Calculation of reinforced concrete ceilings with normal cracks accounting the Chebyshev approximation

Abstract

The article shows the influence of torsional rigidity of reinforced concrete elements on the spatial work of bridges, overlappings, building frames and other complex statically indeterminate systems. It is shown that the determination of torsional stiffnesses by the existing methods assumes the obligatory presence of spatial spiral cracks, and torsional stiffness in the presence of normal cracks is not investigated. A method for determining the torsional rigidity of reinforced concrete elements is described in the presence of normal cracks in them. It is shown that this approach allows calculating the torsion of reinforced concrete elements of any cross-section and taking into account the nonlinear properties of concrete. The article also describes the use of approximation methods, in particular, the apparatus of the best Chebyshev approximation. In Table 2, the displacements obtained as a result of the approximation with the displacements obtained directly from the calculations using the Lira software using volumetric finite elements are compared. In column 6 of the table, the displacement values obtained by software package (Lira software) and in column 7, the displacements obtained on the basis of approximation in the Matlab environment are given.