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ASME B31.3-2016 may occur in localized portions of the system(an unbal- be active in some conditions and not others (e.g.,pipes anced system). Operation of an unbalanced system in lifting off supports), this difference in strains may be the creep range may aggravate the deleterious effects influenced by the changing distribution of sustained due to creep strain accumulation in the most susceptible load. In such cases, the displacement strain range is regions of the system. Unbalance may result from one based on the algebraic difference between the calculated or more of the following: positions of the pipe that define the range. In addition (1) highly stressed small size pipe runs in series to the displacement strain,each calculated position shall with large or relatively stiff pipe runs. include the sustained loads present in the condition (2) a local reduction in size or wall thickness, or under evaluation. See para. 302.3.5(d)for the allowable local use of material having reduced yield strength (for stress range, SA, and para. 319.4.4(a) for the computed example, girth welds of substantially lower strength displacement stress range, SE. than the base metal). 319.2.4 Cold Spring. Cold spring is the intentional (3) a line configuration in a system of uniform size deformation of piping during assembly to produce a in which the expansion or contraction must be absorbed desired initial displacement and reaction. Cold spring largely in a short offset from the major portion of the run. is beneficial in that it serves to balance the magnitude (4) variation of piping material or temperature in of the reaction under initial and extreme displacement a line. When differences in the elastic modulus within conditions. When cold spring is properly applied there a piping system will significantly affect the stress distri- is less likelihood of overstrain during initial operation; bution,the resulting displacement stresses shall be com- hence,it is recommended especially for piping materials puted based on the actual elastic moduli at the respective of limited ductility.There is also less deviation from as- operating temperatures for each segment in the system installed dimensions during initial operation, so that and then multiplied by the ratio of the elastic modulus hangers will not be displaced as far from their original at ambient temperature to the modulus used in the anal- ysis for each segment. Inasmuch as the service life of a system is Unbalance should be avoided or minimized b design gn piping affected more by the range of stress variation than by and layout of piping systems, particularly those using the magnitude of stress at a given time, no credit for materials of low ductility. Many of the effects of unbal- cold spring is permitted in stress range calculations. ance can be mitigated by selective use of cold spring. However,in calculating the thrusts and moments where If unbalance cannot be avoided, the designer shall use actual reactions as well as their range of variations are appropriate analytical methods in accordance with significant, credit is given for cold spring. para. 319.4 to assure adequate flexibility as defined in para. 319.1. 319.3 Properties for Flexibility Analysis 319.2.3 Displacement Stress Range The following paragraphs deal with properties of pip- (a) In contrast with stresses from sustained loads, ing materials and their application in piping flexibility such as internal pressure or weight, displacement stress analysis. stresses may be permitted to attain sufficient magnitude 319.3.1 Thermal Expansion Data to cause local yielding in various portions of a piping (a) Values for Stress Range. Values of thermal displace- system. When the system is initially operated at the ments to be used in determining total displacement condition of greatest displacement (highest or lowest strains for computing the stress range shall be deter- temperature, or greatest imposed movement) from its mined from Appendix C as the algebraic difference installed condition, any yielding or creep brings about between the value at maximum metal temperature and a reduction or relaxation of stress. When the system is that at the minimum metal temperature for the thermal later returned to its original condition (or a condition cycle under analysis. of opposite displacement),a reversal and redistribution (b) Values for Reactions. Values of thermal displace- of stresses occurs that is referred to as self-springing. It ments to be used in determining total displacement is similar to cold springing in its effects. (b) While stresses resulting from displacement strains strains for computation of reactions on supports and connected equipment shall be determined as the alge- diminish with time due to yielding or creep, the alge- braic difference between the value at maximum(or mini- braic difference between strains in the extreme displace- mum)temperature for the thermal cycle under analysis ment condition and the original(as-installed)condition and the value at the temperature expected during (or any anticipated condition with a greater differential installation. effect) remains substantially constant during any one cycle of operation. This difference in strains produces a 319.3.2 Modulus of Elasticity. The reference modu- corresponding stress differential,the displacement stress lus of elasticity at 21°C (70°F), EQ, and the modulus of range,that is used as the criterion in the design of piping elasticity at maximum or minimum temperature, E., for flexibility.In evaluating systems where supports may shall be taken as the values shown in Appendix C for