Abstract
Aim: A new original procedure which can be applied to evaluate the fire resistance of a steel frame, based on the linear programming approach, is presented and discussed in this article. Such a computational technique requires the linearisation of both the classical equilibrium conditions and a condition describing the yield of a critical cross-section relating to the structural member conclusive in assessing the frame resistance. The sections selected for the analysis correspond to the location of the plastic hinges forming as a consequence of fire exposure.
Methodology: The critical temperature, determined for the whole structure, and associated with the structure reaching its fire resistance limit state, is considered to represent the measure of such a fire resistance. This critical temperature corresponds to the realisation of such a potentially possible purely plastic failure mechanism that is bound to the lowest possible formation temperature. Such a specification requires the assumption that throughout the duration of the fire foreseen for the considered bearing structure, all the components of this system will be effectively braced, so that there is no risk of their earlier failure by local or global loss of stability.
Results: The general problem formulation approach, the formulation of the objective function, and the rules governing the development of inequalities defining the representative constraints, are presented in detail. The interaction between the longitudinal force and the bending moment is taken into account as well. The obtained results are illustrated by the numerical example. The estimate resulting from the calculation recommended in this article is related to the corresponding one based on the use of the kinematical approach to the theory of plasticity.
Conclusions: The proposed computational approach seems to be more universal in relation to the possible alternative procedures recommended by the authors of this study in their earlier works. It facilitates an unambiguous and clearly interpretable estimate of the steel frame fire resistance also sought in the case of the frame with complex geometry and a complicated load arrangement. In the light of the assumptions of a formal model discussed in detail in this article, the conclusion can also be made that the reliability of the estimates so obtained is significantly greater in comparison to the corresponding results calculated conventionally.
Keywords: steel frame load bearing structure, fire, fire resistance, critical temperature, linear programming
Type of article: original scientific article