When is time history used? We use this method to simulate short-term, rapid events. Below is an example of analyzing a bank of 4x6-inch natural gas safety valves at pressures of 6.4 MPa/1.15 MPa. Determining the force profile:

• T=0.00 s: Force = 0 Valve closed

• T=0.01 s: Force = 35 kN

• T=0.50 s: Force = 35 kN

• T=0.51 s: Force=0 Valve closing

The AutoPipe model shows the following static analysis results. Ideally, 100% of the B31.3 code stress

A force of 35 kN is applied to the centers of the arches. This force is absorbed by the triunion supports with the LS function.

To demonstrate how the presence or absence of the first support downstream of the PSV valve affects the dynamic results, it was removed from the first set from the top. The absence of the support causes the displacement to dampen the oscillations.

Also, very large force oscillations, which significantly exceed the recoil force of 35 kN, can now be calculated as the actual DLF factor of 61 / 35 = 1.85. This shows that frequently assuming a maximum DLF value of 2.0 can sometimes be justified. In this case, it can be justified by the support failure scenario.

It's interesting to see how the oscillations develop further along the pipeline. For example, at the first elbow of the collector, the force is significantly lower, only 18 kN.

For comparison, in a situation where the support is working properly, the pipeline and the support are so stiff that no oscillation occurs.

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In AutoPipe, the MSRS method is easy to implement. First, you need to group the system segments as needed. Let's say you're using the same model divided into three sections.

We select the segment and group using a dedicated command. This allows us to assign a different SAM combination to each group.

It is very easy to define combinations of seismic sects in very different ways

The results are in a very accessible form: For the MSRS 1 combination:

MARS 2 looks different because the combination of spectra was different.

Caesar, unfortunately, is two classes worse. It doesn't have a convenient menu for dividing into zones. We define dynamic forcing combinations. We can enter a range of nodes, but it's not required. If left blank, it means the entire system will be considered.

The results can only be viewed in table format, which is disappointing compared to AutoPipe. For MSRS 1, it looks like this:

For MSRS 2 is:

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In B31.3 it is also presented in this way, except that there is no mention of the movement of supports during an earthquake.

EN 13480-3, however, uses a more lenient statement (should). Such analyses are typically described with the acronym SAM – Seimic Anchor Movement, although they apply not only to fixed points but also to supports with line guise and line stop functions. Of course, they do not apply to rest functions.

First, I'll return to the SAM static analysis, which is the most common approach. The decision to use statics or dynamics is left to the designer. The model looks as follows: The entire structure is divided into three SIB (Seismic Interface Barrier) segments, the horizontal section being the viaduct, and the vertical section being the approach to the building.

Pipe specification: DN 100 (4'), 6.02mm (STD). The medium is water. A horizontal seismic acceleration of 0.2g and a vertical seismic acceleration of 0.1g was assumed. The vertical section height was 8m. The temperature was 100C and the pressure was 1 MPa. The seismic displacement was determined according to applicable rules, which I will not describe now: NSEW overpass level = 5mm, NSEW building entrance level = 40mm. No seismic rotation at the supports was assumed.

To verify that the correct directions have been chosen, it's worth viewing the displacement results. If all is well, the SIBs will change their displacement direction.

The result of the static SAM analysis in AutoPipe for the fixed point upstream of SIB 1 is as follows. The code stress is 40.8 MPa.

Regarding Caesar, the situation is less convenient. All seismically movable supports must be equipped with Cnodes. For the same point, the stress was 47.6 MPa.

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In Caesar II the model looks like this:

Both models, of course, received identical seismic excitations. The accelerations in each direction are slightly different. They act on the ENTIRE model simultaneously. The acceleration unit is mm/s², meaning 80 mm/s² is just 0.08 m/s², which is very low. There are no defined seismic displacements. For simplicity, wind and snow were omitted. Therefore, the only occasional load is seismic.

The results for the static analysis in AutoPipe are typical and not cause for concern. The stress on the arc ranges from 29 to 45%.

After adding the dynamic analysis, the result appears with the designation R1. This is the Response Spectra result No. 1. The effort is only 3 to 4% for SUS+R1.

Static results on Caesar II are similar. The strain for the same load combination is 33%.

Unfortunately, Caesar II's dynamic analysis results leave much to be desired. First, they're not presented graphically, only numerically. Therefore, we have to exit the dynamics section and open the Input section to see where the node is at its peak intensity. THIS IS TERRIBLE SOLUSION..

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AutoPipe Advanced 2024 has the following standards available for spectral generation. It includes IBC, but surprisingly, it doesn't include ASCE7. Instead, it does have the basic European Eurocode standard and a strange Spanish standard.

Caesar II, however, has a slightly different list. It primarily includes ASCE 7 and IBC, but no European standards. Perhaps it's a sign of the times...

