Iterative methods of beam-structure analysis

Abstract

The article presents the concept of computational analyses of steel beam, composite and reinforced concrete structures accounting for physical and geometric nonlinearities. Due to the magnitude of the task and ease of constructing a calculation model for the static analysis of building structures (especially frame constructions), beam models are still applied. In the beam element, due to limitations connected with discretization, which are based only on a single dimension (length - along the x-axis), not many parameters in terms of the remaining two measurements of the cross-section (y, z) can be accounted for. Most often, the crossection and moments of inertia are introduced to calculate the rigidity of axial compression/tension and flexural rigidity as elastic parameters. The problem arises of how to account for nonlinear laws of physics, local yielding the lack of uniformity among crossections, local instability, the changeability of physical laws due to high temperatures, etc. The authors of the present work attempt to answer these questions and present a synthetic calculation model.