DISPLACEMENTS IN PIVOTAL SYSTEMS OVER ELASTICITY LIMIT

Abstract

One of the provisions of the method for calculating building structures by the limiting state is the satisfaction of the operational requirements in relation to the displacements of their elements under load. An urgent problem is their determination at the stage of elastic-plastic deformation of the material. A technique is proposed for its solution for the case of the Prandtl diagram. The core system is a two-span statically indeterminate beam. Its limiting state in terms of bearing capacity, as well as an intermediate stage of deformation, are considered. The introduction of the reduced moment makes it possible to extend the Mohr-Maxwell formula beyond the limit of linear elasticity. The use of classical physical models of solid mechanics leads to the solution of the problem in an analytical form. Experiments were carried out to test the theoretical results obtained by the proposed method. In one of them, a two-span beam with a span of 50 cm and a cross section of 3×0.42 cm made of duralumin was tested. The mechanical characteristics of the material were previously obtained. Displacements were measured with the help of indicators. The maximum load (428 N) in each of the spans of the beam was 80 % of the limit value. In this case, the beam had elastic-plastic regions. The experiment revealed the dependence of displacements on the load, acceptable for the form of deformation: a linear graph with Hooke's law and a curve in the presence of plastic deformations. Deviations from theoretical values were no more than 3.3 %.