In this situation, the only thing that could be compared are the generation results according to IBC. AutoPipe Advanced 2024 only has the 2006 version, which is somewhat puzzling. However, Caesar II v14 has the 2021, 2018, 2012, 2006, and 2000 versions available. This shows that I can only use the 2006 version for comparison purposes.

In Autopipe Advanced 2024, you can generate a seismic spectrum for any point in the US. Simply enter the longitude and latitude (I entered data for the Midwest here), and the four data points needed to generate the spectrum are automatically populated. There's even a zip code option (!), but I haven't used it.

There is also a very useful option to refine the mesh by using the variable below:

As a result, we get this very nice graph:

Caesar II v14 has a slightly different menu. Note the Importance Factor, which isn't included in this standard. Its values ​​depend on the type of building. I filled in the remaining factor values ​​with the same values ​​as those generated by the AutoPipe generator. In Caesar II, they must be entered manually, which is very tedious and can also generate errors.

The second factor not included in AutoPipe is Response Modification R, which is included in the 2024 IBC version. I don't have the 2006 version, so it's hard for me to say why AutoPipe Advanced 2024 doesn't include this factor.

Caesar II generates a graph but with much less density.

The huge difference in density and the inability to adjust it in Caesar II make the data range for spectrum plotting incomparable. Unfortunately, there's a significant drawback to Caesar II.

Comparison of acceleration results for several points gives satisfactory results.

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The model is identical for both programs: 10′, STD, A106B, air 0.5 MPa, +100C. Length 15m. The natural frequency for a restrained beam is described by the well-known formula given below. For deformation mode I, f = 1.18 Hz

The results in AutoPipe for mode I are 1.16 Hz when dividing the pipe into 10 equal parts

The results in AutoPipe for mode I are 1.13 Hz without division.

The results in CII for mode I are 1.17 Hz when dividing the tube into 10 equal parts and using a lumped mass model.

The CII results for mode I are 0.82 Hz without splitting and with a lumped mass model.

However, for the consistent mass model, the results are much better. It's true that the analysis takes longer, but for simple models, this doesn't matter.

This simple comparison shows that without dividing long sections into relatively short ones, Caesar II, and using a simplified mass model (lumped), produces results that differ significantly from those described by the formula, but also from those of AutoPipe. Furthermore, AutoPipe provides a very nice figure for higher strain modes (see below), which CII does not.

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In the first variant, the RS support, LG is used under the arch at the starting point of the arch, as shown in the figure below. The support acts along the center line of the vertical run and does not limit the rotation of the arch.

Below are the stress results.

Below are the results of the forces on the supports.

In the second variant, the identical RS support, LG, is used under the arch, but at the center point of the arch, as shown in the drawing below. You can't throw LG into the center of the arch because it gives a slightly funny graphic effect.

Therefore, in the second variant, the identical RS support was used under the arch. The LG function was moved to the beginning of the arch. Stress results:

Results of forces at supports.

In the third variant, the pipe arc is to be supported by a triunion placed directly under the pipe. Let's assume that the triunion DN 200/8' is 500 mm long. The beam element is used to model the fictitious leg. The beginning of the triunion is to be placed at the midpoint of the arc. The triunion pipe is the structure element. Unfortunately, for this reason, a regular support cannot be placed on the structure element. Only a fixed point is possible. Regular supports can be simulated on it, but without gaps. The stress results are below.

In the fourth variant, the pipe bend is to be supported by a triunion placed directly under the pipe. A short rigid beam element is used to connect the pipe segment to the bend to model a fictitious triunion pipe. The actual length of the triunion is 500 mm. The triunion pipe is a piping element, which means that any support can already be assumed. Stress results:

Forces at the support.

SUMMARY

Each variant gave different results. The load combination that gives the greatest stress is always the same.

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The results are as follows:

Kellogg: stress in bend 11,664 psi, anchor force 1,649 lb

AutoPipe: 13,557 psi stress in bend, 1751 lb. fixed support force. Assumptions: zero LG gaps, 0.3 friction

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In reality, we do not approach these values. We try to keep to 60-70% Sh. This is because permanent stresses belong to the basic stresses (ang. primary stress). Their impact is permanent, so any errors in assembly are irreparable. Additionally, exceeding the yield point by permanent loads is unstoppable due to the phenomenon of positive feedback.

The second, much more important issue is the phenomenon of lifting supports due to temperature expansion. If we have, for example, 90% permanent stresses, this is definitely too much. You have to be aware that if support F03 is lifted from the temperature (here T3), then it is switched off for GR+Max (P3). In such a situation, we have increased permanent stresses.

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From this case, it is recommended to never connect to the nozzles with a straight section that is supported on one side by another nozzle or a fixed point. The sketch below shows just such a connection between the nozzles marked as two yellow collars.

Here is a model of part of the installation. These are the nozzles at the bottom of the tanks at the end of their conical parts.

The stress results are shown below and are as accurate as possible.

The deformation results are shown below and do not raise any particular doubts.

Finally, the results of exceedances at the nozzles.

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