The allowable stress for thermal expansion and other deformation-induced stresses is substantiallyhigher than for sustained loads. This is due to the difference between load-controlled conditions, suchas weight and pressure, and deformation-controlled conditions, such as thermal expansion or end displacements(e.g., due to thermal expansion of attached equipment).When a load-controlled stress is calculated, it is an actual stress value. It is governed by equilibrium.For example, the stress in a bar when a tensile force is applied to it is the force divided by thearea of the bar. This is not the case for thermal stresses. In the case of thermal stresses, it is the valueof strain that is known. The elastically calculated stress is simply the strain value times the elasticmodulus. This makes essentially no difference until the stress exceeds the yield strength of the material.In that case, the location on the stressstrain curve for the material is determined based onthe calculated stress for load-controlled, or sustained, loads. The location on the stressstrain curvefor the material is determined based on the calculated strain (or elastically calculated stress dividedby elastic modulus) for deformation-controlled (e.g., thermal expansion) loads. This is illustrated inFig. 7.1. Because the stress analyses are based on the assumption of elastic behavior, it is necessaryto discriminate between deformation-controlled and load-controlled conditions in order to properlyunderstand the post-yield behavior.It is considered desirable for the piping system to behave in a substantially elastic manner so that theelastic stress analysis is valid. Furthermore, having plastic deformation every cycle carries with it uncertaintieswith respect to strain concentration and can be potentially far more damaging than calculatedto be in the elastic analysis. One way to accomplish this would be to limit the total stress range to yieldstress. However, this would be overly conservative and result in unnecessary expansion loops and joints.Instead, the concept of shakedown to elastic behavior is used in the Code. The basis for the Code equationsis described by Markl (1960d). Rossheim and Markl (1960) also provide an interesting discussionon some of the thinking behind the rules.The allowable thermal expansion stress in the Code is designed to result in shakedown to elastic behaviorafter a few operating cycles. The equation provided in the Code is11SA = f (1 25Sc + 0 25Sh ) (7.1)