English
Русский 31-46 p.
This article discusses the method of static calculation of multi-span thin-walled beams with bending torsion in the framework of the semi-shear theory of V.I.Slivker. The main advantage of the semi-shear theory is that it is suitable for rods of both open and closed (as well as open-closed and multi-contour) profiles due to the similarity of differential equations according to the theories of V.I. Slivker and A.A. Umansky, and also increases the accuracy of the calculation due to taking into account part of the shear deformation. The analytical solution of the problem is obtained based on three bimoments equations system of, including values of correlating functions for cases of application of torsional loads in the span and on the cantilever of thin-walled multi-span continuous beams. Bimoment func-tions for a number of simple beams are obtained within the framework of the semi-shear theory. It is shown that the values of the parameter of the influence of the shape of the cross-section of the semi-shear theory ranges from 1.000086 to 1.0014 for channel profiles, while the presence of shelf bends (C-profile) in comparison with the channel profile reduces the value of this parameter by 10%, which indicates a lower contribution of part of the shear deformations to the stress strain state at the torsion of the C-profile. It is shown that, despite the convergence of the calculation results by the proposed method, due to the proximity of the values of the shape influence parameter to 1.0 with the similar one according to the theory of V.Z. Vlasov, the area of application of the proposed method are significant-ly wider (both open and closed profiles).
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[3] Bondar V.T. Comparative analysis of the stress-strain state of profiled sheets S-44-1.5 mm, S-21-1.5 mm, CIMC-D02-01A 1.6. Engineering Research. 2022. 3 (8). P. 11 – 19. (rus.)
[4] Gordeeva A.O., Vatin N.I. Computational finite element model of a cold-bent perforated thin-walled rod in the SCAD Office software and computing complex. Civil Engineering Journal. 2011. 3 (21). P. 36 – 46. DOI: 10.18720/MCE.21.2 (rus.)
[5] Nazmeeva T., Sivokhin A. Numerical investigations of the connections between cold-formed steel curtain walls and reinforced concrete slabs. IOP Conference Series: Materials Science and Engineering. 2018. 456 (1). DOI:10.1088/1757-899X/456/1/012081
[6] Vlasov P.P., Lalina I.I., Savchenko A.V., Emelyanov E.V., Nesterov A.A. Finite element analysis of steel support in SCAD PC. Construction of unique buildings and structures. 2015. 11 (38). P. 27 – 41. DOI: 10.18720/CUBS.38.3 (rus.)
[7] Nazmeeva T.V., Vatin N.I. Numerical studies of compressed elements from a cold-bent cut-ting profile taking into account initial imperfections. Civil Engineering Journal. 2016. 2 (62). P. 92 – 101. DOI: 10.5862/MCE.62.9 (rus.)
[8] Rybakov V.A., Gamayunova O.S. Stress-strain state of elements of frame structures made of thin-walled rods. Construction of unique buildings and structures. 2013. 7 (12). P. 79 – 123. DOI: 10.18720/CUBS.12.10 (rus.)
[9] Sovetnikov D.O., Azarov A.A., Ivanov S.S., Rybakov V.A. Methods of calculation of thin–walled rods: statics, dynamics, stability. AlfaBuild. 2018. 3 (1). P. 7 – 33. (rus.)
[10] Vlasov V.Z. Thin-walled elastic rods M.: Gosizdat fizmatlit, 1959. 508 p (rus.)
[11] Gebre T.H., Galishnikova V.V. The impact of section properties on thin walled beam sec-tions with restrained torsion. Journal of Physics: Conference Series. 2020. 1687 (1). DOI:10.1088/1742-6596/1687/1/012020
[12] Bely G.I. Calculation of elastic-plastic thin-walled rods according to a spatially deformable scheme. Inter-university. temat. sb. tr. (Construction mechanics of structures).1983. 42. P. 40 – 48. (rus.)
[13] Umansky A.A. Bending and torsion of thin-walled aircraft structures M.: Oboronizdat, 1939. 112 p. (rus.)
[14] Galishnikova V. A theory for space frames with warping restraint at nodes. Advances in the Astronautical Sciences. 2020. 170. P. 763 – 784.
[15] Tusnin A.R. Numerical calculation of structures made of thin-walled rods of an open profile. Moscow: MSUACE, Publishing House. Assoc. of Build. Universities, 2009. 143 p. (rus.)
[16] Perelmuter A.V., Yurchenko V.V. On the calculation of spatial structures made of thin-walled rods of an open profile. Metal structures. 2014. 20 (3). P. 179 – 190. (rus.)
[17] Kuzmin N.L., Lukash P.A., Mileykovsky I.E. Calculation of structures made of thin-walled rods and shells. Moscow: Gosstroizdat, 1960. 266 p. (rus.)
[18] Grebenyuk G.I., Gavrilov A.A., Yankov E.V. Calculation and optimization of a continuous beam of a thin-walled profile. News of universities. Construction. 2013. 7. P. 3 – 11. (rus.)
[19] Slivker V.I. Construction mechanics. Variational foundations: textbook. Moscow: Publishing House of the ASV, 2005. 736 p. (rus.)
[20] Lalin V.V., Rybakov V.A. Finite elements for the calculation of enclosing structures made of thin-walled profiles. Civil Engineering Journal. 2011. 8 (26). P. 69 – 80. DOI: 10.5862/MCE.26.11(rus.)
[21] Lalin V.V., Rybakov V.A., Morozov S.A. Investigation of finite elements for calculation of thin-walled rod systems. Civil Engineering Journal. 2012. 1 (27). P. 53 – 73. DOI: 10.5862/MCE.27.7(rus.)
[22] Rybakov, V.A. The V.I. Slivker’s semi-shear theory finite elements research for calculation of thin-walled closed profile rods. AlfaBuild. 2022. 24 (4). P. 2403 – 2403. DOI:10.57728/ALF.24.3
[23] Rybakov V.A., Sovetnikov D.O., Jos V.A. Bending torsion in Γ-shaped rigid and warping hinge joints. Magazine of Civil Engineering. 2020. 99 (7). Article No. 9909. DOI: 10.18720/MCE.99.9
[24] Konstantinov I.A., Lalin V.V., Lalina I.I. Construction mechanics. Calculation of core sys-tems using the SCAD program: educational and methodical complex. Part 2. St. Petersburg: Publishing House of the Polytechnic University, 2009. 228 p. (rus.)
[25] Grebennikov M.N., Dibir A.G., Pekelny N.I. Calculation of multi-span continuous beams. The equation of three moments. Kharkiv: Nat. Aerospace University “Kharkiv Aviation University,” 2010. 46 p. (rus.)
Rybakov V.A. Three bimoments equation of V.I. Slivker's semi-shear theory for the calculation of multi-span thin-walled beams. Construction Materials and Products. 2023. 6. (3). P. 31 – 46. https://doi.org/10.58224/2618-7183-2023-6-3-31-46