Published since 1923
DOI: 10.33622/0869-7019
Russian Science Citation Index (RSCI) Web of Science
  • Inverse Numerical-Analytical Method For Calculation Of Light Steel Thin-Walled Rod Elements
  • UDC 624. DOI: 10.33622/0869-7019.2021.03.57-68
    Grigory I. BELYY, e-mail:
    Maksim O. SMIRNOV, e-mail:
    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.
    1. Winter G. Strength of thin steel compression flanges. Transactions ASCE, 1947, 112, pp. 527-554.
    2. Winter G. Thin-walled structures - theoretical solutions and test results. Preliminary Publications of the Eighth Congress, International Association for Bridge and Structural Engineering (IABSE). New York, 1968. Pp. 101-112.
    3. Pekz T. Development of a unified approach to the design of cold-formed steel members. American Iron and Steel Institute Research Report, 1987, CF 87-1, pp. 77-84.
    4. Moldovan A. Compression tests on cold-formed steel columns with monosymmetrical section. Thin-Walled Structures, 1994, vol. 20(1-4), pp. 241-252.
    5. Shafer B. W. Designing cold-formed steel using the direct strength method. 18th International Specialty Conference on Cold-formed Steel Structures, October 26-27, 2006, Orlando, Florida, pp. 475-489.
    6. Shafer B. W. Local, distortional, and Euler buckling of thin-walled columns. Journal of Structuring Engineering, 2002, vol. 128(3), pp. 289-299.
    7. AISI S100-2016. North American specification for the design of cold-formed steel structural members.
    8. AS/NZS 4600:2005. Australian/New Zealand Standard. Cold-formed steel structures.
    9. EN 1993-1-3-2006. Eurocode 3. Design of steel structures. Part 1-3: General rules. Supplementary rules for cold-formed members and sheeting.
    10. Kuznetsov A. Yu. Stress-strained and limit states in sections of bar elements made of galvanized profiles. Vestnik grazhdanskikh inzhenerov, 2013, no. 2(37), pp. 56-60. (In Russian).
    11. Belyy G. I., Kuznetsov A. Yu. Influence of section reduction on the stability of rod elements of structures from paired cold-bent thin-walled profiles. Vestnik grazhdanskikh inzhenerov, 2016, no. 4(57), pp. 57-63. (In Russian).
    12. Belyy G. I. On the strength calculation of rod elements of light steel thin-walled structures with multiparameter loading. Vestnik grazhdanskikh inzhenerov, 2019, no. 4(75), pp. 13-17. (In Russian).
    13. Belyy G. I. Development of methods for calculating bar elements of steel structures under multiparameter loading. Vestnik grazhdanskikh inzhenerov, 2020, no. 3(80), pp. 43-54. (In Russian).
    14. Belyy G. I. An analytical-numerical method for calculating the stability of rod elements of light steel thin-walled structures. Vestnik grazhdanskikh inzhenerov, 2020, no. 4(81), pp. 39-46. (In Russian).
    15. Vlasov V. Z. Tonkostennye uprugie sterzhni [Thin-walled elastic rods]. Moscow, Fizmatgiz Publ., 1959. 505 p. (In Russian).
    16. Vorob'ev L. N. Deformation analysis and stability of thin-walled rods of an open profile. Trudy Novocherkasskogo politekhnicheskogo instituta, 1958, vol. 69/93, pp. 3-48. (In Russian).
    17. Broude B. M. To the theory of thin-walled rods of open profile. Stroitel'naya mekhanika i raschet sooruzheniy, 1960, no. 5, pp. 6-11. (In Russian).
    18. Vorontsov G. V. Small spatial fluctuations, stability and stable strength of thin-walled open-profile rods. Izvestiya vuzov. Stroitel'stvo i arkhitektura, 1965, no. 1, pp. 44-49. (In Russian).
    19. Beylin E. A. General equations of deformation analysis and stability of thin-walled rods. Stroitel'naya mekhanika i raschet sooruzheniy, 1969, no. 5, pp. 35-41. (In Russian).
    20. Beylin E. A., Belyy G. I. To the deformation analysis of elastic systems subject to the simultaneous action of active and parametric loads. Stroitel'naya mekhanika i raschet sooruzheniy, 1976, no. 3, pp. 30-34. (In Russian).
  • For citation: Belyy G. I., Smirnov M. O. Inverse Numerical-Analytical Method for Calculation of Light Steel Thin-Walled Rod Elements. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2021, no. 3, pp. 57-68. (In Russian). DOI: 10.33622/0869-7019.2021.03.57-68.