The Elastic Bifurcation Of The Frame And The Second-order Stress Analysis

Steel structure is very important in today’s architectural structure, with the development of all aspects of the construction industry, the steel structure of the growing number of applications, especially high-level long-span structures. Stability problems are the most important in analysis of the steel structure.The effective length factor method is still the most commonly used method for stability calculation. The method avoids the complicated stability analysis on the overall structure and the core of the method is to determine the effective length of conpression columns. In this regard, some formulas and tables are given in norms of Code for Design of steel structures and Code for Design of Concrete structures, but the application of the formulas and tables is limited because of some assumptions, and it cannot be used to determine the effective length of columns in special cases (it is not universal), therefore formulas and nomograms for determining the effective lengths of columns with different constraints are derived and made respectively in the paper. The nomograms can not only be used in regular cases in the above mentioned norms but also in special cases. In addition, the use of the nomograms is very easy and quick.To determining the accuracy of the nomograms. The hand-derived formulas, not only contraste with the existing norms, but also use ANSYS to simulate the lever member. And through compare the results of the analytic formula and results of the ANSYS analysis, thereby to verify the accuracy of the hand-derived formulas.Therefore formulas and nomograms for determining the effective lengths of columns with four different constraints are derived and made respectively in the paper. These four cases reflect almost all cases in engineering. The formulas and nomograms in this paper can be used as a calculation tool to determine effective length factor quickly. In addition, This way in this paper also can be used to get the formulas and nomograms in other cases. Such as variable order columns and columns along the length with distributed axial load, as well as columns with swing column.