Based on the beginning of the least work, theoretical dependencies were obtained to determine the internal forces in the elements of the combined trussed system. The analysis of the calculation results of a trussed beam with four posts was carried out and the physical side of the phenomenon of bending during the interaction of the main structure of the trussed beam with elements of a multi-post truss was revealed.

Keywords: truss beam, combined system, multi-column truss, relative eccentricity, potential energy

The results of the study of the stability of the core structure of a polygonal ring under the action of a system of self-balanced radial forces are presented. A complete solution of the problem is given in accordance with the fundamental equations of the theory of R. Mises as applied to a statically definable planar structure. It is established that the instability parameter of the core structure of the hexagonal ring is determined solely by the number of nodal points of the hinged rod system.

Keywords: core structure, regular polygon, hyperboloid, annular diaphragm, determinant, characteristic polynomial, cyclic symmetry

Outlines the main provisions of the calculation of the stability of statically indefinable systems of regular structure. A planar structure with an external contour in the shape of a regular hexagon and under the action of nodal radial compression forces is considered. An analysis of the stability of the equilibrium state of the core structure is performed and the full range of numerical values of the instability parameter of the system is determined.

Keywords: core structure, regular hexagon, hinge system, characteristic polynomial, triangular panel