On the influence of multiple loadings to plastic pipe elements. Applications to the pipe whip problem

This paper is a contribution to the study of the pipe whip accident considering various effects (pressurization, presence of bending in two normal planes, shears, torque, normal force) which have been previously neglected by the author in precedent works on the same subject for simplicity reasons. A model for a strain hardening plastic pipe element has been proposed; the main hypotheses are briefly reviewed: plastic flow rule; a strain hardening rule; two models have been proposed in the so-called strain model, the section is supposed to remain plane and not to warp even under the influence of shear loads, in the so-called mixed model while the same hypothesis is made for axial strains a truncated Fourier expansion is assumed for the shear stress distribution; in this way a complete stiffness and the influence of section deformation (ovalization due to radius changes in the plastic range (possibly loading to Brazier type instability) can be taken into consideration. The two models (strain model and mixed model) are compared in terms of the results which may be obtained by the use of each of them: it results that in the cases investigated the differences are not large in terms of curvature changes (while it may be somewhat more important in terms of the shear strains). Tentative conclusions are drawn, in the form of graphs taking the differences with the basic simplified model as a main point. Finally, typical real load time histories for one pipe element are considered and the differences with simplified models in the displacements and stress-strain distribution are shown and discussed