The Elastic Stability Analysis Of The Cantilever Column, The Outriggers Column And The Frame With Leaning Column

At present, according to the steel structure standard there is no stability equation for such structural systems:outriggers column, cantilever column with leaning column, outriggers column with leaning column, and frame with leaning column. Neither there is length calculation coefficient or related charts. However, those structural systems are widely applied. For example, the theoretical model of the stand of pipe could be simplified as an overhanging column model. Therefore, the stability equation of the structural system could be obtained by doing second-order elastic buckling analysis, which makes it possible to get length calculation coefficient and draw related monograph.At first, in this paper, it introduces stability about related theories and calculating methods, mainly the balance equations method and the second order angular displacement method. To get the stability equation of the structural systems, it mainly applies the balance equations method and the second order angular displacement method. Obtaining the stability equation, then the MATLAB software is used to get the answer of the transcendental equation. Therefore, the calculation length coefficient chart could be drafted. There is a creative idea in this paper while drawing the charts. i.e using logarithmic coordinates, not conventional spacing coordinates. And there are some features of this idea:within the relevant range, the values are more accurate, and the calculation length coefficient could be about0.01. While in the other range, the values are less accurate, and the length calculation coefficient could be about0.1. In those cases which the values are not showed in the charts, the answer could be obtained by applying linear interpolation.At the end of the paper, some practical examples are calculated to determine the practicality and convenience of the chart. ANSYS software is used to do eigenvalue buckling analysis to get the buckling load of the above mentioned columns. Compared the answer obtained by the ANSYS software with the analytical answer deduced from the charts of relevant column structures, the result shows that there is a small gap between them. And both answers are within the margin of errors, which shows that the analytical answer matches the ANSYS value well and the calculation length coefficient deduced in this paper can be applied to practical engineering project.