Bearing Capacity of Structures Made of Materials with Different Tensile and Compression Strengths

Abstract:

The paper considers the problem of the ultimate load finding for structures made of a material with different limits of tensile strength and compression. The modulus of elasticity under tension and compression is the same. It is assumed that upon reaching the ultimate strength, the material is deformed indefinitely. The calculations use a simplified material deformation diagram — Prandtl diagrams. The limiting state of a solid rectangular section under the action of a longitudinal force and a bending moment is considered. The dependences describing the boundary of the strength of a rectangular cross section are obtained. Formulas allowing the calculation of the values of the limit forces and under the action of which the cross section passes into the plastic state are derived. Examples of the analytical calculation of the maximum load for the frame and two-hinged arch are given. An algorithm is proposed and a program for calculating arbitrary flat rod systems according to the limit state using the finite element method is compiled. The proposed algorithm does not involve the use of iterative processes, which leads to an exact calculation of the maximum load within the accepted assumptions.

• Periodical: Materials Science Forum (Volume 968)
• Pages: 200-208
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.968.200
• Online since: August 2019
• Authors: Mykola Soroka*
• Keywords: Calculation Program, Longitudinal Force Consideration, Materials Properties, Two-Hinge Arch, Ultimate Load

References

[1] Gvozdev A.A. Raschet nesuschej sposobnosti konstrykcij po metody predelnogo ravnovesiya. Moscow: Stroyizdat, (1949), - 248 p. (in Russian).

[2] Pikovsky A.A. Statika sterzhnevih system so szhatimy elementamy. Moscow: State publishing house of physical and mathematical literature, (1961), 394 p. (in Russian).

[3] Rzhanitsyn A.R. Raschet soorygenij s ychetom plasticheskih svoistv materialov. Moscow: The state publishing house of literature on construction and architecture, (1954), 287 p.

[4] Chiras A.A. Stroitelnaya mekhanika, teorija i algoritmi. Moscow: Stroyizdat, (1989), 256 p.

[5] Popov N.I. O predelnom sostoyanii arki, nagrygenoj sistemoj sosredotochennih sil Works RIIZhT, the issue 29, (1961).

[6] Chan Tkhan Tung. Chislennij method rascheta arok po predelnomy ravnovesiu. Moscow: MGSU bulletin, 2011, No. 1, t. 1, page 232-237 (in Russian).

[7] Darkov A.V., Shaposhnikov N.N. Stroitelnaya mechanika Moscow: Higher school,, (1986), 607 p. (in Russian).

[8] Soroka M.M. Rozvyazok nelineinih zadach budivelnoyi mekhanicki: navch. pos. / M.M. Soroka – Odessa: ODABA, (2018). – 203 p. (in Ukrainian).

[9] Barabash M.S., Soroka M.M., Suryaninov M.G. Nelineina budivelna mekhanika z PK LIRA-SAPR. monografiya, Odessa: Ekologiya, 2018. – 248 p, (in Ukrainian).

[10] Mykola Soroka The limit state of non-hinged arch with a cross-section in the form of an idealized I-beam, http://www.enggjournals.com/ijet/vol10issue6.html.