Published since 1923
DOI: 10.33622/0869-7019
Russian Science Citation Index (RSCI) Web of Science
  • Bearing Capacity Of Strength Of An Axially-Compressed I-Beam Rod Under Restrained Torsion
  • UDC 624.046.3 DOI: 10.33622/0869-7019.2020.09.21-27
    Alexander R. TUSNIN, e-mail:
    Amirshokh Kh. ABDURAKHMONOV, e-mail:
    Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation
    Abstract. The bearing capacity of an axially-compressed thin-walled rod of open cross section under constrained torsion is considered. Theoretical and numerical calculations of axially-compressed cantilever beams of various flexibilities under the action of axial force and bi-moment are presented. A theoretical and numerical analysis of the influence of the bi-moment on the bearing capacity of an axially-compressed thin-walled cantilever rod with an open cross section under the restrained torsion is performed. For the theoretical estimation of the rod stability, the nonlinear dependence of the shelf deflections under compression and torsion is taken into account. The dependence of deformations of the loose end of the shelf of the cantilever rod on the angular twist under the action of the bi-moment is established. An analytical formula for testing the bearing capacity of axially-compressed rods is proposed and the stability coefficient for restrained torsion with an I-beam cross-section for cantilever and propped cantilever rods is determined. A method of numerical calculation in a finite element setting is presented, taking into account the geometric and physical nonlinearity of the system for cantilevered rods. Theoretical and numerical results are compared, the possibility of using the numerical modeling to assess the stability of axially-compressed thin-walled rods of open cross section under the restrained torsion is established.
    Key words: thin-walled rod of open cross section, I-beam rod, flexibility, bi-moment, ultimate stress, , stability coefficient.
    1. Timoshenko S. P. On the stability of the flat shape of the I-beam bend. Izvestiya St. Peterburgskogo politehnicheskogo instituta, 1905, pp. 151-219. (In Russian).
    2. Weber C. Ubertragung des drehmoments in balken mit doppelflanschigem querschnitt. Z. fur angew. Math. und Mech., 1926, Vol. 6, S. 85-97. (In German).
    3. Wagner H. Verdrehung und Knickung von offenen Profilen. NACA Tech. Memo, 1937, N 807, S. 329-343. (In German).
    4. Vlasov V. Z. Tonkostennye uprugie sterzhni [Thin-walled elastic rods]. Moscow, Fizmatlit Publ., 1959. 568 p. (In Russian).
    5. Vlasov V. 3. A new method for calculating prismatic beams made of thin-walled profiles on the combined action of axial force, bending and torsion. Vestnik VIA RKKA im. V. V. Kuibysheva, 1936, no. 20, iss. 2, pp. 86-135. (In Russian).
    6. Vlasov V. Z. Izbrannye trudy [Selected works]. Moscow, Nauka Publ., 1964. 955 p. (In Russian).
    7. Umanskij A. A. Kruchenie i izgib tonkostennyh aviakonstrukcij [Torsion and bending of thin-walled aircraft structures]. Moscow, Oborongiz Publ., 1939. 112 p. (In Russian).
    8. Umanskij A. A. Calculation of thin-walled curved beams. Trudy nauchno-tehnicheskoj konferencii VVA im. N. E. Zhukovskogo, 1944, vol. 2, iss. 2, pp. 35-48. (In Russian).
    9. Dzhanelidze G. Ju., Panovko Ja. G. Statika uprugih tonkostennyh sterzhnej [Statics of elastic thin-walled rods]. Moscow; Leningrad, Gostehizdat Publ., 1948. 208 p. (In Russian).
    10. Dzhanelidze G. Ju. Variational formulation of the theory of thin-walled elastic rods by V. Z. Vlasov. Prikladnaja matematika i mehanika, 1943, vol. VII, iss. 6, pp. 455-462. (In Russian).
    11. Adadurov R. A. Determination of tangential stresses in thin-walled structures. Trudy CAGI, 1947, no. 614, pp. 1-13. (In Russian).
    12. Adadurov R. A. Stresses and deformations in a cylindrical shell with rigid cross sections. Dokl. AN SSSR, 1948, vol. 62, no. 2, pp. 183-186. (In Russian).
    13. Rzhanicyn A. R. Complex resistance of thin-walled profiles with a non-deformable contour beyond the elastic limit. Trudy laboratorii stroitelnoy mehaniki CNIPS. Moscow, 1942, pp. 88-91. (In Russian).
    14. Gorbunov B. N. Calculation of space frames made of thin-walled rods. Prikladnaja matematika i mehanika, 1943, iss. 1, p. 188. (In Russian).
    15. Belyj G. I. Influence of the eccentric bearing of the ends and the level of load application on the stability of the flat bending form of a thin-walled curved rod. Sb. trudov LISI, 1974, pp. 18-25. (In Russian).
    16. Belyj G. I. Calculation of elastic-plastic thin-walled rods using a spatially deformable scheme. Mezhvuz. temat. sb. tr. "Stroitel'naja mehanika sooruzhenij", 1983, no. 42, pp. 40-48. (In Russian).
    17. Perel'muter A. V., Slivker V. I. Ustojchivost' ravnovesija konstrukcij i rodstvennye problemy. Tom 1. Obshhie teoremy. Ustojchivost' otdel'nyh jelementov mehanicheskih system [Stability of equilibrium structures and related problems. Vol. 1. General theorems. Stability of individual elements of mechanical systems]. Moscow, SKAD SOFT Publ., 2007. 670 p. (In Russian).
    18. Beljaev N. M. Soprotivlenie materialov [Theory of strength of materials]. Moscow, Nauka Publ., 1965. 856 p. (In Russian).
    19. Bychkov D. V. Stroitel'naja mehanika sterzhnevyh tonkostennyh konstrukcij [Theory of structures of thin-walled rod structures]. Moscow, Gosstrojizdat Publ., 1962. 475 p. (In Russian).
    20. Bel'skij G. E., Odesskij P. D. On a unified approach to the use of construction steel diagrams. Promyshlennoe stroitel'stvo, 1980, no. 7, pp. 4-6. (In Russian).
  • For citation: Tusnin A. R., Abdurakhmonov A. Kh. Bearing Capacity of Strength of an Axially-Compressed I-Beam Rod under Restrained Torsion. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2020, no. 9, pp. 21-27. (In Russian). DOI: 10.33622/0869-7019.2020.09.21-27.