Tall von-Mises trusses' skew-symmetric deformation
Keywords:distortional buckling, skew-symmetric deformation, tall von-Mises truss, horizontl elastic supports, sloped load, three-hinged truss, ridge joint
The work’s aim is to investigate the tall two-rods three-hinged von-Mises trusses' deformation regularities at the sloped load that applied to the ridge joint.The horizontal elastic support influence in the ridge joint when changing the force's inclination angle in a wide range is also investigated Particular attention is paid to the tall two-rod trusses' skew-symmetric stability loss possibility. The possibility of the skew-symmetric shape of а loss of stability of high trusses with at a very small angle of inclination of the force from the vertical axis was confirmed. The horizontal elastic support's influence on increasing the stability against skew-symmetric deformation was shown.It was found that skew-symmetry deformation is essentially non-linear, but under certain conditions it is not catastrophic.It is also noticed that asymmetric deformation depends on vertical deformation.Scientific novelty lies in a detailed study of the tall two-rod three-hinged trusses' deformation, and the establishment of the tendency of such structures to skew-symmetric buckling.The tall von-Mises trusses' new detailed deformation regularities character at skew-symmetric deformation at small inclination angles of force that applied in the ridge joint has been established. Also, the two-rod structures' new deformation regularities has been revealed with a wide inclination angles range of the concentrated force applied in the ridge joint. It is shown that on increasing the loading's inclination angles, which coincide with the rod's inclination angles, the stability loss of the individual rods is possible, since there is a significant increase in the truss' carrying capacity. The research results can be used in the structure design of large general dimensions, modeling of which gives the real structure work under various loads.
Bazhenov V.A. Budivelna mekhanika i teoriia sporud. Narysy z istorii / V.A.Bazhenov, Yu.V.Vorona, A.V.Perelmuter. – K.: Karavela, 2016. – 428 s.
Bazhenov V. A., Krivenko O. P., Solovei N. A. Nonlinear Deformation and Buckling of Elastic Shells with Inhomogeneous Structure [in Ukrainian] – ZAT «Vipol», (Kyiv), 2010. – 316 p.
Bazhenov V. A., Krivenko O.P., Solovei N. A. Nonlinear Deformation and Buckling of Elastic Shells with Inhomogeneous Structure: Models, Methods, Algorithms, Poorly Studied and New Problems [in Russian]. – Book House "LIBRIKOM" (Moscow), 2013. – 336 p.
Bazhenov V.A., Solovei N.A., Krivenko O.P. Modeling of Nonlinear Deformation and Buckling of Elastic Inhomogeneous Shells // Strength of Materials and Theory of Structures: Scientificand-technical collected articles – Kyiv: KNUBS. – Issue 92, pp. 121-147 (2014), [in Ukrainian]. http://opir.knuba.edu.ua/
Baˇzant Z.P., Cedolin L. (2010) Stability of structures: Elastic, inelastic, fracture and damage theories World Scientific Publishing, Co. 1040 p. https://doi.org/10.1142/7828https://www.scholars.northwestern.edu/en/publications/stability-of-structures-elastic-inelastic-fracture-and-damage-the-4/
Bilyk S. I. Optimal form of the geometrical circuitry of the frame carcase with incline elements around functional cubature / Bilyk S. I. // Applied geometry and engineering graphics: Collection of scientific papers/ KNUBA. –К., 2004. – V. 74. – P. 228–235.
Bilyk S. I. Stability analysis of bisymmetrical tapered I-beams / S. I. Bilyk // Progress in Steel, Composite and Aluminium Structures Proceeding of the XI international conference on metal structures (ICMS–2006): Pzeszow, Poland, 21–23 June 2006-p. – Pzeszow, 2006. – С.254–255.
Bilyk S. Determination of critical load of elastic steel column based on experimental data // Pidvodni tekhnolohii. Promyslova ta tsyvilna inzheneriia. mizhnar. nauk.-vyrob. zhurn. K., KNUBA, Vyp.04/2016, S.89-96.http://repositary.knuba.edu.ua/handle/987654321/821
Bilyk S.I., BilykА.S., Nilova T.O., Shpynda V.Z., Tsyupyn E.I. Buckling of the steel frames with the I-shaped cross-section columns of variable web height // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles – Kyiv: KNUBA, 2018. – Issue 100. – P. 140-154. library.knuba.edu.ua/books/zbirniki/12/201604.pdf.
