Consistent thermodynamics analysis of restrained steel columns in fire – Part 1: Theoretical developments for general application

The present paper proposes a novel way to describe the behaviour of restrained steel columns in fire. It is based on the fundamental concepts of Engineering Thermodynamics. Energy and entropy-based quantities are combined to provide an additional link between the thermal and the thermomechanical problems involved in the process, during the relevant period for structural engineers, that is between the ignition instant and the instant when the column collapses. The Thermodynamics analysis is made here at a macroscopic level and the passage to the particle’s level is made by means of the adequate mathematical tools, such as the Gauss’s Theorem of Divergence. In opposition to the traditional Clausius-Duhem formula, the description clearly distinguishes between external work and internal strain energy. An adequate structural model is adopted for the column, to take into account the interactions between the column and the surrounding frame. The structural behaviour of steel columns in fire is a sequence of two mechanical phenomena: thermal buckling followed by plastic collapse. It involves an energy transfer between a heat source, that is the fire that occurs at the column’s compartment due to any reason beyond our concern, and the thermal sinks, in this case the column itself and the surrounding frame. The proposed methodology proposes a novel way to treat the large data that arises from any sophisticated numerical methodology usually adopted in structural engineering. This means that it is supposed that the structural analysis is already performed, and we focus on the treatment of the information that arises from the structural analyses, to provide a better description of the involved phenomena and to pave the way to novel design strategies, based on the energy absorption capacity of frames during fire. This work is devoted solely to the theoretical developments for general application. A complementary paper applies the concepts and strategies developed here to real illustrative examples, in the context of the voxels-based Rayleigh-Ritz method, and confirms all statements presented in the present work.