Large-Deflection Analysis of Whipping Pipes. I: Rigid, Perfectly-Plastic Model

A theoretical model is constructed for a large-deflection analysis of a rigid, perfectly-plastic cantilever with a tip mass loaded by a transverse follower force pulse. The purpose of building and analyzing such a model is to provide an analytical basis for studying unconstrained motions of a whipping pipe. Such motion can arise from the failure of high-pressure piping systems and is consequently a safety-related phenomenon. A guillotine break in the pipe leads to the expulsion of a jet of high-pressure fluid, and the reaction force pulse exerted on the pipe causes it to accelerate and deform. Generally, the motion of the pipe consists of an initial transient phase and a modal, root rotation phase. The equations for the initial traveling hinge phase and root rotation phase are derived and solved numerically. Pipe kinematics and deformations are deduced and comparisons are made with observations from pipe-whip tests. Finally, the model is used to give indications of the variation in the zone of influence (i.e., the region where the whipping pipe could strike another pipe or other components) for different ratios of tip mass to pipe mass.