THE ELASTOPLASTIC CALCULATION OF FRAMES USING THE DISPLACEMENT METHOD

Abstract

We proposed a method for calculating statical indeterminacy frames taking into account plastic defor­mations, which is based on the use of a schematized diagram of material with hardening. Two types of standard beams with supports are used during the implementation of the displacement method (DM) and the elastic solu­tion of the problem: “fixed” - “pinned” and “fixed” - “fixed”, but unlike the elastic solution, standard beams con­tain plastic zones (PZs). So as the stresses in these zones did not exceed the limit of yielding in the nonlinear frame calculation, we took measures to transform the PZs into equal strength plastic zones (ESPZ). The calcula­tions were made for both types of beams for all single and load impacts. The frame calculation consists of two stages (elastic and plastic). At the elastic stage, we determine an elastic moment diagram and the corresponding load. For a practical use of the DM in a nonlinear frame calculation, we introduced a simplifying prerequisite sup­plementing the well-known hypotheses of the classical version of the method, and formulated a Statement of the limiting load. According to the Statement, each length of the PZ can correspond to the lower boundary of the lim­iting load. The plastic stage of the calculation is performed at a given length of the PZ using the method of se­quential loadings. At each loading stage, incremental equations are written using the DM equations, which estab­lish relations between incremental moments and the incremental load, that allows you to get the resulting moment diagram. This diagram represents a sum of the elastic diagram and the diagrams of incremental moments at all previous loading stages. According to the resulting diagram, we calculate the length of the PZ, together with the limiting load. The calculation is considered complete if the length of the PZ does not exceed the specified value within the margin of error.