An Analysis of Buckling of Nonuniform Beam-column

The buckling equations of variable cross-sectional beam-column are formed by simultaneous differential equations with variable coeffecients which are composed of the moment of inertia I(η) and the cross-sectional area A(η) of members. On analyzing the buckling loads of every type of beam-column with variable cross-section, it is necessary to obtain the solutions of basic differential equations with arbitrary variable coeff icients. However it is impossible to obtain the analytical solutions under these generalities, so we must apply the approximate methods to analyze the buckling problems of every type of beam-column. The well-known approximate methods with generality and simplicity are the finite defference method, the transfer matrix method and the finite element method. The practical approximate methods require the more superior convergency and accuracy of numerical solutiion and the rationality of the time of numerical calculation, other than generality and simplicity. In this paper, the discrete general solutions of the simultaneous differential equation concerning the buckling problem of variable cross-sectional beam-column were obtained by applying the transformation of the differential equation into the integral equation and the Simpson's integral formula, and a practical approximate method is proposed to analyze the buckling problem of every type of beam-column by applying the discrete general solutions. The buckling loads of trancated cone-columns were calculated under the four boundary conditions of fixed-free, hinged-hinged, fixed-hinged and fixed-fixed, and the present method was compared with the other general methods (finite difference method, transfer matrix method, finite element method) concerning the convergency and accuracy of numerical solutions. As the results of numerical analysis the superiority of convergency and accuracy of numerical solution and the rationality of the time of numerical calculation were confirmed on the present method