3.6.1 Consideration of Cold Spring
Cold spring is the process of offsetting (or pre-loading) the piping system with displacement loads (usually accomplished by cutting short or long the pipe runs between two anchors) for the purpose of reducing the absolute expansion load on the system. Cold spring is used to:
hasten the thermal shakedown of the system in fewer operating cycles
reduce the magnitude of loads on equipment and restraints, since often, only a single application of a large load is sufficient to damage these elements
Note that no credit can be taken for cold spring in the stress calculations, since the expansion stress provisions of the piping codes require the evaluation of the stress range, which is unaffected by cold spring (except possibility in the presence of non-linear boundary conditions, as discussed below). The cold spring merely adjusts the stress mean, but not the range.
Many engineers avoid cold spring due to the difficulty of maintaining accurate records throughout the operating life of the unit. Future analysts attempting to make field repairs or modifications may not necessarily know about (and therefore include in the analysis) the cold spring specification.
Due to the difficulty of properly installing a cold sprung system, most piping codes recommend that only 2/3 of the specified cold spring be used for the equipment load calculations.
An example of how to calculate the amount of cold spring necessary to reduce equipment loads is provided in Figure 3-115.
In the example shown, the pipe expands between the anchor and the equipment, placing excessive thermal loads on the nozzle. The idea is to calculate the total thermal expansion which the pipe wishes to make between the two pumps, and then to offset the pipe by approximately half of that amount through the use of cut short elements.
For the case in Figure 3-115, assume that the operating temperature is 1170°F, ambient temperature is 70°F, and the coefficient of mean coefficient of thermal expansion between the two for the material is 7E-6 in/in/°F. In that case:
Therefore, one of the pipe runs in the X-direction should be cut short by approximately 1-5/ 8 inches, one of the runs in the Y-direction should be cut short by approximately 3/4 inches, and one of the runs in the Z-direction should be cut short by approximately 2-1/2 inches, as shown in the figure.
Note that the (1/2) in the equation for the cold spring amount is used such that the mean stress is zero. In some cases it is desirable to have the operating load on the equipment as close to zero as possible. In this latter case the (1/2) should be omitted. The maximum stress magnitude will not change from a system without cold spring, but will now exist in the cold case rather than the hot.
All pipe stress programs provide very specific methods of modeling cold spring. As of this writing (Version 3.18), CAESAR II provides two methods of specifying cold spring. (This is scheduled to change with Version 3.20 of the program, when cold spring will be more easily manipulated as a separate loading case.)
In the first method, elements may be specified as being made of cut short or cut long materials. Cut short describes a cold sprung section of pipe fabricated short by the amount of the cold spring, requiring an initial tensile load to close the final joint. Cut long describes a cold sprung section of pipe fabricated long by the amount of cold spring, requiring an initial compressive load to close the final joint. The software models cut shorts and cut longs by applying end forces to the elements sufficient to reduce their length to zero (from the defined length) or increase their length to the defined length (from zero) respectively. (It should be remembered to make the lengths of these cold spring elements only 2/3 of their actual lengths to implement the code recommendations.) This is effectively what occurs during application of cold spring. The end forces applied to the elements are then included in the basic loading case F (for force), whereby they can be included in various load combinations.
The drawback to this method occurs when other forces are present, such as applied external forces or spring hanger loads. In this case, the cold spring forces cannot be segregated from these other forces in the basic load case F. Therefore, the second method of modeling cold spring is more appropriate — using a second (or third) thermal case to represent the effects of cold spring. In this way the effects of cold spring can be isolated from all other loadings through the specification of the extra thermal case. This is done as follows:
model the system as normal, but use at least one element with a length and direction corresponding to the specified cold spring (the same as in the first method, but make it of the same material as the pipe, not of a special cut short or long material)
apply the normal operating temperatures to all elements of the model as thermal load case T1 — this represents the expansion of the system during operation
create thermal load case T2 representing only the effects of the cold spring—for this case:
a) all non-cold spring elements are given a temperature equal to ambient b) all cut short elements are given an alpha value (instead of a temperature) of -0.6667, representing a shrinkage of 2/3 of its defined length c) all cut long elements are given an alpha value of 0.6667, representing an expansion of 2/3 of its defined length
Note that in order to enter an alpha value on the order of 0.6667, the alpha tolerance value of the CAESAR II setup file will probably have to be changed. For more information on changing the alpha tolerance, and modeling cold spring in general, the user is referred to the CAESAR II User's Manual. When analyzing a system with cold spring, a different set of load cases should be run. Assuming that the cold spring load case is T2 (as described in method 2 above), the following load cases probably constitute a good recommendation:
Load Case 1 - P+W+F+T2 (OPE) — This is effectively a "cold operating" case — i.e., it represents the piping system in the cold condition, but includes both primary (P+W+F) and secondary (T2) loads, so it cannot be used for stress purposes. The reactions from this load case should be used for checking the restraint and equipment loads. Load Case 2 - P+W+F (SUS) — This is a sustained case from the point of view that only primary loads are considered, and should therefore be used for checking the system sustained stresses. However, if there are non-linear effects such as one-way restraints, gaps, etc. present in the system, the restraint configuration should be examined to verify that it is a true representation of the restraint status during hot or cold operation. Load Case 3 - P+W+F+T1+T2 (OPE)—This is the hot operating case, representing the piping system after thermal expansion. It is not used for stress purposes, but again the reactions from this load case are used for checking the restraint and equipment loads (they should be checked for the maximum loads from the cold or hot operating case). Load Case 4 - D1 - D3 (EXP). This is the algebraic difference between, or the range of loading through which the pipe goes when heating up between, the cold and the hot cases. Therefore this is the expansion case, and is used to check the expansion stress requirements of the codes. Note that for completely linear systems, the expansion range (i.e., the difference between load case 3 and load case 1) is Tl, eliminating the effect of the cold spring.
Care must be exercised when running cold spring and hanger design simultaneously. Cold spring in vertical runs of pipe adjacent to hanger design locations can cause inordinate weight loads to appear at the hanger positions. Cold spring effects should be omitted from the restrained weight run and included in the hanger operating run.
Modeling And Analysis Of The Piping System
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