Stability Functions for Three‐Dimensional Beam‐Columns

Abstract

Members carrying both axial force and bending moment are subjected to an interaction between these effects. The analysis of a beam‐column using stability functions as an alternative to the stress stiffness matrix is discussed. Explicit expressions for stability functions for three‐dimensional beam‐columns, in terms of member length, cross‐sectional properties, axial force, and the end moments, are derived. The effect of flexure on axial stiffness and the effect of axial force on flexural stiffness and stiffness against translation are considered in the derivation of stability functions. The effect of axial force on torsional stiffness and the effect of torsional moment on axial stiffness are neglected. The nonlinear stiffness matrix of a three‐dimensional beam‐column using the stability functions is presented by modifying the linear elastic stiffness matrix for a beam‐column (which includes the effect of shear deformations) available in the literature. A numerical example showing the calculation of stability functions for a given beam‐column is also presented.