Convergence of the Axisymmetric Bessel Function Solution to the Pipe Strap Anchor Problem

One of the paradigmatic problems that frequently arise within a piping flexibility analysis is need to quantify the effect of local stresses created by supports and restraints attachments. Over the past twenty years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, it has previously been shown by the author that some pipe clamp anchors can be treated as an axisymmetric elasticity problem. These pipe anchors may be simplified considering the axisymmetric stress and deformation determination within a hollow cylinder (pipe) that is subjected to appropriate boundary and loading conditions, per se. One of the geometries previously considered and addressed is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type structure. The shoe is employed for the purpose of providing a theoretically immoveable base that can be easily attached either by bolting or welding within a pipe rack. Because the Bessel function and Fourier solution relies on the summation of a large number of terms (i.e., a series type solution), convergence becomes an issue when time is of the essence. This paper addresses the two variables that need to be controlled to obtain acceptable results with the series type solution.