Review article

The paper considers construction designs as single-span plates with rib stiffeners located in one direction. The boundary conditions of the considered design are the following: two opposite ends are fixed rigidly and the other two opposite ends are free. in order to calculate the stress-strain state (SSS) of such structures, the authors use numerical methods, such as the finite element method (FEM). it is also approximated that the beam analogy can be applicable for the calculations. The paper gives an analytical justification when the problem of calculating structures can be considered axi-symmetric and proposes a simple, but more accurate than beam analogy, methodology for calculating such structures. The method of L. V. Kantorovich in the first and second approximation is used due to which the variational problem for the double integral is reduced to the variational task for the one-dimensional integral. The ordinary differential equations and boundary conditions are found from the minimum condition of the obtained one-dimensional functional. if ribs stiffness is “smeared” over the plate, a received boundary value problem has exact solution. For ribs of different configurations (box, T-beam, i-beam, continuous section) the stiffness of reinforcements is analyzed to select the most rational one. Stiffness characteristic are provided for every rib type.