Determination of stresses in thin-walled steel fiber reinforced concrete roofs in the form of hyperbolic paraboloid

The authors have determined the absolute values of deformations of steel fiber reinforced concrete (SFRC) in a thin-walled shell in the form of a hyperbolic paraboloid that on the basis of which the experimental stresses arising in the shell are determined. The article presents the results of theoretical studies of stresses in thin-walled shells of steel fiber reinforced concrete in the form of hyperbolic paraboloid (hypar), which were determined on the basis of the developed calculation method based on the equations of the moment theory of shallow shells. To solve the basic equations, the authors generalized the method of double series of Fourier, which takes into account the curvature of torsion of the hypars. The solution for the non-fixed hypars with rectangular shape was found through the double series of Fourier with additional application of the iteration method. The coefficients in the series are determined analytically using recurrence formulas. An approach to the study of the stress-strain state of rectangular hypars with a fixed contour is proposed.