Quartic Formulation for Elastic Beam-Columns Subject to Thermal Effects

Abstract

This paper presents an advanced elastic formulation intended for modeling imperfect beam-columns subject to thermal loading using only one element per member. The new formulation is derived in a local Eulerian (convected) system, where the effects of large displacements and rotations in three-dimensional space are accounted for through transformations between the local and global systems. In the Eulerian system, the proposed formulation utilizes quartic shape functions for the transverse displacements and linear shape functions for the rotational twist, whereas no shape functions are required for the axial displacement since the constant axial force criterion is used. The paper proceeds with the formulation details, where particular emphasis is placed on the modeling of thermal effects. This is followed by a discussion on the modeling of distributed element loads which require special treatment in the context of the large-displacement Eulerian approach. Finally, verification of the new formulation is undertaken using the nonlinear analysis program ADAPTIC, where several examples are presented to illustrate the accuracy and efficiency of the quartic formulation.