Plastic Resistance of Pipe Sections: Upper Bound Solution

Abstract

In a previous paper, interaction relations based on the lower bound theorem of plasticity were derived for moderately thick pipes subjected to biaxial shear and bending, axial force, twisting moments, and internal or external pressure. The developments provided a lower bound solution based on assumed simplified stress fields. In this paper it is demonstrated that the assumptions made in the previous solution were indeed equilibrium requirements. Pipe interaction relations are obtained using the upper bound theorem of plasticity. Because (1) the assumed strain fields are based on the general solution of the compatibility equations; (2) the stress fields meet the equilibrium conditions; and (3) the yield condition is met over the whole pipe cross section, the interaction relations obtained are exact within the limitations of the formulation. The yield surface obtained meets the Drucker convexity requirement and is suitable as a potential surface characterizing the behavior of generalized plastic hinges in the elastoplastic analysis of pipe elements. The yield surface is mathematically described by two intrinsic functions. A simple mathematical procedure is devised in order to express the normality condition to the yield surface.