PLANAR STABILITY OF AN ELASTIC, PLASTIC BEAM DIFFERENTLY RESISTING TO TENSION AND COMPRESSION
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Publication date: 2024-09-30 07:26:00
Authors: N.S. Rzayev; R.D. Aliyev
Category: Engineering
Summary: Nowadays, beams, boards and coatings with new complex properties are widely used in many branches of mechanical engineering and construction. The calculation and analysis of the amplitude characteristics of stability, strength and frequency of a structural element with these properties lead both to significant difficulties in mathematical terms and to the analysis of the results obtained, if ignored, serious errors may be made. Taking these into account, it becomes necessary to build mathematical models characterizing the real properties of the material when using a structural element made of new materials and establishing effective physical connections. There are materials in which the tensile strain diagrams characterizing their properties are diverse in tension-compression and torsion. Such materials include ceramics, some types of copper and cast iron, polymers, and composite materials. The mechanical and physical properties of these materials become strictly dependent on hydrostatic pressure. For materials with the above-mentioned specific property, classical elasticity and elastoplasticity cannot be considered under the conditions accepted by the theory of plasticity. In this paper, a problem of planar stability of an elastic, plastic plane differently resisting to tension and compression in pure bending is solved. It is assumed that the cross-section of the beam has one symmetry axis, under the action of concentrated moments applied at the ends of the bar is subjected to pure bending, and bending happens in the symmetry plane of the beam. Using the state of a neutral axis, absence of longitudinal force, continuity conditions for tension and compression, we determine the boundary of elastic and plastic domains. The equations of the loss of planar stability obtained for the classic case are reduced to the loss of planar stability for various modulus ideal elastic and plastic beams. The expressions of hardness for different modulus materials are obtained and are associated with critical moment and critical length. Expressions for calculating critical parameters for an ideally elastic, plastic beam with a rectangular cross section are obtained.
Author keywords: Beam; Compression; Ideally Plastic; Stability; Tension