Simplified Second Stage Creep/Relaxation Analysis of Moderately Complex Spatially Three-Dimensional Piping Systems

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Abstract
An analysis technique for predicting the second stage creep/relaxation response of moderately complex spatially three-dimensional piping systems is presented herein. The theoretical development of this technique is based on two major assumptions. The first assumption is that at any time the behavior of the piping system can be associated with two components. One is an elastic component which is recoverable, and the other is a creep/relaxation component, which is not recoverable. The second major assumption, the simplifying assumption, is that the creep/relaxation strains due to axial, bending, and torsional loading can be decoupled and strains due to internal pressure can be neglected. Utilizing small displacement linear strain assumptions, the elastic stress-strain and creep/relaxation stress-strain rate laws can be integrated over the pipe’s cross section to yield generalized force-deformation relationships. The method of initial strains associated with the matrix displacement method of structural analysis is now applied to generate the solution of the creep/relaxation problem. This formulation utilizes two distinct types of piping elements. The first is a straight uniform pipe element and the second is a circularly curved pipe element, which incorporates both elastic and creep/relaxation flexibility factors. The end result of this formulation is a digital computer program capable of analyzing spatially three-dimensional piping systems under creep/relaxation conditions that can be represented by a series of straight or circularly curved pipe elements subjected to applied forces, displacements, and/or thermal change. An example analysis is included.

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