Stability of beam-column by geometrically nonlinear analysis

ABSTRACT Stiffness properties of structural members, such as beam, plate and shell, can change drastically in the presence of axial forces due to geometric effects of the nonlinear strain components. In this paper, the stability behaviour of beam-column is investigated using the governing differential equation and compared with the geometrically nonlinear finite element analysis. The lateral deflection obtained from the theoretical model matches quite accurately with the numerical values for wide range of axial to critical load ratio P/P cr . It is shown that bending stiffness decreases linearly with the axial load. By extending the theory, an expression for the membrane stiffness of the beam-column is presented in this paper. The geometrically nonlinear finite element analysis can capture exactly the parabolic variation of the membrane stiffness as per the derived expression. It increases initially up to P/P cr  = 0.35 and decreases rapidly to negligible value near the critical load indicating buckling instability.