Elastic and Inelastic Analysis of Nonprismatic Members

Abstract

This paper deals with the static analysis of nonprismatic members of any arbitrary variation in its moment of inertia $I_x$ and where their materia] is stressed beyond their elastic limit, thus causing the modulus of elasticity $E_x$ to vary along their length. The stress and deflection characteristics of such members for both elastic and inelastic analysis will be determined by using the method of the equivalent systems (see Fertis 1956, 1964, 1973, 1984). This method permits the replacement of the original member of variable stiffness $E_x{I}_x$ with one of uniform stiffness $E_1{I}_1$ whose elastic line is identical to that of the original variable stiffness member. An exact, as well as a very accurate approximate solution is obtained that drastically reduces the mathematical complexity of the problem. The member can be analyzed in both elastic and inelastic ranges to failure, thus permitting observation of progressive deterioration of the member's ability to resist load, stress, and deformation, and establishing useful, practical, critical limits regarding these quantities.