Analysis Of Elastic Stability Of Sway Multi-story Columns With Or Without Leaning Columns

Currently, determine of the effective length is very important in the design of the frame structure. The analysis of effective length factor of components should be analyzed from the stability of the member. In order to provide a theoretical basis for practical application and analyzing the mechanism and influence factors of second-order effect of columns and overcome the limitations of the current design code, such as the analysis methods of the internal forces and the effective length method used in stability of steel columns, and make the design simple and accurate, The application of differential equation method and two order displacement method is used to establish the equilibrium differential equation of the deformed structure, then the transcendent function was derived, and promoting the method for the effective-length factor of columns. The practical calculation charts are derived by authors by using the differential equations, which can be used to quickly determine column effective length and show intuitive trends of the lengths.Firstly, this paper analysis of elastic stability of non-uniform composite columns using differential equation, and solution of elastic buckling differential equation application of stiffness substitution, so as to simplify the buckling load calculation of non-uniform composite columns.Secondly, the elastic buckling is discussed using differential equation method and two order displacement method of stepped columns with spring support and cantilever column with leaning columns. Then using of differential equations derived the columns effective length and made practical charts to determine the columns effective length. Analysis of influence factors of effective length coefficient through the charts, and providing beneficial reference for practical engineering design.Finally, the nonhomogeneous stability problem is discussed of the above structure systems, and obtain the stability calculation formula of internal force, than determine the relationship between displacement and internal force of bar. ANSYS is used to analysis the homogeneous and nonhomogeneous stability problem of the structure system. Through the analysis of the data to prove diagram method is correct and reliable in this paper.