Bilyk Sergiy, Tonkacheiev Vitaliy, Determining sloped-load limits inside von Mises truss with elastic support. Materiali in tehnologije., Ljubljana, Slovenija 52 (2018), 105-109, doi:10.17222/mit.2016.083 http://mit.imt.si/Revija/izvodi/mit182/bilyk.pdf .
Błażejewski P., Marcinowski J., Rotter M.Buckling of externally pressurised spherical shells. Experimental results compared with recent design recommendations/ EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark, Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin • ce/papers 1 (2017), No. 2 & 3, p.1010-1018. https://doi.org/10.1002/cepa.141
Daurov M.K., Bilyk A.S. Providing of the vitality of steel frames of high-rise buildings under action of fire // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles – Kyiv: KNUBA, 2019. – Issue 102. – P. 62-68.
Frantık P. Simulation of the stability loss of the von Mises truss in an unsymmetrical stress state/ Engineering MECHANICS, Vol. 14, 2007, No. 1, p. 155–161 http://www.engineeringmechanics. cz/pdf/14_3_155.pdf
Galambos V., Stability Design Criteria for Metal Structures. John Wiley and Sons, Ltd., 1998, p. 911.
Greco Marcelo, Carlos Eduardo Rodrigues Vicente, Analytical solutions for geometrically nonlinear trusses, Revista Escola de Minas, 62 (2009) 2, 205-214, doi:10.1590/S0370-44672009000200012
Kala Z. Kalina М. Static equilibrium states of von Mises trusses. INTERNATIONAL JOURNAL OF MECHANICS, volume 10, 2016, p. 294-298. https://www.researchgate.net/publication/305175165Kala, Zdenek & Kalina, Martin. (2016).
Kala Z. Stability of von-Misses truss with initial random imperfections.Modern Building Materials, Structures and Techniques, MBMST 2016. Procedia Engineering 172 ( 2017 ) p.473 – 480. https://pdf.sciencedirectassets.com/278653/
Kalina, M. “Static Task of von Mises Planar Truss Analyzed using Potential Energy,” AIP Conference Proceedings, vol. 1558, 2013, pp. 2107-2110,.
Kalina, M. Stability Problems of Pyramidal von Mises Planar Trusses with Geometrical Imperfection. International Journal of Theoretical and Applied Mechanics, volume 1, 2016 p.118-123. https://www.iaras.org/iaras/filedownloads/ijtam/2016/009-0018.pdf
Kaplan, A. & Fung, Y. C. A nonlinear theory of bending and buckling of thin elastic shallow spherical shells. U.S. N.A.C.A. Technical Note 3112, 1954.
Ligarò S.S., Valvo P.S. Large Displacement Analysis of Elastic Pyramidal Trusses. International Journal of Solids and Structures, Vol.43, No.16, 2006, pp. 206-212. 43, pp. 4867-4887. https://www.researchgate.net/profile/Paolo_Valvo/publication/229292690.
Marcinowski J. Statecznosc konstrukcji sprezystych? Wroclaw, DWE, 2017, 278
Makhinko A.V., Makhinko N.O. Some aspects of vertical cylindrical shells’ calculation at the unsymmetrical load // Strength of materials and theory of structures: scientific-and-technical collected articles. – Kyiv: KNUBA, 2019. – Issue 102. – P. 46-52.
Mikhlin Y. V.: Nonlinear normal vibration modes and their applications, Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications Serra Negra, (2010), 151-171, http://www.sbmac.org.br/dincon/trabalhos/PDF/invited/68092.pdf, 23.11.2016
R. V. Mises, Über die Stabilitätsprobleme der Elastizitätstheorie, Z. angew. Math. Mech., 3 (1923), 406–422, doi:10.1002/zamm.19230030602 https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19230030602.
R. von Mises, J. Ratzersdorfer, “Die Knicksicherheit von Fachwerken ZAMM 5, pp. 218-235, 1925/https://doi.org/10.1002/zamm.19250050305
Feodosiev V., Theory of strength of materials chosen problems and questions, Moskow, Nauka, 1967, 376.
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