The stability calculation of a П-shaped hinged frame is considered. The concept of r-like frames is introduced as frames with the same ratio r of the linear stiffnesses of the transom and the strut. It is shown that the parameter vcr , which determines the critical load on the frame, is the same for r-like frames. Approximate formulas allowing to determine the critical load parameter vcr and design lengths of compressed bars with an error not exceeding 2% are obtained.

Keywords: flat frame, stability, critical force, reduced length coefficient, r-like frames, approximation, least squares method

The shear calculation scheme of a multi-storey building, popular in design practice, is considered.The application of the method of displacements is shown, when the mutual displacements of the floors of the frame are taken as unknowns. The indicated technique leads to the solution of the system of equations of the displacement method with the upper two-diagonal matrix, which makes it possible to obtain an analytical solution of the problem.

Keywords: shear calculation scheme of the building, move method, tridiagonal matrix, sweep method, reciprocal movements, analytical solution of the equation system