Geometrically Nonlinear Analysis of Plane Frames Subjected to Temperature Changes

Abstract

Procedure for large displacement and stability analysis of elastic plane frames subjected to temperature changes is presented. The method of analysis is based on an Eulerian (corotational) formulation, which was developed initially for static loads, and is extended herein to include thermal effects. Local element force-deformation relationships are derived using the beam-column theory taking into consideration the effect of curvature due to temperature gradient across the element cross section. The changes in element chord lengths due to thermal axial strain, and bowing due to temperature gradient, are taken into account. This “beam-column” approach, using stability and bowing functions, requires significantly fewer elements per member (i.e., a beam or a column) for the analysis of a framed structure than the “finite-element” approach. A computational technique, using Newton-Raphson iteration, is developed to determine the nonlinear responses of structures. Numerical solutions are presented for a number of benchmark structures to demonstrate the feasibility of the proposed method of analysis.