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 nonl inear 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. A n expression for the first variation of the Total Potential is derived, tha t may be used in a nonlinear equilibrium analysis, and an expression for th e 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 el ement analysis, as described in the companion paper. The results are discus sed 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 ag ree with those presented in this paper. (C) 2000 Published by Elsevier Scie nce Ltd.