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- BUILDING STRUCTURES, BUILDINGS AND FACILITIES
- Development And Approbation Of A Mathematical Model Of Spatial Deformation Of SIN Beams
- UDC 624.046.5 DOI: 10.33622/0869-7019.2021.04.18-25

**Sergey A. MAKEEV**, e-mail: makeev608079@mail.ru

Siberian State Automobile and Highway University (SibADI), prospekt Mira, 5, Omsk 644080, Russian Federation

**Natalia G. SILINA**, e-mail: n.silina@stako.ru

Melnikov Central Research and Design Institute of Steel Structures, ul. Arkhitektora Vlasova, 49, Moscow 117393, Russian Federation

**Zinoviy N. SOKOLOVSKY**, e-mail: ninasok@yandex.ru

Omsk State Technical University (OmSTU), prospekt Mira, 11, Omsk 644050, Russian Federation

**Abstract**. The construction of an adequate mathematical model of the spatial bending of corrugated beams (SIN beams) in an elastic formulation, taking into account large displacements, is an urgent task, the solution of which will make it possible to study the overall stability of corrugated beams, including under loads exceeding critical loads. A mathematical model of a straight rod, including corrugated beams (SIN beams), is constructed in the mode of oblique bending with tension-compression and torsion. The developed model is represented by a system of 12 nonlinear differential equations with the possibility of studying the stress-strain state of beams of variable cross-section loaded with various transverse distributed and concentrated loads, with any boundary conditions of fastening. The constructed model is applicable for the estimation of critical loads by the method of imperfections, as well as for the study of the postbuckling behavior of straight rods with loss of overall stability during bending, including beams with corrugated walls. An algorithm for solving the developed system of differential equations is developed, implemented and verified. With the help of the developed mathematical model, a numerical study of the behavior of an experimental corrugated beam (SIN beam) in the mode of transverse bending in the wall plane was carried out with the verification of loads corresponding to the first form of loss of stability of the beam from the wall plane in LIRA-CAD.

**Key words**: mathematical model, differential equations, corrugated beam (SIN beam), general stability of beam from wall plane, critical load, Euler's method. - REFERENCES

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