Abstract
The derivation of parametric equations for a limiting surface in the space of internal forces and moments that act in the rod cross-sections, using the basic concepts of plasticity theory and conventional hypotheses of the rod theory, is presented. The plastic properties of rod material are described by the Mises criterion. A case of small displacements and strains under static simple loading is considered. The results of solving a number of problems of constructing limiting curves in the planes of internal forces and moments are given.
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Gvozdev, A.A., Raschet nesushchei sposobnosti konstruktsii po metodu predel’nogo ravnovesiya (Calculation of Load-Carrying Capacity of Structures Using the Limiting Equilibrium Method), Moscow: Stroiizdat, 1949.
Chikhladze, E.D., Arslankhanov, A.D., and Salam, A., Strength Analysis of Steel-Concrete Elements of Rectangular Cross-Section under Eccentric Compression and Bending, Stroitel’naya Mekhanika i Raschet Sooruzhenii, 1992, vol. 3, pp. 9–17.
Shen, W.Q., Interaction Yield Hypersurfaces for the Plastic Behavior of Beams. I. Combining Bending, Tension and Shear, Int. J. of Mechanical Sc., 1995, vol. 37, no. 3, pp. 221–238.
Shen, W.Q., Interaction Yield Hypersurfaces for the Plastic Behavior of Beams. II. Combining Bending, Tension, Shear, and Torsion, Int. J. of Mechanical Sc., 1995, vol. 37, no. 3, pp. 239–247.
Mishchenko, A.V., Limiting Equilibrium of Laminated Rod Systems, Doklady AN VSh Rossii, 2004, no. 2, pp. 68–75.
Kachanov, L.M., Osnovy teorii plastichnosti (Fundamentals of Plasticity Theory), Moscow: Nauka, 1969.
Lyav, A., Matematicheskaya teoriya uprugosti (Mathematical Theory of Elasticity), Moscow, Leningrad: ONTI NKTP SSSR, 1935.
Teregulov, I.G., Soprotivlenie materialov i osnovy teorii uprugosti i plastichnosti (Strength of Materials and Fundamentals of Elasticity and Plasticity Theory), Moscow: Vysshaya shkola, 1984.
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Original Russian Text © K.E. Sibgatullin, E.S. Sibgatullin, 2008, published in Izvestiya VUZ. Aviatsionnaya Tekhnika, 2008, No. 2, pp. 14–16.
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Sibgatullin, K.E., Sibgatullin, E.S. A technique of analyzing critical forces and moments for isotropic rods of arbitrary cross-section in the general case of their complex resistance. Russ. Aeronaut. 51, 126–129 (2008). https://doi.org/10.3103/S1068799808020049
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DOI: https://doi.org/10.3103/S1068799808020049