Fire resistance of steel frames using classical and numerical methods

This paper presents a second-order elastic-plastic hinge method and a finite-element model for the analysis of plane frames in fire. Both methods are derived from the same two-node corotational beam element and are based on the plastic theorems. Hence, this paper first presents the extension of the three classical plastic theorems, viz, the Lower-Bound Theorem, Upper-Bound Theorem, and Uniqueness Theorem, to structural analysis incorporating thermal effects. The three plastic theorems are given new definitions, followed by original mathematical proofs. The basic formulations of the two analytical methods are then described. The proposed finite-element model has been validated against a series of published test and analytical results on different structure types. For comparison purposes, numerical examples are presented to examine the relative performance of the three methods investigated in this study. Discussions on the validity of the methods and their limitations are then addressed.