Piping may be modeled in varying detail, depending upon how much accuracy is required. This section looks at the various ways (providing corresponding degrees of accuracy) in which sample piping configurations might be modeled.
Consider the following geometry, of a large diameter pipe supported by a dual spring assembly:
Limitations:
1 - local stress calculations not considered for 50" pipe
2 - stiffness of trunnions not considered
3 - torsional resistance due to the restraint pair is not considered (see Figure 3-16)
4 - local flexibility of the shell of the 50" pipe is not considered
Limitations:
1 - local stress calculations not considered for 50" pipe
2 - stiffness of trunnions not considered
4 - local flexibility of the shell of the 50" pipe is not considered
Limitations: 1 - local flexibilities and stresses only as close as WRC 297 and WRC 107 bulletins (see discussion in this Section 3.4 of these Pipe Stress Analysis Notes) Looking at another configuration, a heavy-wall forged WYE fitting:
Limitations:
1 - weight of forged fitting probably underestimated considerably
2 - rigidity of forged fitting probably underestimated considerably
3 - stress intensification factors may be too conservative
Limitations:
1 - no provision for stress calculations in forging, but this isn't usually a problem, because of the extra heavy wall of the fitting would ensure that the connecting pipe would probably fail first. Any questions regarding load capacity should probably be directed to the fitting manufacturer
Comments:
the flexibility of this model will be more accurate (but only marginally so for a heavy fitting)
stresses (unintensified) will be computed at the crotch; however, there will be some unknown intensification factor existing at the crotch
this model probably does not yield any significant improvement over the previous one
One of the most common types of pipe support is shown in Figure 3-23:
Limitations:
1 - flexibility of the stanchion is not included in the model
2 - the point of application of the stanchion is not at the correct location on the bend curvature
3 - pipe may lift off of (or lock up with) modeled support due to thermal expansion between centerline of horizontal run and point of application on riser
4 - stiffening effect on bend of stanchion not considered
5 - local stresses at stanchion not considered
Limitations:
1 - stanchion doesn't act at the proper point on the bend curvature
2 - stiffening effect on bend of stanchion not considered
3 - local stresses at stanchion not considered
Limitations:
points A and B aren't exactly at the same location (this can be resolved using CAESAR li s "OFFSETS" feature, but other pipe stress software may have a difficult time with this)
modeling the stiffening effect of the stanchion on the bend through the use of a single flange bend is an approximate solution
local stresses at the stanchion are only as accurate as WRC 107 bulletin
A few configurations which illustrate solutions to potentially tricky modeling situations follow below: The distance L in Figure 3-27 may become important if the gap on the guide closes and there is a horizontal restraint force which will cause a torsional moment to exist in both members.
Because the elbow in Figure 3-28 connects directly to the equipment flange and the equipment flange is anchored, the stiffness of the model in this local region is very high. If the stanchion connects at A and the equipment centerline is at B, the differential thermal growth of the elbow between those points could put enormously high loads on both the stanchion and the equipment model. This is also in reality, a difficult problem to design for. Unless the user is willing to put a spring at the stanchion location, the differential thermal growth in this small area might result in large nozzle loads.
In the Figure 3-29, a small, but heavy process monitor and actuator is mounted on the line. The rigidity, weight, and moment due to the offset is best modeled using a weightless rigid element going from the centerline of the pipe out to the center of gravity of the process monitor, at which point a small rigid element with the weight of the equipment should be modeled. The rigidity of the body of the monitor (within the pipeline) should be modeled as a rigid as well. (Note that some engineers may prefer to model the effects of this equipment by applying a force equal to the weight and a moment equal to the weight times offset at the centerline of the pipe. This approach, although acceptable for static analysis, is absolutely incorrect for dynamic analysis, and should therefore be avoided since it cannot be promised that no dynamic analysis will be conducted on a system in the future.)
In Figure 3-30, the large 18 inch line comes directly from a flue-gas furnace, passes through a small exchanger and enters a waste heat boiler. This is a very stiff system relative to the vessel connections. Therefore, instead of modeling the connections as rigid anchors (which would give the same relative stiffness to the restraints and to the piping), WRC Bulletin 297 should be used to estimate and model the nozzle flexibilities. This method will provide the best approximation of the distribution of the piping loads to the vessels.
In Figure 3-31, rectangular ducting connects the two separators, which are rigid relative to the ductwork. In order to size each spring for its share of the distributed weight of the whole assembly plus the connected piping, it is best to simulate the stiffness of the duct through the use of an equivalent structural member or piping element.
An angle valve could be modeled as shown in Figure 3-32. It may be necessary to model it as three rigid elements if the weight of the operator is significant in comparison to the valve body.
The following sections of these seminar notes provide more detailed methods for modeling and analyzing specific components of the piping model.
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