Abstract
• Using GDQ method to solve beam-column differential equation. • Using SBCGS technique to perform second-order and buckling analysis of beam-columns. • Analysis of non-prismatic beam-columns with different boundary conditions. • Beam-columns with different tapered ratios under end or distributed axial load . • Rigorous second-order analysis of beam-column member just by one iteration. While classical matrix and finite-element methods are very powerful for structural analysis, some essential shortcomings such as not placing the transverse and axial loads in their actual locations on a member, as well as necessity of a large number of iterations or subdivisions of the structural element for exact second-order analysis should be still taken into consideration. To overcome such drawbacks, Generalized Differential Quadrature (GDQ) is a new semi-numerical method for analysis of the engineering problems. The aim of this paper is to use SBCGS (Satisfaction of Boundary Conditions in the General Solution) technique to perform second-order and buckling analysis of beam-columns under different geometrical and boundary conditions by solving beam- column differential equation in matrix form. In addition, a comparison is made between the results of SBCGS technique and those of other methods available in literature for the analysis of non-prismatic beam-columns with different tapered ratios when subjected to end or distributed axial loads. Using the proposed method, a rigorous second-order analysis on a beam-column member with variable cross-section and various boundary conditions under different axial and transverse distributed loads can be carried out just by one iteration and without any discretization in the member but instability appears in the results when axial load reaches critical buckling load. Moreover, in order to achieve the accuracy of the results of SBCGS technique, the model must have a large number of subdivisions in FEM method.
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