- STRUCTURAL MECHANICS
- Inverse Numerical-Analytical Method For Calculation Of Light Steel Thin-Walled Rod Elements
- UDC 624.072.2.014.2-415:624.014 DOI: 10.33622/0869-7019.2021.03.57-68

**Grigory I. BELYY**, e-mail: office@erkon.ru

**Maksim O. SMIRNOV**, e-mail: smirnov.maxim.sk@gmail.com

Saint Petersburg State University of Architecture and Civil Engineering, 2-ay Krasnoarmeyskaya ul., 4, Saint Petersburg 190005, Russian Federation

**Abstract**. To improve and develop practical methods for calculating rod elements of light steel thin-walled structures, an inverse numerical-analytical method is proposed, which makes it possible to reduce the calculation time by several orders of magnitude in comparison with existing methods. For a given limiting stress state in an unreduced section under the combined action of a longitudinal force and bending moments in two planes, a reduction is determined that makes it possible numerically, using the "section" algorithm, to establish the forces actually perceived by this section - the inverse solution of strength problems. In problems of spatial stability, the forces obtained in this way are taken in the most loaded section as deformation ones. In this case, additional loading with fictitious efforts compensates for the effect of reduction. Then, given the flexibility of the bar, the corresponding loading conditions are determined by the inverse analytical solution of the deformation problem: end biaxial eccentricities of the actually acting force. In the same way, simpler problems of stability in bending and bending-torsional forms are solved. For the purpose of practical application, the solutions are constructed in dimensionless parameters using the longitudinal force coefficients, relative eccentricities and reduced flexibilities. Comparison of numerous calculation results according to the method proposed and the finite element method using the ANSYS program showed their good agreement, and comparison with Eurocode revealed that the latter significantly underestimate the spatial stability. The design examples also illustrate the effect of the actual section reduction on the bearing capacity, which can be accounted for by the buckling factor and the section shape, thus preserving the traditional strength and overall stability checks.

**Key words**: steel thin-walled rods, strength under general case of loading, spatial stability, loss of local stability and section shape, section reduction. - REFERENCES

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