Abstract-The choice of the global analysis method of a steel structure is essentially related to its sensitivity to second order effects. This sensitivity depends on the structural strength to the lateral displacement's. The classification of structure as "flexible structure" or "rigid structure" allows choosing the required method of analysis for the latter. From a regulatory point of view, a structure can be classified as rigid, if the ratio of the value of elastic critical load for the instability into the sway mode to the value of design vertical load is greater than ten. In practice, the calculation of the elastic total vertical load is not easy. For this reason, studies have been made in this field and have accomplished the proposal of simple expressions computing as an alternative to the direct determination of the critical elastic load of the structure. The main objective of this work is to explore these alternative methods in order to extend the study in this field and to evaluate their robustness and the results of its application on different types of structures.
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