Rigid Plastic Beam Model for Pipe Whip Analysis

A method is developed for the analysis of a rigid-plastic propped cantilever beam with a gap at the support for use in the study of pipe whip. The blowdown thrust is assumed to be a suddenly applied constant force and the restraint is assumed to act as a rigid-plastic spring. The type of response is shown to depend on the lengths of the cantilever and the segment overhanging the restraint as well as the ratio of the blowdown thrust to the restraint reaction. In long cantilevers, the first hinge to form moves to the support after contact is made with the restraint. A second hinge will form at the restraint if the reaction is large enough. It is shown that if the cantilever is long enough and the restraint reaction above a certain critical value, the displacements at the tip and the restraint are independent of length. It is shown that neglecting the fact the hinge moves introduces large errors.