Nonlinear analysis of thin-walled members of variable cross-section. Part I: Theory

The majority of analyses of thin-walled beam-columns in the linear and nonlinear ranges of structural response have been for prismatic sections. This paper presents a theory for the nonlinear axial strain and Kirchhoff stress resultants for a thin-walled beam-column whose cross-section is tapered. An expression for the first variation of the Total Potential is derived, that may be used in a nonlinear equilibrium analysis, and an expression for the second variation of the Total Potential is derived, that may be used in a stability analysis. These variations are used as the basis for a finite element analysis, as described in the companion paper. The results are discussed in light of a previous study of tapered monosymmetric I-beams, and for a linear analysis it is shown that the results of this independent study agree with those presented in this paper.