To the calculation of the stability of lattice elements of steel structures

Introduction. The practical method of calculating lattice elements of steel structures for local and general stability contains an internal contradiction. The general stability check assumes the presence of an additional branch bending arrow in the lattice plane, and the local stability check negates it, which does not guarantee local stability when checking the general stability of the lattice rod. The calculated combinations of forces at the ends of any structural element, under the action of the same calculated combinations of loads, almost always have different values. Consequently, the longitudinal forces in the branches of the lattice elements, separated by the calculated length from the lattice plane, will always be variable, which is not taken into account in the current design standards. Materials and methods. To eliminate the mentioned contradiction, an analytical method is proposed for solving the problem of general stability of lattice elements of steel structures, taking into account the provision of local stability of the most loaded branch. The solution of the problem of stability of a branch from the lattice plane (two-branched elements) is carried out using the inverse numerical-analytical method: according to a given stress-strain state in the most loaded section of the elastic branch, acting and fictitious, compensating for the development of plastic deformations, deformation forces are numerically determined. Then, by the inverse analytical solution of the deformation problem, the actual loading of the branch at its ends is established. Results. The coefficient of overall stability of lattice elements is determined by solving a quadratic equation that includes an additional dependence on the coefficient of stability of the branch in the lattice plane. The stability coefficient of the branch from the lattice plane is obtained in the general case of loading by a longitudinal force with different values of end eccentricities in combination with a uniformly distributed axial load. Conclusions. An analytical solution to the problem of general stability of lattice elements is proposed, taking into account the stability of the branch. The solution of the problem of stability of a branch from the lattice plane (two-branched elements) is obtained when it is actually loaded with a variable longitudinal force acting with different values of terminal eccentricities.