Pipe Stress 102 – How Stress Analysis can Prevent Issues in Your Facility

This is the second article in a series of articles about thermal stress, pipe stress, and the art of pipe stress analysis. The first article provided a look at thermal expansion and contraction and an idea of the magnitude of thermal growth you could expect to see from a hot pipe. This second article will take a closer look at the importance of proper stress analysis and good engineering practice to offset the risks that thermal expansion poses to piping and equipment.

Piping systems are complex, running the length and width of a plant. Piping runs to every major piece of equipment and every tank, often over long distances. The pipes that carry hot liquid, steam, or other hot gasses will experience thermal expansion. If you recall from our previous article, this ultimately serves to increase the pipe’s length. Pipes that carry cryogenic or cold substances will experience thermal contraction and the pipe’s length will decrease. Both of these instances can wreak havoc in the plant unless properly designed and planned for.

What is Pipe Stress Analysis

So what exactly is Pipe Stress Analysis? Pipe Stress Analysis, in simple terms, is the calculation of the forces and movements on a piping system. Movements typically result from thermal expansion or contraction. Forces may result from this same expansion or from external forces such as deadweight, movement of equipment, and wind or seismic loading. In this article, we will focus on the forces generated from thermal expansion and how a stress engineer might deal with them.

Where thermal growth meets a fixed object, like a piece of equipment, you get a force. Forces acting over an area result in a stress. Stress Analysis calculates the forces, and the resulting stresses, and designs flexibility into the piping system so that these forces and stresses do not become excessive. When I use the term flexibility, I don’t mean just the routing but also the specific types of supports or restraints that might be required to control the movement of expanding pipe as well.

I believe the best way to explain something is with an example. Let’s consider the two runs of pipe below. The first is a straight run between two points that are anchored. The second has a perpendicular portion in the middle, with two elbows. If both of these pipes were heated to 300°F which one would generate the most axial force? You might intuitively guess the straight pipe has the higher anchor load, but can you guess the difference between the two?

Figure 1: Two Pipe Routings, Both Anchored at Either End – Shown Cold

The straight pipe, in carbon steel, travels 20 feet from left to right and generates 260,000 lb of force against the anchors at 300°F. There are no additional forces acting on the pipe, so the forces on the anchors are entirely from thermal growth. If you recall from the previous article, carbon steel pipe at 300°F will grow 1.9 inches per every 100 ft, so this 20-foot section will grow 0.38 inches (just about 3/8 of an inch). Remember how I mentioned before that it wasn’t so much the thermal growth in a pipe that was the problem, but what the pipe is pushing against. This pipe, bound on both sides by an anchor generates 260,000 lb of force. Now that anchor out in the world might be a steel from a platform, or a piece of equipment. In either case the loading is likely to be too high.

Figure 2: Same Two Pipe Routings from Figure 1 – Shown Hot

So how much force does the second pipe route generate? You can tell from this second picture, where both pipes are in their hot position. Note that the thermal growth is shown exaggerated a bit so it’s easier to see. It’s evident that the second pipe route has more flexibility. There are two elbows and a change of direction that allows the growth from thermal expansion to bend the pipe and flex the elbows as opposed to just pushing directly against the anchors on either end.

So if I told you both pipes were configured the same, same temperature, same length from left to right, same anchors on both ends, same material, could you guess the axial load on the bottom pipe? Half of the load generated by the top pipe? One quarter? How about less than 1%? Where the straight run of pipe generates nearly 260,000 lb of force on its anchors, the bottom run of pipe generates only 2,020 lb of axial force on its anchors. Yes, there is some bending moment from the pipe flexing, but in comparison to the loading from the straight run of pipe the moment at the anchor is still less than 1.5%.

Engineering Methods for Handling Thermal Expansion

The example above helps explain why hot piping isn’t usually routed in long straight runs. However, sometimes long straight runs of pipe can’t be avoided in the distances between major pieces of equipment in a facility. This is where stress engineers can employ special geometry, like an expansion loop, to absorb the thermal growth of the pipes. You will typically find these loops located in pipe racks, where typical expansion loop may look something like the piping shown in figure 3 below.

Figure 3: Straight Pipe Route with Expansion Loop – Shown Cold

In figure 4, the same pipe route with expansion loop is shown when it’s at 300°F. Note how the thermal growth occurs at the inner elbows of the loop. In this configuration, the axial load on the anchors is about 2,040 lb, similar to the bent configuration in figures 1 and 2. It is interesting to point out that while the axial movement at the inside elbows is 0.35 inches on each side, the perpendicular movement at the same point is nearly 1 inch. The piping is more flexible in the perpendicular direction so when thermal growth forces the inner elbows together the piping naturally bows.

Figure 4: Straight Pipe Route with Expansion Loop – Shown Hot

If this perpendicular movement were too high, perhaps there are other pipes nearby that we don’t want to grow into, or perhaps this bowing creates an excessive moment at the anchors on either end of the line, then there are special supports designed with this in mind that help restrain the piping laterally while allowing the pipe to grow axially. These supports are called Guides. See how, in figure 5, the thermal growth is restrained to the axial direction of the pipe when using Guides on either side of the expansion loop.

Figure 5: Straight Pipe Route with Expansion Loop and Guides – Shown Hot

In this configuration, the axial movement at each inner elbow is about 0.35 in, similar to the unguided configuration in Figure 4. However, the perpendicular movement of the pipe had dropped to just 0.24 inch. The axial force at each anchor is a little higher at 2,500 lb, but still less than 1% of the forces generated by the straight pipe in the first figure.

Remember Pipe Stress Analysis isn’t just about determining what forces or stresses are generated, but also about calculating how much flexibility is in a run of pipe. The stress engineer has to determine whether a particular run of pipe is flexible enough and if loads on equipment and supporting steel are too high. If so, the engineer then has to determine what changes to the routing and supports might be necessary to reduce the loads. In later articles, we will go into more detail about the different types of supports, their uses, and how the design of piping for thermal expansion and corresponding forces on equipment are governed by various Codes. In the next article however, we will discuss what to look for in your own facility. Are there telltale signs of uncontrolled thermal expansion at your site?

Matrix Technologies is one of the largest independent process design, industrial automation engineering, and manufacturing operations management companies in North America. To learn more about thermal expansion and pipe stress analysis, contact Chris Mach, Senior Consultant or Brandon Grodi, Mechanical Department Manager.

© Matrix Technologies, Inc.

Tags: / Oil & Gas  / Pipe Stress  / Piping Engineer  / Process Engineer  / Stress Analysis  / Thermal Contraction  / Construction  / Manufacturing 

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