At high temperatures, steel suffers from great losses in strength and stiffness. Different design methods must therefore be considered to predict the resistance of steel in the exceptional situation of fire. Current standards propose simplified methods to predict the resistance of steel at high temperatures. However, these methods are inspired by steel design equations used at room temperature and are therefore generally not suitable to predict accurately the resistance of steel elements in fire situation. This thesis presents research investigations pursued to propose a new design method for open steel cross-sections subjected to high temperatures by means of the Overall Interaction Concept (O.I.C.). This calculation method is based on the interaction between resistance and stability and allows to consider geometrical and material imperfections. The advantage of this new calculation method is that it allows to obtain precise results and to keep continuity between predictions contrarily to standards that use the cross-section classification. A numerical model, initially developed for open steel cross-sections at ambient temperature, was improved to predict the resistance of steel at high temperatures. It was then verified against experimental test results to ensure its accuracy. After validation, the numerical model was used to conduct simulations using different geometries, temperatures, yield limits and load cases. Results were then used to formulate new design proposals for cross-sections at high temperatures in the O.I.C. format. The performance of the new proposal was then evaluated et compared with the performance of existing standards. This evaluation allowed to conclude that the proposition is much more accurate than existing standards. Finally, the evolution of the behaviour of steel between cold and high temperature was briefly analysed. As this point was only briefly discussed, it opens the door for future studies on the subject.