surface of the reinforcement τad and a special force for the effect of discontinuity (ΔT); displacements for mutual shifts of the crack edges (Δ1); movement from the width of the crack opening (Δ2 = acrc ); angle of rotation for the fixed ends; variable longitudinal force in the fixed ends.