ANALYTICAL SOLUTION OF STATICALLY INDETERMINATE BEAM-COLUMN

In this paper, the problem of statically indeterminate beam-column bending is studied by using the asymptotic integral method. Firstly, the fourth order deflection differential equation of statically indeterminate beam-column is established. Considering the boundary condition and continuous smooth condition, the exact analytical solution of the deflection is obtained by using continuous piecewise independent integration method. In order to meet the requirements of engineering design, the statically indeterminate beam-column of the fourth order equation is constructed. The deflection line of statically indeterminate beam without axial force is selected as the initial function of beam. The initial function is substituted into the fourth-order deflection differential iterative equation of the beam for integration. The boundary condition and continuous smooth condition are used to determine the integral constant to get the next iteration deflection function. The iterative integral operation is carried out in turn. The polynomial analytical function solutions of the maximum deflection, the maximum angle and the maximum bending moment expressed by the axial force amplification coefficient are calculated. The statically indeterminate beam-column subjected to distributed forces under two boundary conditions are analyzed in this paper. The calculation results show that when the axial force of statically indeterminate beam-column is less than half of Euler critical force, the error can be controlled within 1% after six iterations. Not only the beam-column’s maximum displacement and shear force increase with the increase of axial force, but also the position of the maximum displacement and internal force migrate with the increase of axial force. The research in this paper is of great significance to reveal the influence of axial force on statically indeterminate beam-column deformation and internal force, and provides a certain theoretical basis for the practical design of statically indeterminate beam-column.