The stability of structures is an important aspect that the designer must pay particular attention to in order to ensure safety against collapse. This investigation is concerned with analytical and numerical analyses of the dynamic buckling of plane structures. A rigorous mechanical model is proposed, consisting of a beam-column element with nodal ends possessing two rotational springs of rigidities acting in parallel with the bending stiffness of the beam-column. The model is first analyzed with respect to the dynamic behavior by investigating the influence of the variation in the stiffness of the nodal springs on the fundamental frequency of the proposed mechanical model. Compression axial loading is applied to the beam-column in order to study the nonlinear dynamic behavior by introducing buckling. This novel approach is used to highlight the interaction between the fundamental frequency and the critical buckling load. Simple examples are treated using the approach and the results are compared with those obtained from a global analysis. The results revealed that it is possible to reproduce the stability analysis of a global structure by simply analyzing a target element, taking into account all elements adjacent to it with less than 1% error on the results.
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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