Calculation of the stiffness of reinforced concrete structures under the action of torsion and bending

Abstract

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.